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The Effect of Resource Limits and Task Complexity on Collaborative Planning in Dialogue

This paper shows how agents' choice in communicative action can be designed to mitigate the effect of their resource limits in the context of particular features of a collaborative planning task. I first motivate a number of hypotheses about effective language behavior based on a statistical analysis of a corpus of natural collaborative planning dialogues. These hypotheses are then tested in a dialogue testbed whose design is motivated by the corpus analysis. Experiments in the testbed examine the interaction between (1) agents' resource limits in attentional capacity and inferential capacity; (2) agents' choice in communication; and (3) features of communicative tasks that affect task difficulty such as inferential complexity, degree of belief coordination required, and tolerance for errors. The results show that good algorithms for communication must be defined relative to the agents' resource limits and the features of the task. Algorithms that are inefficient for inferentially simple, low coordination or fault-tolerant tasks are effective when tasks require coordination or complex inferences, or are fault-intolerant. The results provide an explanation for the occurrence of utterances in human dialogues that, prima facie, appear inefficient, and provide the basis for the design of effective algorithms for communicative choice for resource limited agents.


Introduction
Agents may engage in conversation for a range of reasons, e.g. to acquire information, to establish a contract, to make a plan, or to be social. At each point in a dialogue, agents must make communicative choices about what to say and how and when to say it. This paper focuses on agents' communicative choice in collaborative planning dialogues, dialogues whose purpose is to discuss and agree on a plan for future action, and potentially execute that plan. I will argue that agents' choices in communicative action, their algorithms for language behavior, must be determined with respect to two relatively unexplored factors in models of collaborative planning dialogues: (1) agents' resource limits, such as limits in attentional and inferential capacity; and (2) features of collaborative planning tasks that affect task difficulty, such as inferential complexity, the degree of belief coordination required, and tolerance for errors.
A primary dimension of communicative choice is the degree of explicitness. For example, consider a simple task of agent A and agent B trying to agree on a plan for furnishing a two room house. Imagine that A wants B to believe the proposition realized by 1 and believes that B can infer this from the propositions realized in 2: 1 (1) If we agree to put the green couch in the study, we will have a matched-pair of furniture in the study.
(2) a. I propose that we put the green couch in the study.
b. We intend to put the green chair in the study.
c. Two furniture items of the same color in the same room achieve a matched pair.
(3) A: I propose that we put the green couch in the study.
(4) A: We intend to put the green chair in the study. I propose that we put the green couch in the study.
(5) A: Two furniture items of the same color in the same room achieve a matched pair. We intend to put the green chair in the study. I propose that we put the green couch in the study.
(6) A: I propose that we put the green couch in the study. That will get us a matched pair.
The communicative choices in 3 through 6 illustrate a general fact: for any communicative act, the same effect can be achieved with a range of acts at various levels of explicitness. This raises a key issue: On what basis does A choose among the more or less explicit versions of the proposal in 3 to 6?
The single constraint that has been suggested elsewhere in the literature is the redundancy constraint: A should not say information that B already knows, or that B could infer. The redundancy constraint appears in the form of simple dictums such as 'Don't tell people what they already know', as Grice's Quantity Maxim 'do not make your contribution more informative than is required' [Grice, 1975] and as constraints on planning operators for the generation and recognition of communicative plans [Allen and Perrault, 1980, Cawsey, 1991, Cohen, 1978, Moore and Paris, 1993, Litman and Allen, 1990]. So, if we assume that B knows 2b and 2c, then the only possibility for what A can say is 3.
The redundancy constraint is based on the assumption that agent A should leave implicit any information she believes that B already knows or she believes that B could infer, in other words, that agent B can always 'fill in what is missing' by a combination of retrieving facts from memory and making inferences. In section 2, I will show that agents in natural dialogues consistently violate the redundancy constraint. I will argue that this should not be particularly surprising since the redundancy constraint is based on several simplifying assumptions: 1. unlimited working-memory assumption: everything an agent knows is always available for reasoning; 2. logical omniscience assumption: agents are logically omniscient; 3. fewest utterances assumption: utterance production is the only process that should be minimized; 4. no autonomy assumption: assertions and proposals by Agent A are accepted by default by Agent B.
When agents are autonomous and resource-limited, these assumptions do not always hold, and the problem of communicative choice remains.
The plan for the paper is as follows: section 2 motivates a number of hypotheses about the relationship of communicative choice, resource limits and task features using evidence from natural collaborative planning dialogues. These hypotheses are the basis of a model of collaborative planning presented in section 3. Then section 4 describes how the model is implemented in a testbed for collaborative planning dialogues called Design-World, which supports experiments on the interaction of agents' communicative choice, resource limits, and features of the task. At this point, in section 4.1, I review the steps of the method applied so far, and motivate the use of simulation as a method for testing the hypotheses. Section 5 presents the experimental results and discusses the extent to which the hypotheses were confirmed, and then section 6 discusses the theoretical implications of these results and the extent to which they can be generalized to other tasks, agent properties, and communication strategies.

Communicative choice in Dialogue
Naturally occurring collaborative planning dialogues are design, problem solving, diagnostic or advice-giving dialogues [Cawsey et al., 1992, Cohen, 1987, Reichman, 1985, Grosz, 1977, Webber and Joshi, 1982, Clark and Schaefer, 1989, Whittaker and Stenton, 1988. In order to generate hypotheses about the relation of communicative choice to agent properties and task features, this section examines communicative choice in naturally occurring collaborative planning dialogues. Most of the examples discussed below are excerpts from a corpus of dialogues from a radio talk show for financial planning advice [Pollack et al., 1982], 2 but I will also draw on data from collaborative design, collaborative construction, and computer support dialogues [Cohen, 1984, Walker and Whittaker, 1990, Whittaker and Stenton, 1988, Whittaker et al., 1993.
Dialogue, in general, is modeled as a process by which conversants add to what is assumed to be already mutually believed or intended. This set of assumed mutual beliefs and intentions is called the discourse model, or the common ground [Webber, 1978, Stalnaker, 1978. In collaborative planning dialogues, the conversants are attempting to add mutual beliefs about the current state of the world and mutual beliefs and intentions about a plan for future action to the discourse model. It is obvious that the efficacy of the final plan and the efficiency of the planning process must be affected by agents' algorithms for communicative choice.
However previous work has not systematically varied factors that affect communicative choice, such as resource limits and task complexity. Furthermore, most previous work has been based on the redundancy constraint, and apparently, its concomitant simplifying assumptions (but see [Zukerman and Pearl, 1986, Zukerman and McConachy, 1993, Lenke, 1994).
To explore the relation of communicative choice to effective collaborative planning, the analysis of naturally occurring collaborative planning dialogues in this paper focuses on communicative acts that violate the redundancy constraint. These acts are informationally redundant utterances, IRUs, defined as: 3

Definition of Informational Redundancy
An utterance u i is informationally redundant in a discourse situation S 1. if u i expresses a proposition p i , and another utterance u j that entails p i has already been said in S.
2. if u i expresses a proposition p i , and another utterance u j that presupposes or implicates p i has already been said in S.
A statistical analysis of the financial advice corpus showed that about 12 % of the utterances are IRUs. As mentioned in section 1, this should not be particularly surprising since the definition of IRUs reflects several simplifying assumptions. For example, the definition reflects the logical omniscience assumption because it assumes that all the entailments of propositions uttered in a discourse and certain default inferences from propositions uttered in a discourse become part of the discourse model. 4 The definition reflects the no autonomy assumption because it assumes that merely saying an utterance 2 The corpus consists of 55 dialogues from 5 hours of live radio broadcast, where each dialogue ranged in length from 23 to 100 turns. 3 The first part of the definition is a variation on Hirschberg's definition of redundant [Hirschberg, 1985] which is used in her theory of scalar implicature. This view of information is also the basis of information theoretic work such as [Barwise, 1988]. 4 Presuppositions and implicatures are two types of default inferences [Grice, 1967, Karttunen and Peters, 1979, Gazdar, 1979, Levinson, 1983, Thomason, 1990a. The corpus analysis tagged defaults separately from entailments but found no evidence for a functional difference (see Walker93c). u j that expresses a proposition p i is sufficient for adding p i to the discourse model. The fact that IRUs occur shows that the simplifying assumptions are not valid.
The distributional analysis suggests that there are at least 3 functional categories of IRUs: Communicative Functions of IRUs: • Attitude: to provide evidence supporting beliefs about mutual understanding and acceptance • Attention: to manipulate the locus of attention of the discourse participants by making a proposition salient.
• Consequence: to augment the evidence supporting beliefs that certain inferences are licensed IRUs have antecedents in the dialogue which are the utterances that originally realized the content of the IRU either through direct assertion or by an inferential chain; in the definition above u j is an antecedent for u i . The 3 communicative functions of IRUs were identified by correlations with distributional features based in part on relations between the IRU and its antecedent, such as textual distance, discourse structure relations, and logical relations. The distributional analysis also analyzed utterance features such as the intonational realization of the IRU, the form of the IRU, and the relation of the IRU to adjacent utterances.
Below, I will briefly give examples of each type of IRU. 5 For each type I will explain how the four simplifying assumptions of previous dialogue models predict that the utterance is informationally redundant. Then we will consider hypothetical agent and task properties under which IRUs function as hypothesized above.

Attitude IRUs
Attitude IRUs provide evidence supporting beliefs about mutual understanding and acceptance by demonstrating the speaker's attitude to an assertion or proposal made by another agent in dialogue. An Attitude IRU, said with a falling intonation typical of a declarative utterance, is given in 7-27, where M repeats what H has asserted in 7-26. M and H have been discussing how M and her husband can handle funds invested in IRAs (Individual Retirement Accounts). In 7, and in the other naturally occurring examples below, the antecedents of the IRUs are italicized and the IRUs are in CAPS. 5 Each communicative function given above includes a number of subtypes that will not be represented by these examples. In addition, the hypothesis that IRUs are a rehearsal mechanism, i.e. agents repeat propositions as an aid to memory, is tested in every experiment by the model of Attention/Working memory. The hypothesis that agents say IRUs because they cannot think of anything else to say, (the dead air hypothesis), was considered in [Walker, 1992], but I as yet have found no evidence to support it. For example, other indications of hesitation or planning what to say, such as disfluencies and long pauses, are not associated with IRUs.
(29) M: And the fact that I have a, an account of my own from a couple of years ago, when I was working, doesn't affect this at all.
The IRU in 27 provides direct evidence that M heard exactly what H said [Clark andSchaefer, 1989, Brennan, 1990]. According to arguments elaborated below and elsewhere [Walker, 1992, Walker, 1993b], M's response indirectly provides evidence that she accepts and therefore believes what H has asserted. header: inform(speaker, hearer, proposition) precondition: know (speaker,proposition) want-precondition: speaker want inform(speaker, hearer, proposition) effect: know (hearer,proposition) Figure 1: Definition of the inform plan operator in Allen and Perrault, 1980 The classification of 7-27 as an IRU follows from the no-autonomy assumption. The no-autonomy assumption is usually characterized as an agent being "co-operative" or "helpful". For example, the motivation for the plan effect of the inform planning operator from [Allen and Perrault, 1980] in figure 1 is that the hearer is cooperative. In other words, a cooperative hearer always accepts and therefore believes (or knows) what the speaker has previously asserted. But if the effect of the inform act always goes through, then there is no reason for M to choose to produce an Attitude IRU in 7-27, in response to H's inform in 7-26.
In recent work, the plan effect shown in figure 1 is treated as a default , Reiter, 1980, Perrault, 1990, Grosz and Sidner, 1990. Perrault's Belief Transfer Rule handles inferring the default acceptance of assertions (inform acts), while Grosz and Sidner's Conversational Default Rule CDR2 handles inferring the default acceptance of proposals [Grosz andSidner, 1990, Perrault, 1990]. In both cases, the default inference of acceptance of an assertion of P or a proposal to achieve P depends on the cooperativity of the hearer and on whether or not the hearer previously believed or intended to achieve ¬P. However, Attitude IRUs are produced in many situations, where there is no reason for the default not to go through. In advice giving dialogues, the hearer is cooperative and the hearer does not previously believe or intend to achieve ¬P, yet Attitude IRUs are common when the caller asks a the talk show host a question and then repeats or paraphrases his response to the question with an Attitude IRU.
Clark and Schaefer proposed that Attitude IRUs provide positive evidence of understanding [Clark and Schaefer, 1987, Clark and Schaefer, 1989, Brennan and Hulteen, 1995. They allow for understanding to be implicitly conveyed, but say that the amount of explicit positive evidence should be 'sufficient for current purposes'. However, Clark and Schaefer do not address the question of belief transfer since they do not distinguish between indicating understanding and indicating acceptance. Furthermore, they make no predictions about what features of current purposes require more or less positive evidence, and thus lead an agent to produce an Attitude IRU.
Thus, neither the addition of defaults nor the positive evidence model makes any predictions about when an agent should produce an Attitude IRU, since the inference of acceptance goes through by default without the Attitude IRU.
In order to explain the function of Attitude IRUs, the no-autonomy assumption must be replaced with the assumption that hearers always either explicitly or implicitly accept or reject each utterance act that is intended to change their beliefs or intentions. In section 3, these observations are incorporated into ahe model of collaborative planning dialogue. Results from testing hypotheses related to the choice to produce Attitude IRUs are presented elsewhere [Walker, 1992, Walker, 1993b, Walker, 1994b, and will not be discussed further in this paper.

Consequence IRUs
Consequence IRUs make inferences explicit. For example, consider 8-17: The definition of 8-17 as an IRU follows from the logical omniscience assumption. If all entailments of utterances are automatically added to the discourse model then 8-17 should not occur. However it is well known that neither human nor artificial agents are logically omniscient [Norman and Bobrow, 1975, Johnson-Laird, 1991, Goldman, 1986, Konolige, 1986, Hayes-Roth and Thorndyke, 1979. Agents might not have enough time to make all the relevant inferences even when they know all the relevant inference rules [Konolige, 1985], especially since producing and interpreting speech in real time has heavy planning and processing requirements. Thus plausible hypotheses are that: • HYPOTH-C1: Agents choose to produce Consequence IRUs to demonstrate that they made the inference that is made explicit.
• HYPOTH-C2: Agents choose to produce Consequence IRUs to ensure that the other agent has access to inferrable information.
These hypotheses are motivated by the fact that agents are not logically omniscient. In addition, in the case of hypothesis C2, agents may choose to produce Consequence IRUs to ensure that the other agents have access to inferrable information in a timely manner, even when, in principle, they believe the other agent is capable of making the inference.
However, much of communicative efficiency relies on the fact that agents do make some inferences from what has been said. Thus plausible refinements of hypotheses C1 and C2 are that: • HYPOTH-C3: The choice to produce a Consequence IRU is directly related to a measure of 'how hard' the inference is.
• HYPOTH-C4: The choice to produce a Consequence IRU is directly related to a measure of 'how important' the inference is.
• HYPOTH-C5: The choice to produce a Consequence IRU is directly related to the degree to which the task requires agents to be coordinated on the inferences that they have made.
Confirmation of these hypotheses entails that the fewest utterances assumption does not hold whenever processing effort is relevant to achieving the conversational goals.

Attention IRUs
Attention IRUs manipulate the locus of attention of the discourse participants by making a proposition salient. Attention IRUs often realize facts that are inferentially related to the assertion or proposal that the speaker is making. For example, consider 9 said by agent A to agent B while walking to work: (9) a. Let's walk along Walnut St.
Agent B already knew that the Walnut Street route was shorter, so, by the redundancy constraint, A should have simply said 9a.
The classification of 9b as an IRU reflects the unlimited working memory assumption. If everything an agent knows is always available for reasoning, then agents should never make communicative choices to include utterances such as 9b. However, it is well known that human agents have limited attention/working memory [Miller, 1956, Norman and Bobrow, 1975, Baddeley, 1986, and resource bounded artificial agents with limited time to access memory also have limited attentional capacity.
If we define salient propositions as those that are accessible to a resource limited agent at a particular point in time [Prince, 1981, Prince, 1992, then a possible hypothesis is that A said 9b to provide B with a salient reason to accept A's proposal to walk along Walnut St. Similar observations apply to (10): (10) a. Clinton has to take a stand on abortion rights for poor women.
b. HE'S THE PRESIDENT.
Here (10b) is already known to the discourse participants, but saying it makes it salient. In order to account for 10b we must modify the specific hypothesis above to reflect the difference in utterance type between 9a and 10a. Utterance 9a is a proposal whereas 10a is an inform. In 10, A said 10b to provide B with a salient reason to accept A's assertion about Clinton's obligations. Utterance 9b is a warrant for adopting A's proposal in 9a, and 10b is support for belief in A's assertion. 6 • HYPOTH-A1: Agents produce Attention IRUs to support the processes of deliberating beliefs and intentions.
Hypothesis A1 means that the production of Attention IRUs is a surface manifestation of the fact that agents' limited working memory limits the accessibility of beliefs used as the basis of deliberation. The hypothesis that the function of Attention IRUs is to make information salient to support interpretation and reasoning is formulated in the discourse inference constraint: HYPOTH-A2: There is a discourse inference constraint whose effect is that inferences in dialogue are derived from propositions that are currently discourse salient (in working memory).
The discourse inference constraint is quite general since the inferences that A intends B to make may be any inferences related to the dialogue such as logical deductions, commonsense defaults, inferring part of A's plan, or inferring relations such as warrant or support , Moore and Paris, 1993, Walker, 1994a.
A more complex example illustrating the relationship of limited working memory, inferential processing, and agents' communicative choice is dialogue 11. The caller E has been telling H, the talk show host, how all her money is inveted and then poses a question in 10-3: The utterances in 22b and 22c realize two propositions established as mutually believed in utterances 4 to 7, thus they are IRUs. Utterance 8 initiates a subdialogue digression about retirement investments. Since the discussion about retirement investments consist of 14 utterances in which the information in 4 to 7 is not discussed, a plausible hypothesis is that, at 22a, H believes that the information expressed in 4 to 7 is no longer salient [Walker, 1995a]. However, H expects E to use this information to make two inferences: (1) that having all your investments in 6 month certificates is an instance of the negatively evaluated condition of having all your eggs in one basket; and (2) that this is a warrant for E to adopt the intention to spread the certificates out a little bit. Here, therefore, we see two types of inferences: a content-based inference, instance of, in the first case and a deliberation-based inference, warrant, in the second. It appears that H produces IRUs to ensure that these inferences get made and that H is basing his communicative choice on the discourse inference constraint.
In addition to the naturally occurring examples of Attention IRUs, another source of evidence for the discourse inference constraint is the distribution of IRUs that make inferences explicit such as the Consequence IRU in dialogue 8, 7. Figure 2 contrasts the distribution of Consequence IRUs and paraphrases, which are two different ways in which an IRU can relate logically to the prior discourse. 7 Paraphrases are syntactic or semantic transformations of a single antecedent utterance [McKeown, 1983, Joshi, 1964 A key difference is that inferences have multiple antecedents while paraphrases do not. A priori we would not expect inferences and paraphrases, as two types of entailments, to distribute differently with respect to whether their antecedents are salient. 8 However figure 2 shows that inferences are more likely to have salient premises than paraphrases (χ 2 = 4.835, p < .05, df = 1). This distributional fact provides evidence for the discourse inference constraint because whenever we have evidence that an inference has been made, the premises are likely to be salient. The data discussed above provide evidence for the discourse inference constraint, however it is clear that the effect of the constraint is strongly determined by the limits on working memory. In particular, a corollary of the constraint is that inferential complexity can be directly related to the number of premises that must be simultaneously salient for the inference to be made. These hypotheses can be summarized as follows: • HYPOTH-A3: The choice to produce an Attention IRU is related to the degree of inferential complexity of a task as measured by the number of premises required to make task related inferences.
• HYPOTH-A4: The choice to produce an Attention IRU is related to the degree to which an agent is resource limited in attentional capacity.
Finally, it is obvious that various tasks can be characterized in terms of the degree of inferential complexity, and that observations about belief coordination similar to those made about Consequence IRUs also apply to Attention IRUs, giving hypothesis A5.
• HYPOTH-A5: The choice to produce an Attention IRU is related to the degree to which the task requires agents to be coordinated on the inferences that they have made.
In the next sections we will see how we can test these hypotheses. to include IRUs could either improve the efficacy of a collaborative plan or the efficiency of the dialogue by which that plan was constructed. In this section, I will specify the details of a model of collaborative planning that will be used as the basis of the dialogue simulation testbed in which the hypotheses can be tested. In thinking about models of collaborative planning, I have found it useful to consider models in terms of 6 features: 1. agent architecture 2. role of resource limits: whether the agents constructing the collaborative plan have limited resources, and thus whether there is an attempt to either maximize or minimize any aspect of resource consumption, and if so which aspects.
3. the mutual belief model: whether the function of the dialogue is to establish mutual beliefs, and whether the mutual belief model is binary or allows for defaults in mutual beliefs.
4. utterance act types: types of acts available for agents to communicate with other agents and the effects of each act on the cognitive state of the agents and the collaborative planning process.
5. mixed-initiative: whether one agent is the initiator or both agents have equal initiative. 9 6. plan evaluation: how the collaborative plan is evaluated and what factors determine how good the collaborative plan is.
Most accounts of collaborative planning dialogues are not specific about all of these features, although some accounts provide rich models of particular features. For example, Smith and Guinn provide a richer model of mixedinitiative than that provided here , Smith et al., 1992, and there are precise models of how hearers infer the utterance act type or the intention underlying a particular communicative action [Allen, 1983, Sidner, 1985, Litman and Allen, 1990. However, to my knowledge no previous work has included a specification of the agent architecture, the relationship of the architecture to language behavior, the role of resource limits, and the plan evaluation process. The remainder of this section provides a specification for each of these features.

Agent Architecture, Mutual Belief and Resource Limits
Both the agent architecture and the role of resource limits are addressed by adopting an agent architecture based on the IRMA architecture for resourcebounded agents, shown in figure 3 [Bratman et al., 1988, Pollack andRinguette, 1990]. The IRMA architecture has not previously been used to model the behavior of agents in dialogue. The basic components of the modified IRMA architecture are: • Beliefs: a database of an agent's beliefs. This includes beliefs that an agent believes to be mutual to some degree.
• Belief deliberation: decides what an agent wants to believe when there is conflicting evidence.
• Intentions: a database of an agent's intentions. This includes intentions that an agent believes to be mutual to some degree.
• Plan Library: what an agent knows about plans as recipes to achieve goals.
• Means-end reasoner: reasons about how to fill in existing partial plans, proposing options that serve as subplans for the plans an agent has in mind.
• Filtering Mechanism: checks options for compatibility with the agent's existing plans. Options deemed compatible are passed along to the deliberation process. 10 • Desires: Agents may have different types of desires but here I assume that their only desire is to maximize utility [Doyle, 1992].
9 This is also called 'control' [Whittaker andStenton, 1988, Smith, 1980]. Walker and Whittaker and Guinn argued that the distribution of control in natural dialogue is primarily determined by whether information relevant to the task is distributed between the agents or primarily known by one agent [Walker andWhittaker, 1990, Guinn, 1993]. 10 The filtering mechanism presented in [Bratman et al., 1988] and used in Tileworld is more complex than that presented here because that work explored the issue of when current intentions get over-ridden.
• Intention Deliberation: decides which of a set of options to pursue (by an evaluation based on desires such as maximizing utility).
• Attention/Working memory (awm): the limited attention module constrains working memory and the retrieval of current beliefs and intentions that are used by the means-end reasoner.
For the purpose of modeling dialogue, the architecture has been extended with a model of mutual belief that allows for different degrees of mutual belief. For the purpose of exploring the effects of resource-bounds on attention, this architecture has been extended with a model of limited attention. All of the modules are standard except for the awm module described in detail below, and the mutual belief module which will be briefly described.
Attention/working memory model The model of limited awm is a cognitively based model adapted from [Landauer, 1975], which fits many empirical results on human memory and learning [Hellyer, 1962, Landauer, 1969, Collins and Quillian, 1969, Sternberg, 1967, Tulving, 1967, Anderson and Bower, 1973, Solomon, 1992. The motivation for using a cognitively based model of awm is to model the behavior of agents in naturally occurring dialogues and to test a theory of collaborative communication with humans. 11 The key properties of the model are that (1) limits on awm are a parameter of the model and can be varied to explore different limits [Baddeley, 1986]; (2) items encountered more recently are more likely to be salient [Landauer, 1975]; (3) items encountered more frequently are more likely to be salient [Hintzmann and Block, 1971].
These recency and frequency effects are a key aspect of the awm model for testing the hypothesized functions of IRUs. Below I will discuss a particular implementation of this model and its role in testing the hypotheses.
awm is modelled as a three dimensional space in which propositions acquired from perceiving the world are stored in chronological sequence according to the location of a moving memory pointer. The sequence of memory loci used for storage constitutes a random walk through memory with each loci a short distance from the previous one. If items are encountered multiple times, they are stored multiple times [Hintzmann and Block, 1971]. The fact that the sequence of storage locations is random means that the recency and frequency effects are stochastically determined. This means that when this model is used in simulation, the simulation produces different results each time.
When an agent retrieves items from memory, search starts from the current pointer location and spreads out in a spherical fashion. The resource limited aspect of awm follows from the fact that search is restricted to a particular search radius defined in Hamming distance. For example, if the current memory pointer loci is (0 0 0), the loci distance 1 away would be (0 1 0) (0 -1 0) (0 0 1) (0 0 -1) (-1 0 0) (1 0 0). The actual locations are calculated modulo the memory size.
The limit on the search radius defines the subset of the belief and intentions database that is salient. In addition, the fact that the pointer moves has the effect that the salient subset is always changing. Effectively, as new facts are added, others are displaced and become no longer salient, so that the salient predicate is dynamic.
The search radius limit defines the awm parameter that will be varied in the experiments in section 5 in order to test the effect of different resource limitations. Experiments that Landauer performed showed that, for a task requiring remembering whether a word belonged to a list of words, the model can be parameterized so that an awm of 7 reproduces the human performance results in [Hellyer, 1962]. Since no systematic tests have been performed for human performance on the collaborative planning tasks investigated below, the experiments are run at low, mid and high awm settings. Human performance is assumed to fall somewhere in the middle of these ranges.
Using awm to implement the discourse inference constraint The model of Attention/Working Memory (awm) provides a means of testing the hypothesized discourse inference constraint introduced in section 2.3. Remember that the discourse inference constraint states that inferences in discourse are derived from propositions that are currently in working memory. The awm model, as shown in figure 3, limits the beliefs accessible for means-end reasoning and deliberation to the subset of beliefs that are currently in awm [Hayes-Roth and Thorndyke, 1979, Joshi, 1978, Joshi et al., 1984, Norman and Bobrow, 1975. These beliefs are defined as being salient.
This model contrasts with the standard view of inference, where if an agent believes P and believes P→Q, then the agent believes Q. The discourse inference constraint provides a principled way of limiting inference in modeling humans by requiring the premises of P and P→Q to be salient. An axiomatization requires the predicate salient and inference rules as follows for each inference rule schema [Walker, 1993b, Hobbs, 1994: The first inference rule states that whenever agent A says an utterance to B that realizes proposition P, that P becomes salient for B. The second rule states that whenever a proposition P and an inference rule, P→Q, are both believed by B and salient for B, then B can use them to infer Q. The model of awm must be consulted to determine when the salient predicate holds.
Mutual belief model The model of mutual belief is based on Lewis's Shared Environment model of mutual belief [Lewis, 1969, Clark and Marshall, 1981, Barwise, 1988, extended to support different degrees of mutual belief by tagging beliefs with qualitative endorsements at the time that they are formed and stored in the beliefs database , Gardenfors, 1988, Galliers, 1991a. Different degrees of mutual belief allow some actions to be left to inference and some inferences to be defaults. This makes it possible to distinguish between the explicit acceptance of a proposal and the acceptance of a proposal inferred in the absence of evidence to the contrary. When agents are not logically omniscient, it is possible to distinguish between mutual beliefs about what has been mutually inferred and information that has been discussed in the dialogue. See [Walker, 1992, Walker, 1993b] for more detail.

Discourse Acts, Utterance Acts, and Mixed Initiative
The overall structure of the discourse in collaborative planning dialogues is primarily determined by the task structure [Power, 1974, Grosz, 1977 May be IMPLICIT  Sibun, 1991]. Each subpart of the task consists of a dialogue segment in which agents negotiate what they should do for that part of the task.
As discussed in section 2.1, we wish to abandon the no autonomy assumption. The model should allow either agent to initiate the dialogue or initiate a subdialogue about a new part of the task [Walker andWhittaker, 1990, Dahlback, 1991]. For each agent to be able to do this, knowledge about the task must be distributed between the participants so that each participant has a basis for means-end reasoning and deliberation. Furthermore, agents should be able to accept or reject one another's proposals. Each plan step contributing to a higher level goal must remain open for negotiation even if both agents are committed to coming up with a collaborative plan for the higher level goal. This contrasts with models in which proposals for each plan substep that the initiator makes must be accepted by the non-initiator, once the non-initiator has agreed to work on a collaborative plan [Cohen andLevesque, 1991, Grosz andSidner, 1990].
Discourse Acts and Mixed Initiative To engage in collaborative planning, agents take turns sending messages, and each turn may consist of one or more discourse acts. Discourse acts are opening, closing, proposal, acceptance, rejection and clarification. These are higher level acts that are composed of primitives called utterance acts, which will be described below.
The schema of discourse actions shown in figure 4 controls the sequence of discourse acts and which discourse acts can be combined into a single turn. 12 The discourse act schema is the basis of an algorithm by which agents achieve a collaborative-plan. For each step in the domain plan: 1. individual agents perform means-end reasoning about options in the domain; 2. individual agents deliberate about which options are preferable; 3. then one agent initiates a subdialogue consisting minimally of a proposal to the other agent, based on the options identified in a reasoning cycle, about actions that contribute to the satisfaction of their goals; 4. then the proposal may be subject to clarification, after which it is either accepted or rejected by the other agent, by calculating whether it maximizes utility This algorithm ties the discourse act schema in figure 4 to the IRMA architecture. The requirement that agents must indicate whether they accept or reject each proposal follows from replacing the assumption of cooperativity in earlier work [Allen andPerrault, 1980, Grosz andSidner, 1990] with the collaborative principle: collaborative principle: Conversants must provide evidence of a detected discrepancy in belief as soon as possible.
The collaborative principle was proposed in [Walker, 1992], and is an abstraction of the collaborative planning principles of Whittaker and Stenton (1988) and Walker and Whittaker (1990). The collaborative principle means that speakers must monitor the next action by the hearer in order to detect the effects of their utterances. If the hearer continues the dialogue and provides no evidence of a belief discrepancy, the inference of acceptance is licensed as a default [Galliers, 1990, Walker, 1992.
The fact that agents evaluate both assertions and proposals before deciding what to believe or intend follows from the IRMA agent architecture in figure 3. As the figure shows, incoming messages about intentions and beliefs are subject to intention or belief deliberation. This provides the basis for abandoning the no autonomy assumption while specifying why an agent would accept or reject another agent's proposal (see also [Galliers, 1989, Galliers, 1991b, Doyle, 1992). Agents evaluate assertions and proposals from other agents by assessing the support for assertions and the warrants for proposals. Finally, as figure 3 shows, this evaluation takes place under constraints of limited working memory, since the beliefs that can serve as supports or warrants must be salient for these processes to use them. Figure 4 shows the discourse act schema that provides the basis for dialogue. Discourse acts are composed of utterance acts, which are the primitive acts that an agent can actually perform. Each discourse act can be performed in different ways by varying the number and type of utterance acts that it consists of. For example, a proposal may or may not include additional information that can convince the hearer, as in example 9b.

Utterance Acts
There are seven utterance act types: open, close, propose, accept, reject, ask and say, which are realized via the schemas below: The content of each utterance act can be an options and intentions representing a domain plan act constructed by means-end reasoning and deliberation as shown in figure 3. An option is an act that has not been committed to by both agents. An intention is an act that has been committed to by both agents [Pollack andRinguette, 1990, Bratman et al., 1988]. An option only becomes an intention in the collaborative plan if it is accepted by both agents, either explicitly or implicitly. The option in a reject schema is a counterproposal and what is rejected is the current proposal.
The content of an utterance act may also be a belief. These beliefs are either those that an agent starts with, beliefs communicated by the other agent, or inferences made by the agent during the conversation. Beliefs in ask actions have variables that the addressee attempts to instantiate. The belief in a rejection schema is a belief that the speaker believes is a reason to reject the proposal, such as a belief that the preconditions for the option in the proposal do not hold [Walker and Whittaker, 1990].
Examples of these utterance acts in dialogue will be given in section 4. Below how B processes each of the 7 messages that A can send is specified. In the effects specified below, Store means store in awm, for eventual long-term storage in the beliefs database. The processing involved with each incoming message should be understood with reference to the IRMA agent architecture. These acts and their effects determine the structure of the dialogue and its effect on the mental state of the conversants.

Plan Evaluation
There are three components of the plan evaluation process that have different effects on collaborative planning. Two features are related to the task definition and the third to the model of evaluation applied: 1. the degree of belief coordination: whether some or all of the intentions associated with a plan must be mutually intended and whether any beliefs related to the intended acts must also be mutually believed; 2. task determinacy and fault tolerance: whether the task has only one solution, or is fault tolerant or more or less satisfiable.
3. the model must specify what is to be optimized and whose resource consumption is to be minimized for performance evaluation.
Different theories of collaborative planning reflect different views of the degree of belief coordination required for agents have a collaborative plan. The minimal approach is to not require the agents to establish mutual beliefs at all [Durfee et al., 1994. Rather agents divide up the plan into subcomponents and separately plan each component, without requiring agreement on how the subcomponents are planned. At the next level of belief coordination, it is common to require the intended acts of the collaborative plan to be mutually intended [Grosz and Sidner, 1990, Levesque et al., 1990, Thomason, 1990b. At the highest level of belief coordination, the agents must both mutually intend all intentions and mutually believe any beliefs that support the plan such as the warrant beliefs that provide reasons for adopting a step of the plan. In addition, it is possible to require that inferences about other goals that the intended actions will satisfy should also be mutually believed.
In this work, the assumption is that the degree of belief coordination required is a feature of the task. The minimal level in the experiments discussed below will be that all intentions must be mutually intended, and the experiments will vary whether warrants, and inferred intentions that are derived from explicitly discussed intentions.
Task determinacy and fault tolerance have an effect on communicative choice in collaborative planning because they are directly related to how much uncertainty is tolerable in the plan. If a partial plan has some utility, then making a mistake or only constructing a partial plan is not catastrophic. For task determinacy, I assume that a measure of the quality of the final plan can be determined from the utility of each step in the plan, and that partial plans can also be evaluated, so that the task is more or less satisfiable.
With respect to evaluating performance, I assume that the agents in a collaborative planning dialogue are working as a team, and as a team they attempt to optimize the team's performance and minimize the team's consumption of resources. This follows from Clark's assumption that conversants in dialogue attempt to achieve their dialogue purpose with least collaborative effort [Clark and Schaefer, 1989, Clark and Wilkes-Gibbs, 1986, Clark and Brennan, 1990. This approach contrasts with other approaches in which agents only participate in communication to the degree that it maximizes their own expected utility [Durfee et al., 1994].
A final choice has to do with which processes collaborative effort consists of. A common assumption is that the number of utterances is the primary efficiency measure [Grice, 1975, Chapanis, 1975; this is the fewest utterances assumption. Since all types of IRUs violate this assumption, in this work collaborative effort is defined with reference to the agent architecture and to all the processes required in collaborative planning, i.e. (1) retrieval processes necessary to access previously stored beliefs in memory; (2) communicative processes related to generating and interpreting utterances; and (3) reasoning processes that operate on beliefs stored in memory and those communicated by other agents. With respect to the IRMA architecture (figure 3), retrieval processes are those that access awm, the plan library and the beliefs and intentions databases, communicative processes are the modules for perception and generation of messages, and inferences are the combined processes of deliberation, means-ends reasoning, and filtering. Collaborative effort includes the costs for both agents for all of these processes: collaborative effort = (the total cost of communication for both agents) + (the total cost of inferences for both agents) + (the total cost of retrievals for both agents) Collaborative effort is defined for the whole dialogue and not on a per utterance basis. This definition and the other assumptions support the specification of the plan evaluation process. Given the above definitions, performance is the difference between a measure of the quality of the problem solution and collaborative effort.
Since the agents' desires are simply to maximize utility, the quality of the solution is measured by the utility of the resulting plan with respect to the agents' utility functions.

Methodological Basis of Design-World
Design-World is a testbed for a theory of collaborative communication, which instantiates the model of collaborative planning in dialogue discussed in section 3. In order to motivate the use of the Design-World testbed in developing and testing a defeasible theory of communication in collaborative planning, this section first describes Design-World as an instance of a general method, and then describes the testbed and its implementation as well as the task and communication parameters. The method can be characterized by the steps below: 1. Generate hypotheses about the features of a model of collaborative planning dialogues from a statistical analysis of human-human dialogue corpora.
2. Produce a functional characterization of the model, specifically including the parameters that could affect task outcome, or claims about the efficacy of the model.
3. Implement the model as a testbed so that (some of ) these parameters can be controlled, while using independently motivated modules for other aspects of testbed.
4. Test the hypotheses and the resulting model against different situations controlled by parameter settings.
The hypotheses that were generated by the statistical analysis of the dialogue corpora were discussed in section 2. These hypotheses are roughly that under constraints of resource bounds, task inferential complexity, task fault tolerance, and task requirements for belief coordination, communicative choices to include IRUs can reduce collaborative effort or increase the quality of solution of the collaborative plan.
The next step is to produce a functional characterization of the model (a partial formalization). In section 3, I discussed features of a model of collaborative planning that interact with an agent's autonomy, resource limits and communicative choices. In nonexperimental work, the model is the final result of the research. However, this leaves the model and the claims that motivated the model empirically unverified. In formal characterizations, many simplifying assumptions need to be made, and it is not always clear that the results carry over to complex domains where the simplifying assumptions do not hold. While the model presented here is empirically based on statistical analysis of a corpus of naturally occurring dialogues, many of the hypotheses discussed above are related to models of agents' processing. Corpus analysis can only provide weak support for these hypotheses. Thus another source of empirical verification is desirable in order to develop a well-specified and defeasible theory. This is the motivation for the Design-World testbed.
Next, it is necessary to consider the parameters that could affect the outcome or claims about the efficacy of the model and then implement the model as a testbed so that at least some of these parameters can be controlled. The use of independently motivated modules for other aspects of the testbed guarantees that the testbed actually tests something, and also makes it less likely that the testbed is a case of 'experimentation in the small' [Hanks et al., 1993].
Parameters that affect the efficacious use of IRUs have already been discussed: these include resource bounds, task inferential complexity, and requirements for belief coordination. The awm model introduces a parameter for resource bounds, and is implemented as part of the IRMA architecture for resource limited agents, which is independently motivated [Bratman et al., 1988, Pollack andRinguette, 1990]. The awm model itself is also independently motivated, since it reproduces in simulation many well known results on human memory and learning [Landauer, 1975, Solomon, 1992. In addition, the utterance acts and their effects are independently motivated by other research on collaborative planning dialogues and by the statistical analysis of dialogue corpora [Whittaker and Stenton, 1988, Walker and Whittaker, 1990, Stein and Thiel, 1993, Reithinger and Maier, 1995, Carletta, 1992, Chu-Carrol and Carberry, 1995.
To introduce parameters related to tasks, the testbed is designed around a simple task where two agents must form a collaborative plan as to how to arrange some furniture in the rooms of a two room house. The task is based on cooperative design tasks used for experiments on distributed cooperative work for which a corpus of dialogues was available [Whittaker et al., 1993]. However, the simple task can be varied along three dimensions: (1) inferential complexity; (2) degree of belief coordination required; (3) tolerance for errors and usefulness of partial solutions.
These three task dimensions represent very different tasks. For example, varying the task by increasing inferential complexity provides information on the performance of agent communication algorithms in simple versus inferentially complex tasks. The dimensions enable us to generalize from the specific task in Design-World to real world tasks. Section 4.2 will introduce the Standard version of the task, and then Section 4.4 will describe the task variations.
To introduce parameters related to the interaction of communicative choice with task complexity and resource limits, agents are designed so that they vary their communication strategies to include or not include IRUs. Section 4.5 will describe the communicative choice parameters that will be used in the experimental results presented in section 5.
The experiments reported in section 5 will examine the interaction of three factors: (1) resource limits; (2) communicative strategies; and (3) task definition. The experiments in the testbed have several functions: (1) they demonstrate that the model can be implemented; (2) they highlight potential flaws in the model; and (3) they provide empirical verification of hypotheses about the function of particular communicative strategies beyond that provided by corpus analysis and researcher's intuitions. This section describes the domain, the implementation of the collaborative planning model in this domain, the communicative strategies and the task variations.

Design World Collaborative Planning Domain
In Design-World, two artificial parametrizable agents converse in order to agree on the design of the floor plan of a two room house [Whittaker et al., 1993, Walker, 1993b. The design-house plan requires the agents to agree on how to design-room-1 and design-room-2. At the beginning of the simulation, both agents know the structure of the design-house plan and that it requires four furniture items in each room. Each agent has 12 items of furniture that can be used in the plan. A potential final collaborative design plan negotiated via a (simulated) dialogue is shown in Figure 5.
Each furniture item has a value that is used both as a warrant to support deliberation (the utility of an act that is under consideration), and as the basis for calculating the quality of solution of the final plan, as discussed in section 3. The values on the furniture items range from 10 to 56, and both agents' furniture items range over these values. Since beliefs about these values will be used to test hypotheses about the function of IRUs, both agents know Design-World agents negotiate a collaborative plan following the collaborative planning algorithm discussed in section 3. Each agent carries out means-end reasoning about the furniture items that can be used in the design. Means-end reasoning generates options -these options are the content of proposals to the other agent to put a furniture item into a room. This is illustrated by Dialogue 12, which includes the artificial language that the agents communicate with and a gloss automatically generated from that language in italics for part of designing room-1.
(12) 1: BILL: First, put the green rug in the study.
(reject agent-bill agent-kim option-56: put-act (agent-bill green couch room-1)) At the beginning of the dialogue, Agent-Kim has stored in memory the proposition that (score green-rug 56). When she receives Bill's proposal as shown in (12-1), she evaluates that proposal in order to decide whether to accept or reject it. As part of evaluating the proposal she will attempt to retrieve the score proposition stored earlier in memory. Thus the propositions about the scores of furniture items are warrants for supporting deliberation.
As discussed in section 3, the agents retain their autonomy even though the agents both want to agree on a plan for designing the house. Thus, on receiving a proposal, an agent deliberates whether to accept or reject it [Doyle, 1992, Walker, 1994b. Proposals 1 and 2 are inferred to be implicitly accepted because they are not rejected [Whittaker andStenton, 1988, Walker andWhittaker, 1990]. This follows from the collaborative principle discussed in section 3. If a proposal is accepted, either implicitly or explicitly, then the option that was the content of the proposal becomes a mutual intention that contributes to the final design plan [Power, 1984, Walker, 1992.
Agents reject a proposal if deliberation leads them to believe that they know of a better option, based on evaluating the utility of the competing options they have generated by means-end reasoning. For example, in (12-4) Kim rejects the proposal in (12-3), for pursuing option-45, and proposes option-56 instead. The form of the rejection as a counter-proposal is based on observations about how rejection is communicated in naturally-occurring dialogue as codified in the collaborative planning principles [Walker and Whittaker, 1990]. When an agent intends to reject another agent's rejection, as in 12-5 and 6, the agent includes additional information to support its proposal. In 12-5, agent-bill reminds agent-kim of the value of the green couch, before rejecting agent-kim's proposal.

Agent architecture implementation in Design-World
The agent architecture used in the Design-World simulation environment is the modified IRMA architecture, shown in figure 3 and discussed in section 3 [Bratman et al., 1988, Pollack andRinguette, 1990]. The only aspects of the architecture that are specific to Design-World are the plan library, the way that awm is implemented, and the way that belief deliberation is implemented.
For the experiments below, the total size of awm is set to 16, but memory is wrap-around, and there is no overwriting. If the path of the memory pointer retraces its steps so that the current memory loci already has something stored in it, the new item is simply added. Thus memory capacity is unbounded.
Since hypothesis A4 relates to the degree to which awm is limited, we want to be able to compare the performance of agents who are more or less attention limited. Thus, all experiments make comparisons between different communicative strategies over three ranges of of awm settings; the awm search radius parameter varies from low awm (radius of 3 and 4), to mid awm (radius of 6 and 7) to high awm (radius of 11 and 16). low awm agents are severely attention limited agents, wherease almost everything an agent knows is salient for high awm agents.
The limits on awm plays a critical role in determining agents' performance. Remember that only salient beliefs can be used in means-end reasoning and deliberation, so that if the warrant for a proposal is not salient, the agent cannot properly evaluate a proposal. However, if the agent only knows of one option, the agent can accept the proposal on the assumption that any option is better than doing nothing. Section 5 will show the impact of resource limits on performance. For more detail see [Landauer, 1975, Walker, 1994b.
The implementation of belief deliberation, for the purpose of Design-World was tied directly to Landauer's awm model. In that model, nothing stored in memory is ever deleted or modified. Rather, new beliefs are added which effectively compete with beliefs that are already present. Thus an agent's belief deliberation process depends on collecting a set of related beliefs which may be contradictory, and applying an algorithm to determine what the agent believes (see [Galliers, 1990, Gardenfors, 1990). The fact that new information about the the state of the world supercedes old information is an emergent property of the belief retrieval mechanism: beliefs recently added are more likely to be retrieved. However the stochastic aspect of retrieval means that it is possible for an agent to decide to believe "out-of-date" propositions, and "forget" recent changes in the world. As we will see in section 5, this means that, in cases where the outdated beliefs were encountered with greater frequency and thus stored in memory repeatedly, that agents who can access all of their beliefs are more likely to decide to believe out of date beliefs. 15 The plan library contains domain plans for Design-House and its subgoals, as well as discourse plans for the discourse acts shown in figure 4. The discourse plans will be discussed in detail in section 4.5.

Design-World Tasks
The Design-World task as a plan is simple since it involves linear planning of subgoals which contribute to higher level goals, as shown in figure 6. However, the task is easily modified according to the general task features discussed above so that it is more difficult to perform well. These modifications are applicable to other tasks besides the testbed task, and affect the degree to which different aspects of the task contribute to the performance evaluation.
There are 4 versions of the task that will be used to test the hypotheses introduced in section 2: Standard, Zero-Nonmatching-Beliefs, Matched-Pair, and Zero-Invalid. The Standard task is inferentially simple, fault tolerant and requires low levels of belief coordination. The other tasks are more difficult because they increase the degree of belief coordination required, and magnify the effect of mistakes. The Zero-Nonmatching-Beliefs and Matched-Pairs tasks each explore different aspects of belief coordination and inferential complexity. The Zero-Invalids task is fault intolerant.

Standard Task
The Standard task provides a baseline and is inferentially simple, fault tolerant and requires low levels of belief co-ordination. The Standard task is defined so that the quality of solution for a particular dialogue consists of the sum of all the furniture pieces for each valid step in the plan. In addition, the task is defined so that partial solutions are possible. Any number of furniture items in a room is a valid plan, rather than requiring that each room must have all four furniture items. This choice about task determinacy makes it possible to see the gradient effect on performance of different resource restrictions.
In addition the Standard task is fault tolerant. If agents make a mistake in planning and insert invalid steps in their collaborative plan, the point values for invalid steps in the plan are simply subtracted from the score. Thus in the Standard task agents are not heavily penalized for making mistakes due to inserting steps in plans that are not actually executable. The Standard task is inferentially simple because the agent's only inferences are those by means-end reasoning to generate options, those by deliberation to evaluate options, and act-effect inferences after committing to an action. Each of these inferences rely on one premise: the premise (has ?agent ?item) supports means-end reasoning, the premise (score ?item ?score) supports deliberation, and the premise (intend A B ?option) supports inferring the effect of ?option. Thus, none of these processes require multiple premises to be simultaneously salient. However, it is possible to test hypotheses about processing effort in the Standard task by making it easier to access these inferential premises. It is also possible to test the effect of resource limits since these premises must be accessible to perform optimally on the task.
The degree of belief coordination in the Standard task is low because agents are only required to coordinate on the intentions corresponding to put-acts as shown in figure 6. These intentions are always explicitly discussed so that coordination is always achieved.
The Zero-Nonmatching-Beliefs task The Zero-Nonmatching-Beliefs task increases the degree of belief coordination by requiring agents to base their deliberation process on the same beliefs. They must have the same warrants for adopting an intention in order to do well on this task. Figure 7 shows the structure of beliefs about intentions and warrants for the Design-House goal. In the Zero-Nonmatching-Beliefs task, as shown, the warrants underlying intentions must also be mutually believed. This is not generally required in forming a collaborative plan because agents A and B can mutually believe that they have maximized utility without necessarily agreeing on what that utility is. Furthermore, in the general case, when agents have only one option under consideration, they do not need to evaluate the utility of that one option in order to decide whether to accept or reject it.
The Zero-Nonmatching-Beliefs task provides a basis for testing hypotheses A1 and A5, introduced in section 2 by increasing the degree of belief coordination required to perform well on the task, where the beliefs are those used in deliberation.
The Zero-Nonmatching-Beliefs task models particular types of real-world tasks since it is not always necessary for agents to agree on the reasons for carrying out a particular action. For example, in the negotiation between the union and the management of a company, any agreement that is reached is agreed to by each party for different reasons. An agreement for a shorter work week is supported by the union because more overtime pay is possible for those who want to work more and is supported by the management because the company's insurance premiums will be lower. However, if two agents agree on a plan, but have different reasons for doing so, they may change their beliefs and their intentions under different conditions. The most stable, long-term, collaborative plans will be those in which agents agree on both the actions to be performed, as well as the reasons for doing those actions. Under these conditions the agents will be more likely to revise their intentions in a compatible way and intention revision should be simpler. Thus the Zero-Nonmatching-Beliefs task examines one extreme of belief coordination for deliberation.
Matched Pair Tasks Another aspect of belief coordination has to do with coordinating beliefs based on inferences. There are two task definitions that increase inferential complexity by increasing the number of independent premises that must be simultaneously available in working memory. These are: (1) Matched Pair Same Room, and (2) Matched Pair Two Room. Figure 8 shows the Matched Pair Two Room version of the task. Each intention to put a furniture item in a room can potentially contribute to another intention of achieving a matched pair goal. A Matched-Pair is two furniture items of the same color. The inference of a Matched-Pair is based on the minor premises shown in 13: Making this inference is more demanding for resource limited agents, than the processing needed in the Standard task. In the standard task, in order to agree on one step of the plan, the agents must access at least one belief about a In order to properly evaluate the option represented by that furniture item they must access the warrant for that option. In contrast, in both Matched Pair tasks, the warrant for both beliefs must be accessed for both furniture items that could contribute to a Matched-Pair goal.
In addition, the premises in 13 must also be accessed, and furthermore, each version of the Matched-Pair task requires one additional premise. The difference in the two Matched Pair tasks is whether the matches are in the same or different rooms. Matched-Pair Same Room requires the additional premise that (Equal ?room-1 ?room-2) while Matched Pair Two Room requires the additional premise that NOT (Equal ?room-1 ?room-2). Because premise 13a is inferred and stored in memory at the time that a proposal is accepted, and because the agents always complete one room before starting another, the necessary premise shown in 13a is more likely to be salient in the Matched-Pair-Same-Room task.
As discussed in sections 1 and 2, we wish to provide a test of hypothesis A2, the discourse inference constraint, and examine how it affects the coordination of inference in collaborative planning. Hypotheses A3 and A5 together imply that the complexity of inference should interact with the agent's ability to stay coordinated on inferences. Since our measure of inferential complexity is the number of independent premises required to draw an inference, both the Matched-Pair-Same-Room task and the Matched-Pair-Two-Room task increase inferential complexity.
Evaluating the quality of solution for the Matched-Pair tasks reflects the emphasis on coordinating on inferences, since both Matched-Pair tasks require that both agents make the matched pair inferences in order to score points for matched-pairs. The task measures how well agents are coordinated on the inferred intentions that follow from the intentions that were explicitly agreed upon. Only the intentions that contribute to Matched-Pairs are counted in the final solution, and the utility of these intentions is the sum of the utilities of the two furniture items, plus the utility of the Matched-Pair (50 points). Zero-Invalids Task The Zero-Invalids task is fault intolerant (see figure 9) The assumption in the Zero Invalids Task is that any mistake invalidates the whole plan. This is a feature of task determinacy: while there are still many possible 8 step plans, all of the solutions with less than 8 items that would be counted as valid solutions for the Standard Task are not valid solutions for the Zero Invalids Task. This task is an example of one extreme of fault intolerance. In general, how fault tolerant a task is depends on the interdependency of different subparts of the problem solution. For some tasks, a mistake can invalidate the whole solution, for other tasks, partial solutions without the invalid step may be adequate. For example, in a task like furnishing a room it may be desirable to have both a couch and a chair, but if the agents make a mistake and assume they can use a chair that will end up in a different room, the room is still partially furnished and usable. On the other hand, in a task such as building a tower, each step depends on the successful execution of the previous step and the whole plan may be invalid if a step to put down a foundation block cannot be executed.
Note that an agent can reject another agent's proposal based on believing that it would add an invalid step to the plan, as shown in the rejection utterance act schema in section 3.2. Since agents have to agree on each step of the plan, an invalid step can only be inserted into the plan if both agents have failed to remember that the preconditions for the plan do not hold.

Varying Communicative Strategies
Section 3 discussed the discourse act schema that controls how agents participate in dialogue, and discussed the types of utterance acts that the discourse acts are composed of. Which utterance acts a discourse act decomposes into depends on communicative strategies which codify different communicative choices for how to do a particular discourse action. Agents are parameterized for different communicative strategies by placing different expansions of discourse plans in their plan libraries.
Varying an agent's communicative strategies provides the basis for testing the hypotheses about the potential benefits of IRUs. Varying the degree of explicitness of a discourse act is the basis of the four communicative strategies tested below: (1) All-Implicit; (2) Close-Consequence; (3) Explicit-Warrant; and (4) Matched-Pair-Inference-Explicit. All of these strategies are hypothesized to mitigate agents' attentional and inferential resource limits, under the assumptions about their architecture and the definition of quality of solution for the task. Figures 10, 11, 12 and 13 show a plan operator for each strategy. These operators draw on work by Walker and Rambow [Walker and Rambow, 1994], and also make use of Moser and Moore's definitions of discourse acts and the integration of Rhetorical Structure Theory (RST) and Grosz and Sidner's theory of discourse [Mann and Thompson, 1987, Moser and Moore, 1993, Moser and Moore, 1995. The predicates in the plan operators are precisely defined by the collaborative planning model and agent architecture discussed in section 3. Each discourse act such as a proposal, is composed of a core act which represents the primary purpose of the act such as a propose utterance act, as well as a contributor act, such as a warrant, whose purpose is to increase the likelihood of achieving the intention of the core [Moore and Paris, 1993, Young and Moore, 1994.

name:
Proposal-All-Implicit (?speaker, ?hearer, ?act) effect: (desire ?hearer (do ?hearer ?act) ?utility-act) constraints: (and (option ?act) (salient ?hearer (utility ?act ?utility-act))) core: (propose ?speaker ?hearer ?act) Figure 10: The Proposal plan operator for an All-Implicit Agent All-Implicit Strategy The All-Implicit strategy is an expansion of a discourse plan to make a proposal, in which a proposal decomposes trivially to the communicative act of propose. See the plan-operator in figure 10. This strategy is the communicative choice shown in 3 in section 1, and provides a baseline strategy that is consistent with the redundancy constraint. The experiments below will compare the performance of agents using the All-Implicit strategy with the performance of agents using the other proposal strategies discussed below. In dialogue 12 on page 22, both Design-World agents communicate using the All-Implicit strategy, and the proposals are shown in utterances 1, 2, and 3. As figure 10 shows, the All-Implicit strategy includes no additional information in proposals, leaving it up to the other agent to retrieve them from memory.
The constraints on using the All-Implicit strategy are that (1) the proposed ?act is an option generated by means-end reasoning and (2) that the utility is salient to the hearer. In the experiments below, agents are parameterized to use this strategy consistently, so that an agent using the All-Implicit strategy assumes everything the hearer knows is always salient. The effect of the proposal is that the hearer will evaluate that proposal and deliberate the degree to which the hearer desires the act. However, whether the hearer will accept or reject the proposal depends on other options the hearer knows about. Clearly the speaker cannot predict these other options. Thus the effect of the proposal does not specify that the action will be intended by the hearer. This holds for all proposal operators.
The All-Implicit strategy can be used by agents in any of the Design-World tasks discussed in section 4.4, since the agents are capable of making inferences or accessing memory to fill in what has been left implicit with this strategy. Other inferences drawn by the hearer from the proposal utterance act are not shown in figure 10. For example, an agent can use the All-Implicit strategy in either of the Matched-Pair tasks, leaving it up to the other agent to infer which other intention makes a match with the option currently under consideration.

Figure 11: The Closing plan operator for a Close-Consequence Agent
Close Consequence In dialogue 14, agent CLC uses the Close-Consequence strategy. The plan-operator for this strategy is shown in figure 11. The core of the strategy is explicit closing statements, such as 14-2, on the completion of the intention associated with a discourse segment. A contributor to CLC's closing discourse act is an IRU such as 14-3: CLC makes the inference explicit that since they have agreed on putting the green rug in the study, they no longer have the green rug (act-effect inference).
(14) 1: BILL: Then, let's put the green rug in the study.
(propose agent-bill agent-clc option-30: put-act (agent-bill green rug room-1)) 2: CLC: So, we've agreed to put the green rug in the study.
(say agent-clc agent-bill bel-48: hasn't (agent-bill green rug)) The Close-Consequence strategy of making inferences explicit at the close of a segment models the naturally occurring example in 8. In both cases an inference is made explicit that follows from what has just been said, and the inference is sequentially located at the close of a discourse segment. This strategy can be used by agents in any of the Design-World tasks discussed in section 4.4.
The Close-Consequence strategy will be used to test hypothesis C2 about potential benefits of making inferences explicit, and will be contrasted with the All-Implicit strategy where no closing acts are produced. Note in dialogue 12 on page 22 that both the agents go on to the next phase of the plan, leaving the inference of both Acceptance and Closing for the other agent to make. However, Close-Consequence is not a good test of other hypotheses because in the experiments both agents always make act-effect inferences, and these inferences are not difficult to make. See [Walker, 1995b] for a discussion of experiments which vary an agent's capability to make these inferences.

Explicit Warrant
The Explicit-Warrant strategy varies the proposal discourse act by including warrant IRUs in each proposal. The plan operator is given in figure 12 and exemplified by the dialogue excerpt in 15. Remember

name:
Proposal-Explicit-Warrant (?speaker, ?hearer, ?act) effect: (and (desire ?hearer (do ?hearer ?act) ?utility-act) (salient ?hearer (utility ?act ?utility-act))) constraints: (and (option ?act) (not-salient ?hearer (utility ?act ?utility-act))) contributor: (say ?speaker ?hearer (utility ?act ?utility-act)) core: (propose ?speaker ?hearer ?act) Figure 12: The Proposal plan operator for an Explicit-Warrant Agent that a warrant for an intention is a reason for adopting the intention, and here warrants are the score propositions that give the utility of the proposal, which are mutually believed at the outset of the dialogues. In 15, the warrant IRU in 15-1 contributes to the proposal (core act) in 15-2.
(propose agent-iei agent-iei2 option-2: put-act (agent-iei green rug room-1)) The plan operator in figure 12 specifies that an effect of using this plan is that the utility of the proposal option is salient. Since warrants are used by the other agent in deliberation, the Explicit-Warrant strategy can save the other agent the processing involved with determining which facts are relevant for deliberation and retrieving them from memory. A constraint on using the Explicit-Warrant plan operator is that the utility of the proposal act is not already salient.
In the experiments below, agents are parameterized to use this strategy consistently, with the result that an agent using the Explicit-Warrant strategy assumes that the warrant is never salient for the hearer. See [Jordan and Walker, 1995] for experiments in which an agent attempts to maintain a dynamic model of what is salient for the other agent. The Explicit-Warrant strategy also occurs in natural dialogues as shown in the naturally occurring example in dialogue 9b.
This strategy can be used by agents in any of the Design-World tasks discussed in section 4.4. The Explicit Warrant strategy provides a test of hypothesis A1: agents produce Attention IRUs to support the processes of deliberating beliefs and intentions. It can also be used to test hypothesis A4: the choice to produce an Attention IRU is related to the degree to which an agent is resource limited in attentional capacity. In the Standard task this is predicted to improve the performance of resource limited agents. In the Zero-NonMatching beliefs task this strategy should increase the likelihood that agents coordinate their beliefs about the warrants underlying different plan steps.
(propose agent-imi2 agent-imi option-80: put-act (agent-imi2 purple rug room-2)) The statement in 16-6 is an IRU, because it realizes information previously inferred by both agents, and models the IRU in dialogue 11. Matched-Pair-Inference-Explicit is the variation discussed in section 1 in choice 4. This strategy is only intended to be used in the Matched-Pair tasks as a way of testing hypothesis A2, the discourse inference constraint. As figure 13 shows, a constraint on using this plan is that the speaking agent has inferred a Matched-Pair for the option being proposed.
Although this strategy is specifically tied to Matched-Pair inferences, it provides a test of a general strategy for making premises for inferences salient, in tasks that are inferentially complex, and which also require agents to remain coordinated on inferences. For example, to generalize this strategy to other cases of plan-related inferences, the clauses for (Matched-Pair ?act1 ?act2) could be replaced with the more general (Generates ?act1 ∧ ?act2 ?act3), where the generates relation is to be inferred , Di Eugenio, 1993.
Note that the effect of using this strategy is not that the hearer makes the matched pair inference, rather the effect is that the premise for the desired inference is salient. A constraint on using this strategy is that this premise is not already salient. However, agents parameterized with this strategy always assume that the premise is not salient for the hearer. See [Jordan and Walker, 1995] for experiments in which agents attempt to maintain a dynamic model of the other agent's attentional state.

Plan Evaluation
Section 3.3 specified a model of how collaborative plans are evaluated in terms of quality of solution and collaborative effort. Design-World is constructed in order to be able to measure the quality of a solution as well as collaborative effort. Section 4.4 defined quality of solution for all of the Design-World tasks. We want to examine trade-offs in performance between strategy choices.
It is obvious that these trade-offs can be related to the relative contributions of total cost of communication versus the total cost of inference versus the total  Figure 15: Performance distributions showing the effect of increased retrieval cost for each awm range for dialogues between two All-Implicit Agents. The three performance distributions are for low, mid and high awm agents. retcost = .001 cost of retrieval for both agents' collaborative effort. Thus, to calculate collaborative effort, we cannot simply add up the number of retrievals, inferences and messages. Consider that a Consequence IRU that makes an inference explicit ensures that an inferred belief becomes part of the discourse model. However, if the inference would have been made anyway, the benefit of the strategy is dependent upon whether the effort to make the inference without the consequence IRU would have been greater than the cost of processing the extra utterance of the Consequence IRU. A similar argument holds for the potential benefit of Attention IRUs. Whenever an Attention IRU reduces overall effort for retrieval while not increasing communication effort to the same degree, it will be beneficial. This hypothesis is given below in a general form.
HYPOTH-I1: Strategies that reduce collaborative effort without affecting quality of solution are beneficial.
This hypothesis follows directly from the definition of performance repeated here for convenience from section 3.3:

performance = quality of solution -collaborative effort
We need to introduce parameters for the effort involved with each of the component processes because they are not strictly comparable, and because these modules are implementation dependent. Thus agents' retrieval, inference and communicative costs are parameterized by (1) commcost: cost of sending a message; (2) infcost: cost of inference; and (3) retcost: cost of retrieval from memory. Collaborative effort is then defined as: collaborative effort = (commcost × total messages for both agents) + (infcost × total inferences for both agents) + (retcost × total retrievals for both agents) We will use these cost parameters to explore three extremes in this space: (1) when processing is free; (2) when retrieval effort dominates other processing costs; and (3) when communication effort dominates other processing costs. The parameters support modeling various instantiations of the agent architecture given in figure 3. For example, varying the cost of retrieval models different assumptions about how the beliefs database, plan library and working memory are implemented. Varying the cost of communication models situations in which communication planning is very costly. The relation between the values of these parameters and the utilities of the steps in the plan determines experimental outcomes, rather than the absolute values.
As an example of the effect of varying these costs, consider the plots of performance distributions shown in figures 14 and 15 for low, mid and high awm. In these figures, performance is plotted on the x-axis and number of simulations at that performance level are given by bars on the y-axis. The performance distributions in figure 14 demonstrate the increase in quality of solution that we would expect with increases in awm, given no processing costs. 17 Figure 15 shows what happens when processing is not free: here a retrieval cost of .001 means that every memory access reduces quality of solution by 1/1000 of a point (remember that the utilities of plan steps range between 10 and 56). As figure 15 shows, the ability to access the whole beliefs database in reasoning does not always improve performance since high awm agents perform similarly to mid awm agents.

Summary: Mapping from Naturally Occurring Data to Design World Experiments
Section 2 proposed hypotheses about the function of IRUs in human to human collaborative planning dialogues, and then section 3 presented a model for collaborative planning dialogues based on the observations in section 2. Section 4 then described Design-World as a testbed of the model, and sections 4.4 and 4.5 introduced a number of parameters of the testbed that are intended to model 17 These distributions approximate Beta distributions [Wilks, 1962], and this approximation was used to determine that 200 runs would guarantee stable results. The Beta distribution with the largest variance, for parameters R and S greater than or equal to 1, is the uniform distribution. This largest variance distribution would require approximately 133 samples [Siegel, 1956, Wilks, 1962]. An empirical evaluation of the adequacy of this sample size for three different strategies was tested to see if any differences showed up in alternate runs of 100; no differences were found. the features of the human-human dialogues and support testing of the hypotheses. Here I wish to summarize the mapping between the naturally occurring dialogues and the design of the testbed in order to clarify the basis for the experiments in the next section.
The testbed and the experimental parameters are based on the following mapping between human-human collaborative planning dialogues and the testbed. First, the planning and deliberation aspects of human processing are modeled with the IRMA architecture, and resource limits on these processes are modeled by extending the IRMA architecture with a model of Attention/Working Memory (awm) which has been shown to model a limited but critical set of properties of human processing. Second, the processing of dialogue is tied to the agent architecture. Third, the mapping of a warrant relation between an act and a belief in naturally occurring examples such as 9b is modeled with a warrant relation between an act and a belief in Design-World as seen in the Explicit-Warrant communication strategy in section 4.5. Fourth, the mapping assumes that arbitrary content based inferences in natural dialogues such as that discussed in relation to example 11 can be mapped to content based inferences in Design-World such as those required for doing well on the Matched-Pair tasks. Fifth, the mapping is based on the assumption that task difficulty in naturally occurring tasks such as those in the financial advice domain can be related to three abstract features: (1) inferential complexity as measured by the number of premise required for making an inferences; (2) degree of belief coordination required on intentions, inferences and beliefs underlying a plan; and (3) task determinacy and fault tolerance. Finally the mapping assumes that it is reasonable to evaluate the performance of the agents in collaborative planning dialogues by using domain plan utility for a measure of the quality of solution and defining the cost to achieve that solution as collaborative effort, appropriately parameterized.
The details of this mapping specifies how the testbed implements the model of collaborative planning and provides the basis for extrapolating from the testbed experimental results to the human-human dialogues that are being modeled. The testbed provides an excellent environment for testing the hypotheses to the extent that the model captures critical aspects of human-human dialogues.

Statistically Evaluating Performance
The experiments examine the interaction between tasks, communication strategies and awm resource limits. Every experiment varies awm over three ranges: low, mid, and high. In order to run an experiment on a particular communicative strategy for a particular task, 200 dialogues for each awm range are simulated. Because the awm model is probabilistic, each dialogue simulation has a different result. The awm parameter yields a performance distribution for very resource limited agents (low), agents hypothesized to be similar to human agents (mid), and resource unlimited agents (high). Sample performance distributions for quality of solution (with no collaborative effort subtracted) from runs of two All-Implicit agents for each awm setting are shown in figure  14.
To test our hypotheses, we want to compare the performance of two different communicative strategies for a particular task, under different asssumptions about resource limits and processing costs. To see the effect of communicative strategy and awm over the whole range of awm settings, we first run a two-way analysis of variance (anova) with awm as one factor and communication strategy as another. 18 The anova tells us whether: (1) awm alone is a significant factor in predicting performance; (2) communication strategy alone is a significant factor in predicting performance; and (3) whether there is an interaction between communication strategy and awm.
However, anova alone does not enable us to determine the particular awm range at which a communication strategy aids or hinders performance, and many of the hypotheses about the benefits of particular communication strategies are specific to how resource limited an agent is. Furthermore, whenever strategy affects performance positively for one value of awm and negatively for another value of awm, the potential effects of strategy cannot be seen from the anova alone. Therefore, we conduct planned comparisons of strategies using the modified Bonferroni test (hereafter MB) [Keppel, 1982], within each awm range setting to determine which awm range the strategy affects , Keppel, 1982. 19 On the basis of these comparisons we can say whether a strategy is beneficial for a particular task for a particular awm range.
A strategy A is beneficial as compared to a strategy B, for a particular awm range, in the same task situation, with the same cost settings, if the mean of A is significantly greater than the mean of B, according to the modified Bonferroni test (MB) test.

The converse of beneficial is detrimental:
A strategy A is detrimental as compared to a strategy B, for a particular awm range, in the same task situation, with the same cost settings, if the mean of A is significantly less than the mean of B, according to the modified Bonferroni test (MB) test.
Strategies need not be either beneficial or detrimental, there may be no difference between two strategies. Also with the definition given above a strategy may be both beneficial and detrimental depending on the range of awm that the two strategies are compared over, i.e. A strategy may be beneficial for low awm agents and detrimental for high awm agents.
A difference plot such as that in figure 16 is used to summarize a comparison of two strategies, strategy 1 and strategy 2. In the comparisons below, strategy 1 is either Close-Consequence, 20 Explicit-Warrant, or Matched-Pair-Inference-Explicit and strategy 2 is the All-Implicit strategy. Differences in performance means between two strategies are plotted on the Y-axis against awm ranges on the X-axis. Each point in the plot represents the difference in the means of 200 runs of each strategy at a particular awm range. These plots summarize the information from 1200 simulated dialogues.   Figure 17: Explicit-Warrant is beneficial for mid and high awm agents when Retrieval dominates processing costs: Strategy 1 is two Explicit-Warrant agents and strategy 2 is two All-Implicit agents: Task = Standard, commcost = 1, infcost = 1, retcost = .01

Standard Task
Remember that the Standard task is defined so that the quality of solution that agents achieve for a design-house plan, constructed via the dialogue, is  Figure 18: Explicit-Warrant is detrimental for low and high awm agents when communication effort is high: Strategy 1 is two Explicit-Warrant agents and strategy 2 is two All-Implicit agents: Task = Standard, commcost = 10, infcost = 0, retcost = 0 the sum of the utilities of each valid step in their plan. The task has multiple correct solutions and is fault tolerant because the point values for invalid steps in the plan are simply subtracted from the score, with the effect that agents are not heavily penalized for making mistakes. Furthermore, the task has low inferential complexity: the only inferences agents are required to make are those for deliberation and means-end reasoning. In both of these cases, to make these inferences, agents are only required to access a single minor premise All-Implicit agents do fairly well at the Standard task, under assumptions that all processing is free, as shown in the performance plot in figure 14. However, as retrieval costs increase, high awm agents don't do as well as when retrieval is free, because they expend too much effort on retrieval during collaborative planning. Compare the high awm distribution in figure 14 with that in figure 15. Thus for the Standard task, high awm agents have the potential to benefit from communication strategies that reduce the total effort for retrieval, when retrieval is not free. In addition, although the task has minimal inferential complexity, easy access to information that is used for deliberation, which the Explicit-Warrant strategy provides, could benefit low awm agents, since they might otherwise make nonoptimal decisions. Furthermore, although the task is fault tolerant, agents are still penalized for making errors since errors do not consame over different samples, however anova is robust against the violation of these assumptions under the conditions in these experiments , Keppel, 1982.
19 According to the modified Bonferroni test, the significant F values for the planned comparisons reported below are 3.88 for a p < .05, 5.06 for a p < .025, 6.66 for a p < .01, and 9.61 for a p < .002. 20 In experiments with Close-Consequence only one agent in a dialogue uses the Close-Consequence strategy because the use of this strategy is constrained to when the dialogue segment is open. See figure 11. Since only one agent will ever produce a closing statement for any dialogue segment, only one agent is given the option in the simulations. tribute to performance. Thus for the Standard task, communication strategies such as Close-Consequence that can reduce the number of errors could be beneficial. Below we will compare the All-Implicit strategy to the Explicit-Warrant strategy and the Close-Consequence strategy.

Explicit-Warrant
The Explicit-Warrant strategy can be used in the Standard task to test hypothesis A1: agents produce Attention IRUs to support the processes of deliberating beliefs and intentions. It can also be used to test hypothesis A4: the choice to produce an Attention IRU is related to the degree to which an agent is resource limited in attentional capacity. Thus one prediction is that the Explicit-Warrant strategy will result in higher performance for low awm agents even when processing is free by ensuring that they can access the warrant and use it in deliberation, thus making better decisions. Figure 16 plots the differences in the performance means between the Explicit-Warrant strategy and the All-Implicit strategy for low, mid and high awm agents. A two-way anova exploring the effect of awm and the Explicit-Warrant strategy for the Standard task shows that awm has a large effect on performance (F= 336.63, p< .000001). There is no main effect for communicative strategy (F = 1.92, p < 0.16). However, there is an interaction between awm and communicative choice (F=1136.34, p< .000001).
By comparing performance within a particular awm range for each strategy we can see which awm settings interact with communicative strategy. The planned comparisons using the Modified Bonferonni (mb) test show that the Explicit-Warrant strategy is neither beneficial nor detrimental in the Standard task, in comparison with the All-Implicit strategy, if all processing is free (mb(low) = 0.29, ns; mb(mid) = 2.79, ns; mb(high) = 0.39, ns). Note that there is a trend towards the Explicit-Warrant strategy being detrimental at mid awm.
The hypothesis based on the corpus analysis was that low awm agents might benefit from communicative strategies that include IRUs. However, this hypothesis is disconfirmed. Further analysis of this result suggests a hypothesis not apparent from the corpus analysis: any beneficial effect of an IRU can be cancelled for resource limited agents because IRUs may displace other information from working memory that is more useful. In this case, despite the fact that the warrant information is useful for deliberation, making the warrant salient displaces information that can be used to generate other options. When agents are very resource-limited making an optimal decision is not as important as being able to generate multiple options.
The Explicit-Warrant strategy can also be used in the Standard task to test hypothesis I1: strategies that reduce collaborative effort overall may be beneficial. Thus, another prediction is that by providing the warrant used in deliberating a proposal with every proposal, the Explicit-Warrant strategy has the potential to reduce resource consumption when accessing memory has some processing cost. Figure 17 plots the differences in the performance means between the Explicit-Warrant strategy and the All-Implicit strategy for low, mid and high awm agents when retrieval effort dominates processing. A two-way anova exploring the effect of awm and the Explicit-Warrant strategy for the Standard task, when retrieval cost dominates processing, shows that awm has a large effect on performance (F= 330.15, p< .000001). There is also a main effect for communicative strategy (F = 5.74, p < 0.01), and an interaction between awm and communicative choice (F= 1077.64, p< .000001).
The planned comparisons using the MB test to compare performance at each awm range show that, in the Standard task, in comparison with the All-Implicit strategy, the Explicit-Warrant strategy is neither beneficial nor detrimental for low awm agents (mb(low) = 0.27, ns). However, hypothesis I1 is confirmed because the Explicit-Warrant strategy is beneficial for mid awm agents mb(mid) = 86.43, p< .002. The Explicit-Warrant strategy also tends towards improving performance for high awm agents mb(high) = 2.07, p < .10). For higher awm values, this trend is because the beliefs necessary for deliberating the proposal are made available in the current context with each proposal, so that agents don't have to search memory for them.
As an additional test of hypothesis I1, a final experiment tests the Explicit-Warrant strategy against the All-Implicit strategy in a situation where the cost of communication dominates other processing costs. Figure 18 plots the differences in the performance means between the Explicit-Warrant strategy and the All-Implicit strategy for low, mid and high awm agents when communication effort dominates processing. A two-way anova exploring the effect of awm and the Explicit-Warrant strategy for the Standard task, when communication effort dominates processing, shows that awm has a large effect on performance (F= 409.52, p< .000001). There is also a main effect for communicative strategy (F = 28.12, p < 0.000001), and an interaction between awm and communicative choice (F= 960.24, p< .000001).
The planned comparisons using the MB test to compare performance at each awm range show that in this situation, when communication effort dominates processing, the Explicit-Warrant strategy is neither beneficial nor detrimental for mid awm agents (mb(mid) = 0.12, ns. However, the Explicit-Warrant strategy is detrimental for both low and high awm agents, mb(low) = 7.69, p< .01; mb(high) = 39.65, p < .01). Since this strategy includes an extra utterance with every proposal and provides no clear benefits, it is detrimental to performance in the Standard task when communication effort dominates processing. Below, when we compare this situation with that in the Zero-NonMatching-Beliefs task, we will see that this is due to the fact that the Standard task has low coordination requirements.

Close-Consequence
The Close-Consequence strategy of making inferences explicit can be used in the Standard task to test hypothesis C4: the choice to produce a Consequence IRU is related to a measure of 'how important' the inference is. Even though the Standard task is fault tolerant, every invalid step reduces the quality of solution of the final plan. Making act-effect inferences explicit decreases the likelihood of making this kind of error.
The difference plot in figure 19 plots performance differences between the Close-Consequence strategy and the All-Implicit strategy, in the Standard task, when all processing is free. A two-way anova exploring the effect of awm and the Close-Consequence strategy in this situation shows that awm has a large effect on performance (F= 249.20, p< .000001), and that there is an interaction between awm and communicative choice (F= 919.27, p< .000001).
Planned comparisons between strategies for each awm range shows that the Close-Consequence strategy is detrimental in comparison with All-Implicit for low awm agents (mb(low) = 8.70, p < .01). This is because generating options contributes more to performance for agents with low awm than avoiding errors, and the additional utterances that make inferences explicit in the Close-Consequence strategy has the effect of displacing facts that could be used in means end reasoning to generate options. There is no difference in performance for mid awm agents (mb(mid) = .439, ns).
However, comparisons between the two strategies for high awm agents  Figure 19: Close-Consequence can be detrimental in the Standard Task for low awm agents and beneficial for high awm agents. Strategy 1 is the combination of an All-Implicit agent with a Close-Consequence agent and Strategy 2 is two All-Implicit agents, Task = Standard, commcost = 0, infcost = 0, retcost = 0 shows that the Close-Consequence strategy is beneficial in comparison with All-Implicit (mb(high) = 171.71, p < .002). See figure 19. This is because the belief deliberation algorithm increases the probability of high awm agents choosing to believe out of date beliefs about the state of the world. The result is that they are more likely to have invalid steps in their plans. Thus the Close-Consequence strategy is beneficial because reinforcing the belief that a furniture item has been used makes it less likely that agents will believe that they still have that furniture item. This result is not predicted by any hypotheses, but as discussed in section 4.3, this property of the belief deliberation mechanism has some intuitive appeal. In any case, this result provides a data point for the benefit of a strategy for making inferences explicit when the probability of making an error increases if that inference is not made.

Zero NonMatching Beliefs Task
Remember that the Zero-Nonmatching-Beliefs task requires a greater degree of belief coordination by requiring agents to agree on the beliefs underlying deliberation (warrants). 21 Thus, it it increases the importance of making particular deliberation-based inferences, and can therefore be used to test hypotheses A1, A4 and A5. Below we will compare the performance of agents using the All-Implicit strategy with the Explicit-Warrant strategy in the Zero-NonMatching-Beliefs task. Figure 20 plots the mean performance differences of the Explicit-Warrant   Figure 21: Explicit-Warrant is beneficial for Zero-NonMatching-Beliefs Task, for low and mid awm agents, even when communication cost dominates processing: Strategy 1 is two Explicit-Warrant agents and strategy 2 is two All-Implicit agents: Task = Zero-Nonmatching-Beliefs, commcost = 10, infcost = 0, retcost = 0 strategy and the All-Implicit strategy in the Zero-NonMatching-Beliefs task. A two-way anova exploring the effect of awm and communicative strategy for the Zero-NonMatching-Beliefs task, shows that awm has a large effect on performance (F= 471.42, p< .000001). There is also a main effect for communicative strategy (F = 379.74, p < 0.000001), and an interaction between awm and communicative choice (F= 669.24, p< .000001).
Comparisons within each awm range of the two communicative strategies in this task shows that the Explicit-Warrant strategy is highly beneficial for low and mid awm agents (mb(low) = 260.6, p < 0.002; mb(mid) = 195.5, p < 0.002). The strategy is also beneficial for high awm agents mb(high) = 4.48, p < 0.05). When agents are resource limited, they may fail to access a warrant. The Explicit-Warrant strategy guarantees that the agents always can access the warrant for the option under discussion. Thus, even agents with higher values of awm can benefit from this strategy, since the task requires such a high degree of belief coordination.
Hypothesis I1 can also be tested in this task. We can ask whether it is possible to drive the total effort for communication high enough to make it inefficient to choose the Explicit-Warrant strategy over All-Implicit. However, the benefits of the Explicit-Warrant strategy for low and mid awm agents for this task are so strong that they cannot be reduced even when communication cost is high (mb(low) = 246.4, p < 0.002; mb(mid) = 242.7, p < 0.002). See figure 21. In other words, even when every extra warrant message increases collaborative effort by 10 and reduces performance by 10, if the task is Zero-NonMatching-Beliefs, resource-limited agents using Explicit-Warrant do better. Contrast figure 21 with the Standard task and same cost parameters in figure  18.
However, when communication cost is high, the strategy becomes detrimental for high awm agents (mb(high) = 7.56, p < 0.01). These agents can usually access warrants and the increase in belief coordination afforded by the Explicit-Warrant strategy does not offset the high communication cost.

Inferential Tasks: Matched pairs
The two versions of the Matched-Pair tasks described in section 4.4 (1) increase the inferential complexity of the task and (2) increase the degree of belief coordination required by requiring agents to be coordinated on inferences that follow from intentions that have been explicitly agreed upon. Both tasks increases inferential difficulty to a small degree: All-Implicit agents do fairly well at making matched pair inferences. The Matched-Pair-Same-Room task requires the same inferences as the Matched-Pair-Two-Room task, but these inferences should be easier to make in the Matched-Pair-Same-Room since the inferential premises are more likely to be salient.
The Matched-Pair tasks provide an environment for testing hypotheses A2, A3, A4 and A5. The Attention strategy that is used to test these hypotheses is the Matched-Pair-Inference-Explicit strategy; this strategy makes the premises for matched-pair inferences salient, thus increasing the likelihood of agents making matched-pair inferences. The predictions are that this strategy should be beneficial for low and possibly for mid awm agents, but that high awm agents can access the necessary inferential premises without Attention IRUs. Furthermore, we predict that the beneficial effect should be stronger for the Matched-Pair-Two-Room task. Figure 22 plots the performance differences between All-Implicit agents and Matched-Pair-Inference-Explicit agents for the Matched-Pair-Same-Room task.    Comparisons within awm ranges between agents using the All-Implicit strategy and agents using the Matched-Pair-Inference-Explicit strategy in the Matched-Pair-Same-Room task (figure 22) shows that Matched-Pair-Inference-Explicit strategy is beneficial for low awm agents (mb(low) = 4.47, p < .05), but not significantly different for either mid or high awm agents). In the Matched-Pair-Same-Room task the content of the IRU was recently inferred and is likely to still be salient, thus the beneficial effect is relatively small and is restricted to very resource limited agents.
In contrast, in the Matched-Pair-Two-Room task, the effect on performance of the Matched-Pair-Inference-Explicit strategy is much larger, as we predicted. Figure 23 plots the mean performance differences of agents using the Matched-Pair-Inference-Explicit strategy and those using the All-Implicit strategy. The All-Implicit agents do not manage to achieve the same levels of mutual inference as Matched-Pair-Inference-Explicit agents. A two-way anova exploring the effect of awm and communicative strategy in this task, shows that awm has a large effect on performance (F= 171.79, p< .000001). There is a main effect for communicative strategy (F = 57.12, p < .001), and an interaction between awm and communicative choice (F= 567.34, p< .000001).
Comparisons within awm ranges between agents using the All-Implicit strategy and agents using the Matched-Pair-Inference-Explicit strategy in the Matched-Pair-Two-Room task (figure 23) shows that Matched-Pair-Inference-Explicit strategy is beneficial for low, mid and high awm agents (mb(low) = 21.94, p < .01); mb(mid) = 7.71, p < .01); mb(high) = 38.85, p < .002). In other words, this strategy is highly effective in increasing the ability of low, mid and high awm agents to make matched pair inferences in the Matched-Pair-Two-Room task.
We predicted the strategy to be beneficial for low and possibly for mid awm agents because it gives agents access to premises for inferences which they would otherwise be unable to access. This confirms the effect of the hypothesized discourse inference constraint. However, we did not expect it to be beneficial for high awm agents. This surprising effect is due to the fact that, in the case of higher awm values, the Matched-Pair-Inference-Explicit strategy keeps the agents coordinated on which inference the proposing agent intended in a situation in which multiple inferences are possible. In other words, when agents have high awm they can make divergent inferences, and a strategy of making inferential premises salient improves agents' inferential coordination. Thus the strategy controls inferential processes in a way that was not predicted based on the corpus analysis alone.
Hypothesis I1 can also be tested in this task. We can ask whether it is possible to drive the effort for communication high enough to make it inefficient to choose the Matched-Pair-Inference-Explicit strategy over All-Implicit. Figure 24 plots the mean performance differences between these two strategies when communication cost is high. Comparisons within each awm range shows that this strategy is still beneficial for low, mid and high awm agents even with a high communication cost (mb(low) = 19.10, p < .01); mb(mid) = 3.94, p < .05); mb(high) = 10.46, p < .01). In other words it would be difficult to find a task situation that required coordinating on inference in which this strategy was not beneficial. This result is strong support for the discourse inference constraint, which may explain the prevalence of this strategy in naturally occurring dialogues [Sadock, 1978, Webber and Joshi, 1982, Cohen, 1987,

Zero Invalids Task
Remember that the Zero-Invalids Task is a fault-intolerant version of the task in which any invalid intention invalidates the whole plan. Thus the Zero-Invalids task provides an environment for testing hypotheses C2 and C4 with respect to the inferences made explicit by the Close-Consequence strategy. Figure 25 plots the mean performance differences between agents using the Close-Consequence strategy and agents using the All-Implicit strategy in the Zero-Invalids task. A two-way anova exploring the effect of awm and communicative strategy in this task, shows that awm has a large effect on performance (F= 223.14, p< .000001). There is a main effect for communicative strategy (F = 75.81, p < .001), and an interaction between awm and communicative choice (F= 103.38, p< .000001).
The Close-Consequence strategy was detrimental in the Standard task for low awm agents. Comparisons within awm ranges between agents using the All-Implicit strategy and agents using the Close-Consequence strategy in the Zero-Invalids task shows that there are no differences in performance for low awm agents in the fault-intolerant Zero-Invalids task (mb(low) = 3.64, ns). However, the Close-Consequence strategy is beneficial for mid and high awm agents (mb(mid) = 26.62, p < .002); mb(high) = 267.72, p < .002). In other words, this strategy is highly beneficial in increasing the robustness of the planning process by decreasing the frequency with which agents make mistakes. This is a direct result of rehearsing the act-effect inferences, making it unlikely that attention-limited agents will forget these important inferences.

Figure 25
: Close Consequence is beneficial for the Zero-Invalids Task for mid and high awm agents. Strategy 1 is the combination of an All-Implicit agent with a Close-Consequence agent and Strategy 2 is two All-Implicit agents, Task = Zero-Invalid, commcost = 0, infcost = 0, retcost = 0

Discussion
This paper showed how agents' choice in communicative action can be designed to mitigate the effect of their resource limits in the context of particular features of a collaborative planning task. In section 3, I presented a model of collaborative planning in dialogue and discussed a number of parameters that can affect either the efficacy of the final plan or the efficiency of the collaborative planning process. Then in section 5, I presented the results of experiments testing hypotheses about the effects of these parameters on collaborative planning dialogues. These results contribute to the development of the model of collaborative planning dialogue presented here. In addition, since the testbed implementation is compatible with many current theories, these results could be easily incorporated into other dialogue planning algorithms [Logan et al., 1994, Grosz and Sidner, 1990, Levesque et al., 1990, Grosz and Kraus, 1993, Chu-Carrol and Carberry, 1995, inter alia. A secondary goal of this paper was to argue for a particular methodology for dialogue theory development. The method was specified in section 4.1. The Design-World testbed was introduced in section 4 and sections 4.4 and 4.5 described the parameterizations of the model that support testing the hypotheses. Four parameters for communicative strategies were tested: (1) All-Implicit; (2) Close-Consequence; (3) Explicit-Warrant; and (4) Matched-Pair-Inference-Explicit. Four parameters for tasks were tested: (1) Standard; (2) Zero-Nonmatching-Beliefs; (3) Matched-Pair (MP); (4) Zero-Invalid. Three situations of varying processing effort were tested.
In this section, I will first summarize the hypotheses and the experimental results in section 6.1, then I will discuss how the experimental results might generalize to situations not implemented in the testbed. Section 6.4 proposes future work and section 6.5 consists of concluding remarks.

Summary of Results
The hypotheses that were generated by the statistical analysis of the dialogue corpora are repeated below for convenience from sections 2 and 4.6.
• HYPOTH-C1: Agents produce Consequence IRUs to demonstrate that they made the inference that is made explicit.
• HYPOTH-C2: Agents choose to produce Consequence IRUs to ensure that the other agent has access to inferrable information.
• HYPOTH-C3: The choice to produce a Consequence IRU is directly related to a measure of 'how hard' the inference is.
• HYPOTH-C4: The choice to produce a Consequence IRU is directly related to a measure of 'how important' the inference is.
• HYPOTH-C5: The choice to produce a Consequence IRU is directly related to the degree to which the task requires agents to be coordinated on the inferences that they have made.
• HYPOTH-A1: Agents produce Attention IRUs to support the processes of deliberating beliefs and intentions.
• HYPOTH-A2: There is a discourse inference constraint whose effect is that inferences in dialogue are derived from propositions that are currently discourse salient (in working memory).
• HYPOTH-A3: The choice to produce an Attention IRU is related to the degree of inferential complexity of a task as measured by the number of premises required to make task related inferences.
• HYPOTH-A4: The choice to produce an Attention IRU is related to the degree to which an agent is resource limited in attentional capacity.
• HYPOTH-A5: The choice to produce an Attention IRU is related to the degree to which the task requires agents to be coordinated on the inferences that they have made.
• HYPOTH-I1: Strategies that reduce collaborative effort without affecting quality of solution are beneficial.
Below I will summarize the experimental results reported in section 5 with respect to the hypotheses above.
Hypotheses C3 and C4 were tested by comparing the Close-Consequence strategy with the All-Implicit strategy in the Standard task. In this experimental setup, the inference made explicit by the Consequence IRU was neither hard to make nor critical for performance. Hypothesis C3 was only weakly tested by the experiments because agents always make this inference. The results in figure 19 show that the Close-Consequence strategy is detrimental for low awm agents. This is because IRUs can displace useful information from working memory and because the inference made explicit with this IRU is not 'hard enough'.
The Standard task also provides a weak test of hypothesis C4. The fact that the Standard task is fault tolerant means that making the inference is not as critical as it might be. However, errors can results from either not making the inference or forgetting it once it is made. At lower values of awm, the probability of such errors is not that high. However, the results shown in figure  19 show that the probability of error is higher for high awm agents in this case, because of their belief deliberation algorithm, and thus the Close-consequence strategy is beneficial for high awm agents, even in the Standard task. The Zero-Invalids task provides another test of hypothesis C4 by increasing the importance of the inference made explicit by the Close-consequence strategy. Figure 25 shows that hypothesis C4 is confirmed because the Close-Consequence strategy is beneficial for low, mid and high awm agents. In addition to the reasons discussed for the Standard task, this strategy is beneficial for high awm agents because they have more potential to improve their scores by ensuring that they don't make errors.
The experiments did not test hypothesis C1 because agents in the testbed are not designed to actively monitor evidence from other agents as to what inferences they might have made. Hypothesis C5 was not tested by the experiments because agents always rectify the situation if they detect a discrepancy in beliefs about act effect inferences: they reject proposals whose preconditions do not hold.
Hypotheses A1, A4 and A5 were tested by experiments in which the Explicit-Warrant strategy was compared with the All-Implicit strategy in the Standard task. Hypothesis A1 is disconfirmed for low awm agents. Figure 16 shows that the Explicit-Warrant strategy is neither beneficial nor detrimental for low awm agents for the Standard task, when processing is free. This counterintuitive result arises because, when agents are highly resource limited, IRUs can displace other information that is more useful.
To test hypothesis I1 in this situation, we also examined two situations where processing is not free. When communication cost dominates other processing costs, the Explicit Warrant strategy is detrimental for low and high awm agents. However, when retrieval cost dominates other processing costs, the Explicit Warrant strategy is beneficial for mid awm agents and there is a trend toward a beneficial effect for high awm agents. Thus these two situations show that hypothesis I1 is confirmed: processing effort has a major effect on whether a strategy is beneficial.
We also tested hypotheses A1, A4 and A5 with experiments in which the Explicit-Warrant strategy was compared with the All-Implicit strategy in the Zero-Nonmatching-Beliefs task (see figures 20 and 21). This task increases the importance of making deliberation based inferences by requiring agents to be coordinated on these inferences in order to do well on the task. In this situation, we saw a very large beneficial effect for the Explicit-Warrant strategy, which is not diminished by increasing communication effort. Thus in situations in which agents are required to be coordinated on these inferences, strategies which include Attention IRUs can be very important.
Hypotheses A2, A3, A4, and A5 were tested by experiments comparing the Matched-Pair-Inference-Explicit strategy with the All-Implicit strategy in the two versions of the Matched-Pair task. The results shown in figures 22 and 23 provide support for these hypotheses. However these results also included an unpredicted benefit of Attention IRUs for inferentially complex tasks where agents must coordinate on inferences. Figure 23 shows that both mid and high awm agents' performance improves with the Matched-Pair-Inference-Explicit strategy. This can be explained by the fact that Attention IRUs increase the likelihood that agents will make the same inference, rather than divergent inferences, when multiple inferences are possible.
Furthermore, although the Matched-Pair-Inference-Explicit strategy is specifically tied to Matched-Pair inferences, it provides a test of a general strategy for making premises for inferences salient, when tasks are inferentially complex and require agents to remain coordinated on inferences. Thus it provides strong support for the discourse inference constraint. To generalize this strategy to other cases of plan-related inferences, the clauses in the strategy plan operator that specifically refer to matched-pair inferences can be replaced with a more general inference, e.g. the more general (Generates ?act1 ∧ ?act2 ?act3), where the generates relation is to be inferred , Grosz and Sidner, 1990, Di Eugenio, 1993.
Hypothesis I1 was tested by examining extremes in cost ratios for retrieval effort and communication effort whenever a hypothesis about the beneficial effects of IRUs was confirmed. Figure 18 shows that high communication effort can make the Explicit-Warrant strategy detrimental in the Standard task. Figure 21 shows that high communication effort does not eliminate the benefits of the Explicit-Warrant strategy in the Zero-Nonmatching-Beliefs task. Figure and  24 shows that high communication effort does not eliminate the benefits of the Matched-Pair-Inference-Explicit strategy in the Matched-Pair-Two-Room task. Thus the strategy of making premises for inferences salient is robust against extremes in processing effort.

Generalizability of the Results
This section addresses concerns raised in [Hanks et al., 1993] that simulation is ' experimentation in the small'. Hanks writes that ([Hanks et al., 1993], section 5.1.5): The ultimate value-arguably the only value -of experimentation is to constrain or otherwise inform the designer of a system that solves interesting problems. In order to do so the experimenter must demonstrate three things: 1. that her results -the relationships she demonstrates between agent characteristics and world characteristics -extend beyond the particular agent, world, and problem specification she studied, 2. that the solution to the problem area she studied in isolation will be applicable when that same problem area is encountered in a larger, more complex world, and 3. that the relationship demonstrated experimentally actually constrains or somehow guides the design of a larger more realistic agent.
The list in 1 to 3 are all different ways of saying that the results should generalize beyond the specifics of the experiment, and this after all is a basic issue with all experimental work. Typically generalizations can be shown by a series of multiple experiments modifying multiple variables as we have done here. For example, the modifications to the task are specifically designed to test whether beneficial communicative strategies generalize across tasks. However, we might also ask to what extent do the variables manipulated in the simulation abstract out key properties of real situations? Below I will briefly discuss why the results presented above are potentially generalizable. I will focus on generalizations along three dimensions: (1) task (or environmental) properties; (2) agent architectural properties; and (3) agent behaviors. These dimensions are the same as those in Cohen's 'ecological triangle' .
Generalizations about tasks The Design-World task was selected as a simple planning task that requires negotiation of each step. The structure of this task is isomorphic to a subcomponent of many collaborative planning tasks. In addition, to test generalizability of hypothesized benefits across tasks, we examined more complex variants of the task by manipulating three abstract features: (1) inferential complexity as measured by the number of premises required for making a task related inference and (2) degree of belief coordination required on intentions, inferences and beliefs underlying a plan; and (3) the task determinacy and fault tolerance of the plan. These general features can certainly be applied to other tasks in other domains. In fact it is difficult to think of a task or domain in which these features could not be applied.
Generalizations about agent properties Design-World agents are artificial agents that are designed to model the resource limited qualities of human agents. The planning and deliberation aspects of human processing are modeled with the IRMA architecture, and resource limits on these processes are modeled by extending the IRMA architecture with a model of Attention/Working Memory (awm) which has been shown to model a limited but critical set of properties of human processing. The way that agents process dialogue is tied to the agent architecture.
The experimental results will extend to dialogues between artificial agents to the extent that those agents exhibit similar cognitive properties. Here, we looked at a resource bound on access to memory as modeled by a size of memory subset limit, however size is directly correlated to time to access memory. Artificial agents are often time limited in rapidly changing worlds, so it seems quite plausible that artificial agents would benefit from similar communicative strategies. For example, I would predict that agents in the Phoenix simulation testbed would benefit from the strategies discussed here . In other work artificial agents do 'make inferences explicit' by communicating to other agents partial computations when the other agent might have been able to make these computations , Durfee et al., 1987, Turner, 1994]. In addition, defining inferential complexity as a direct consequence of the number of premises simultaneously in memory bears a strong resemblance to problems artificial processors have when a computation requires a large working set [Stone, 1987].
The experimental results should extend to dialogues between humans and artificial agents because Design-World agents are designed to model humans. However it may be desirable to change the definition of collaborative effort for modeling human-computer interaction to allow the computer to handle processing that is easy for the computer to do and for the human to handle processing that is easy for the human to do. Furthermore, most of the claims about the awm model are based on a limited set of human working memory properties, and these properties will also hold for other cognitively based architectures such as SOAR .
Generalizations about agent behaviors In this work the agent behaviors that were tested were the agent communication strategies. One reason to believe that the strategies are general to human-human discourse is that they were based on observed strategies in different corpora of natural collaborative planning dialogues. It is possible to find all three types of IRUs in the Trains, Map-Task and Design corpora , Carletta, 1992, Whittaker et al., 1993, as well as in the financial advice domain.
In addition to this empirical evidence, there are further reasons why we might expect generalizations.
The communicative acts and discourse acts used by Design-World agents are similar to those used in [Carletta, 1992, Cawsey et al., 1992, Stein and Thiel, 1993. Thus communicative strategies based on these acts should be implementable in any of these systems.
The experimental results based on these strategies should generalize to other discourse situations because the strategies are based on general relations between utterance acts and underlying processes, such as supporting deliberation and inference. For example, the mapping of a warrant relation between an act and a belief in naturally occurring examples such as 9b was modeled with a warrant relation between an act and a belief in Design-World, as seen in the Explicit-Warrant communication strategy. The claims made about the use of the Explicit-Warrant communication strategy should generalize to any dialogue planning domain where agents use warrants to support deliberation.
Similarly, content based inferences in natural dialogues such as that discussed in relation to example 11 were modeled with content based inferences in Design-World such as those required for doing well on the Matched-Pair tasks. This inferential situation was designed to test the discourse inference constraint, that inferences in dialogue are restricted to premises that are currently salient. Both experimental and corpus based evidence was provided in support of the discourse inference constraint. The claims made about the use of the Matched-Pair-Inference-Explicit communication strategy, based on experimental evidence, should generalize to any dialogue strategy where agents make premises for inferences available, and to any planning domain where agents are required to make content based inferences in support of deliberation or planning.
The evaluation metrics applied to these strategies should also generalize whenever domain plan utility is a reasonable measure of the quality of solution for a dialogue task.
Since the testbed architecture is consistent with that assumed in other work, the experimental results should be generalizable to those frameworks.
The relationship between discourse acts and domain-based options and intentions in this work is based on Litman's model of discourse plans  and is similar to the approach in [Carletta, 1992, Cawsey et al., 1992. The emphasis on autonomy at each stage of the planning process and the belief reasoning mechanism of Design-World agents is based on the theory of belief revision and the multi-agent simulation environment developed in the Automated Librarian project [Galliers, 1989, Galliers, 1991a, Cawsey et al., 1992, Logan et al., 1994.
The Design-World testbed is based on the methods used in the TileWorld and Phoenix simulation environments: rapidly changing robot worlds in which an artificial agent attempts to optimize reasoning and planning [Pollack and Ringuette, 1990, Hanks et al., 1993. TileWorld is a single agent world in which the agent interacts with its environment, rather than with another agent. Design-World uses similar methods to test a theory of the effect of resource limits on communicative behavior between two agents.
Design-World is also based on the method used in Carletta's JAM simulation for the Edinburgh Map-Task [Power, 1974, Carletta, 1992. JAM is based on the Map-Task Dialogue corpus, where the goal of the task is for the planning agent, the instructor, to instruct the reactive agent, the instructee, how to get from one place to another on the map. JAM focuses on efficient strategies for recovery from error and parametrizes agents according to their communicative and error recovery strategies. Given good error recovery strategies, Carletta argues that 'high risk' communicative strategies are more efficient, but did not attempt to quantify efficiency. In contrast, the approach here provides a way of quantifying what is an effective or efficient strategy, and the results suggest that a combination of the agents' resource limitations and the task definition determine when strategies are efficient. Future work could test Carletta's claims about recovery strategies within this extended framework.
To my knowledge, none of this earlier work has considered the factors that affect the range of variation in communicative choice, or the effects of different choices, or measured how communicative choice affects the construction of a collaborative plan and the ability of the conversants to stay coordinated. Nor have other theories of collaborative planning been explicit about the agent architecture, or tested specific ideas about resource bounds in dialogue, and none have used utility as the basis for agents' communicative choice. In addition, no earlier work on cooperative task-oriented dialogue argued that conversational agents' resource limits and task complexity are major factors in determining effective conversational strategies in collaboration.

Future Work
A promising avenue for future work is to investigate beneficial strategies for teams of heterogeneous agents. In the experiments here, pairs of agents in dialogue were always parameterized with the same resource limits. Pilot studies of dialogues between heterogeneous agents suggest that strategies that are not effective for homogeneous agents may be effective for heterogeneous ones. For example, in [Walker, 1993b] I tested an Attention IRU strategy in which agents would tell one another about all the options they knew about at the beginning of planning each room. This strategy is not beneficial for homogeneous agents because IRUs can displace other useful information. However if one agent is not limited, then it can be helpful for the resource limited agent to exploit the capabilities of the more capable agent by telling the other agent important facts before it forgets them.
Another extension would be to extend the agent communication strategies or to test additional ones. For example, other work proposes a number of strategies for information selection and ordering in dialogue and provides some evidence that these strategies are efficient or efficacious [Carenini and Moore, 1993, Suthers, 1993, Zukerman and McConachy, 1993, Chu-Carrol and Carberry, 1995. Support for these claims could be provided by Design-World experiments in which agents used these strategies to communicate.
Future work could also modify the properties of the world or of the task. For example, it would be possible to make Design-World more like Tileworld by making the world change in the course of the task, by adding or removing furniture.
These results may also be incorporated as input into decision algorithms in which agents decide online which strategy to pursue, and investigate additional factors that determine when strategies are effective in collaborative planning dialogues. The results presented here show what information an agent should consider. For example, a comparison between low, mid and high awm agents shows how to design decision algorithms for agents who have to decide whether to expend additional effort.
Another promising avenue is make the agents capable of remembering and learning from past mistakes so that they can adapt their strategies to the situation [Alterman et al., 1991].
Finally, these results should be incorporated into the design of multi-agent problem-solving systems and into systems for human-computer communication, such as those for teaching, advice and explanation, where for example the use of particular strategies might be premised on the abilities of the learner or apprentice.

Concluding Remarks
The goal of this paper was to show how agents' choice in communicative action, their algorithms for language behavior, can be designed to mitigate the effect of their resource limits in the context of particular features of a collaborative planning task. In this paper, I first motivate a number of hypotheses based on a statistical analysis of natural collaborative planning dialogues. Then a functional model of collaborative planning dialogues is developed based on these hypotheses, including parameters that are hypothesized to affect the generalizability of the model. The model is then implemented in a testbed in which these parameters can be varied, and the hypotheses are tested.
The method used here can be contrasted with other work on dialogue modeling. Much previous work on dialogue modeling only carries out part of the process described above: only the initial part of the process up to specifying a functional model is completed. Followon research that is based on these models must judge the model according to subjective criteria such as how well it fits researcher's intuitions or how elegant the model is. The models developed here on the basis of empirical evidence can also be judged according to these subjective criteria, but this work carries out additional steps to further test and refine the model suggested by the corpus analysis. Implementing a model with parameters to test the generalizability of the model and testing hypotheses in a testbed implementation provides a way to check subjective evaluations and suggests many ways in which our initial hypotheses must be refined and further tested.
The Design-World testbed is the first testbed for conversational systems that systematically introduces several different types of independent parameters that are hypothesized to affect the efficacy of a collaborative plan negotiated through a dialogue, and the efficiency of that dialogue process. Experiments in the testbed examined the interaction between (1) agents' resource limits in attentional capacity and inferential capacity; (2) agents' choice in communication; and (3) features of communicative tasks that affect task difficulty such as inferential complexity, degree of belief coordination required, and tolerance for errors. The results verified a number of hypotheses that depended on particular assumptions about agents' resource limits that were not possible to test by corpus analysis alone.
Several unpredicted and counterintuitive results were also demonstrated by the experiments. First, the task property of belief coordination in combination with resource limits (as in the Zero-Nonmatching-Beliefs and Matched-Pair tasks), were shown to produce the most robust benefits for IRUs, rather than resource limits alone as originally hypothesized. Second, I predicted that IRUs would always be beneficial for low awm agents, but found that IRUs can be detrimental for these agents through a side effect of displacing other, more useful, beliefs from working memory. Third, it would seem plausible that high awm agents should always perform better than either low or mid awm agents since these agents always have access to more information. However the results showed that there are two situations in which this is not an advantage: (1) when accessing information has some cost; and (2) when access to multiple beliefs can lead agents to make divergent inferences. In this case, restricting agents to a small shared working set is a natural way to limit inferential processes. This limit intuitively corresponds to potential benefits of limited working memory for humans and explains how humans manage to coordinate on inferences in conversation [Levinson, 1985, Grosz, 1977, Joshi, 1978.
These results clearly demonstrate that factors not previously considered in dialogue models must be taken into account of claims if cooperativity, efficiency, or efficacy are to be supported. In addition, I have shown that a theory of dialogue that includes a model of resource-limited processing can account for both the observed language behavior in human-human dialogue and the experimental results presented here.