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Compositional Mechanisms of Japanese Numeral Classifiers

This paper suggests that Generative Lexicon Theory (Pustejovsky, 1995, 2006, 2011) offers a new analysis of numeral classifiers, focusing on Japanese having various kinds of classifiers. It is often said that classifiers agree with quantified nouns, that is, the nouns have to match the semantic requirements of the classifiers. This paper examines their lexical structures and compositional mechanisms. Though Huang and Ahrens (2003) explain the compositional mechanisms between the classifiers and the quantified nouns using “coercion” instead of the agreement, this paper indicates that other mechanisms including Type Matching (Pustejovsky, 2011) also occur in Japanese depending on the type required by the classifier and the source type of the quantified noun, following Mano and Yonezawa’s (to appear) suggestion.


Introduction
Japanese has various counters, called josuushi in Japanese, including so-called "numeral classifiers (Aikhenvald, 2000)," as well as other East Asian languages such as Chinese, Indonesian, Korean, and Thai. In Japanese, nouns cannot be directly modified by numerals but must be quantified by counters, as shown in (1).
Most of the previous studies on classifiers assume that the modified nouns agree with the classifiers, because the classifiers can only count nouns which have particular meanings. Many studies have been done on the semantic restrictions of numeral classifiers (concerning Japanese, see Matsumoto (1991Matsumoto ( , 1993; Downing (1996), Iida (1999), and Nishimitsu and Mizuguchi (2004).). Huang and Ahrens (2003), however, suggest that the classifiers do not simply agree with the quantified nouns but coerce particular meanings to them, focusing on the numeral classifiers of Mandarin Chinese. This paper shares the view that classifiers can coerce the nouns to refer to particular types, but as Mano and Yonezawa (to appear) point out, it seems that they may agree with the nouns without changing their source types.
There are some contradictory examples in Japanese, however. Taking chuusha 'injection,' for example, which is a polysemous noun that means a physical object 'syringe' and also an event 'injection.' It can be counted by the classifiers, -本 hon and -回 kai. -Hon requires one dimensional (i.e. long and thin) physical objects (phys), and -kai is a classifier for events. Given that classifiers coerce the quantified nouns to be required types, ni-hon-no chuusha (2-CL-GEN injection) should be of type phys meaning 'two syringes,' while nikai-no chuusha should mean an event 'having injection(s) two times.' But that is not the case. The verb, owaru 'end,' is the predicate that selects for event as its complement, so it is predicted that only ni-kai-no chuusha is allowed. In fact, -hon is also allowed as in (2), however, contrary to the coercion analysis.
(2) ni-{hon/kai}-no chuusha-ga owat-ta. 2-CL/CL-GEN injection-NOM end-PST '(I) had {two injections/injection(s) two times}.' With regard to this issue, we examine the lexical structures of Japanese numeral classifiers and the compositional mechanisms more closely. The lexical structures of classifiers are examined in Section 2, and the compositional mechanisms are demonstrated in Section 3. Section 4 shows a conclusion and further issues.

Classifiers and their Lexical Structures
According to Iida (1999), there are about 360 counters in Japanese, and Kageyama et al. (2011) divide them into "numeral classifiers" and "measure specifiers" depending on their functions, which will be shown in 2.1. This paper focuses on only numeral classifiers. Their lexical structures will be examined in 2.2 and 2.3.

Classifiers and Measure Specifiers
Some categorizations of Japanese counters have been proposed (cf. Matsumoto, 1991Matsumoto, , 1993Downing, 1996;Iida, 1999;Nishimitsu and Mizuguchi, 2004). This paper adopts Kageyama et al.'s (2011) categorization, which divides them into "numeral classifiers" and "measure specifiers" according to their functions 3 . Numeral classifiers (classifiers, henceforth) classify and count limited and specific groups of nouns, which means their function is "categorization (cf. Bisang, 1993)" of objects. On the other hand, measure specifiers can be used as measures for a wide variety of nouns as in (4b), and their function is considered to be "individuation (cf. Bisang, 1993)" of objects. Some examples are shown in (3-4) (the simplified semantic restrictions of each classifier are in round brackets 4 .).
(3) a. classifiers: This paper focuses on classifiers because they have more semantic restrictions on the quantified nouns than measure specifiers, which enables us to examine their compositional mechanisms more clearly.

Previous studies on the Lexical Structures of Classifiers
Only a few Generative Lexicon approaches have so far been attempted on classifiers (cf. Bond and Paik, 1997;Huang and Ahrens, 2003;Kageyama et al., 2011;Mano and Yonezawa, to appear), and there seems to be still room for argument. Bond and Paik (1997) propose a basic lexical structure for Japanese sortal classifiers, assuming that the Formal qualia are allowed to take at least two values: a sortal typing of the argument and a feature of dimensionality. (5) is a lexical structure for -個 ko (3D phys). There are two variables in the argument structure: one is a numeral+ (which includes numerals, quantifiers, and interrogatives), and another is a quantified noun. The latter is a default argument, because it is not necessarily expressed overtly in Japanese, as in (6).
(Bond and Paik, 1997) (6) san-ko(-no hako-ga) aru. 3-CL(-GEN box-NOM) be.PRES 'There are three (boxes).' Huang and Ahrens (2003) and Kageyama et al. (2011) develop the idea further and show that classifiers may have some requirements also in the Constitutive, Telic, and Agentive roles in addition to the Formal role. (7) shows some examples of classifiers that have semantic requirements in the qualia structures of their objects pointed out by Kageyama et al. (2011).

Semantic Restrictions by Classifiers
Following these studies, Mano and Yonezawa (to appear) propose more detailed lexical structures for Japanese classifiers. The basic lexical structure of classifiers suggested by them is given in (8). Each classifier is considered to have specifications on the quantified noun, i.e. D-ARG1.
(8) CL -α ARGSTR = ARG1 = x: quantity 5 D-ARG1 = y: entity QUALIA = [FORMAL = quantify (x, y)] (Mano and Yonezawa, to appear) They assume that the most basic type of classifiers is the one that specifies the Formal role of their objects, i.e. (7a). For example, (9) shows the lexical structures of the classifiers for animates, and -kai, a classifier to count events, is also considered to have a similar structure, as in (10) (It should be noted that only the relevant parts of lexical structures are shown in this paper.). We agree with them with regard to this type. Next, we will review other types, (7b-d), which have semantic requirements on the roles other than the Formal role. The lexical structure for -串 kushi, a classifier to count skewered foods, is shown in (11). It requires skewers to be included in the Constitutive role of the objects. They also point out that the Formal, Agentive, and Telic roles are also specified because -kushi counts foods only as shown in (12).
(13) -機 ki ARGSTR=D-ARG1=y: machine QL= FORMAL=machine (y) TELIC=fly (e, y) AGENT=make (e, z, y) (ibid.) (14) san-ki-no {hikooki/*kami-hikooki/*tori} 3-CL-GEN plane/paper-plane/bird 'three planes/paper planes/birds' There are two problems with their analysis, however. One is that the specifications are sometimes redundant (e.g. artifacts must have particular Agentive and/or Telic roles), though it might be true that they have multiple specifications. Another is that they ignore the importance of the Formal role. It should be noted that all Japanese classifiers have particular type requirements on the Formal role of their objects (the animacy is strictly restricted in Japanese classifiers 6 ). In addition to it, note that the Formal role is considered a head type, and the additional qualia values can be seen as structural complementation to it in Pustejovsky (2011Pustejovsky ( :1409. Following Pustejovsky (2011), we suggest the following simplified representations in (15-16) for the lexical requirements of classifiers in order to solve the problems above. These representations are consistent with the characteristics of Japanese classifiers: though some classifiers have multiple requirements, they usually focus on "one" role in addition to the Formal role (cf. (7)).  Huang and Ahrens (2003) analyze the Mandarin classifier system and suggest that classifiers coerce nominal semantic types:

Problems of the Previous Studies
"…classifiers can coerce nouns to have a particular individual reading depending on the information entailed in the classifier itself. The classifier can vary in the Constitutive, Formal, Telic or Agentive roles that it carries (p.361)." The situation in Japanese, however, is considered to be more complex because there are some cases where type coercion does not seem to take place, as pointed out in Section 1. Therefore, we adapt the four mechanisms suggested by Pustejovsky (2011) and show that all of the mechanisms occur when classifiers count nouns in Japanese. Mano and Yonezawa (to appear) also take the same view, but their discussion is limited. Pustejovsky (2011Pustejovsky ( :1411 suggests the following mechanisms in (17) 7 for the selection of an argument, which allow for modulation of types during semantic composition.
(17) a. SELECTION (Type Matching): The target type for a predicate, F, is directly satisfied by the source type of its argument, A: F(A α ) α b. ACCOMMODATION SUBTYPING: The target type a function requires is inherited through the type of argument, A: F(A β ) α , β ⊆ α c. COERCION BY INTRODUCTION: the type a function requires is imposed on the argument type. This is accomplished by wrapping the argument with the type required by the function: F(A α )⊙ σ , α ⊆ β (domain-preserving) F(A α ) β , α→β (domain-shifting) d. COERCION BY EXPLOITATION: the type a function requires is imposed on the argument type. This is accomplished by taking a part of the argument's type to satisfy the function: F(A α⊙τ ) β , τ ⊆ β

Mechanisms
Here we will show that all four mechanisms in (17) are observed when classifiers modify and count nouns in Japanese. What is the most crucial is whether the head type (i.e. the Formal role) of the quantified noun is changed or not. First, Selection (Type Matching: TM) will take place when the type required by a classifier is directly satisfied by the quantified noun. It is predicted that the quantified source noun stays the same type in this case because the operation does not change the type. In (18a), the noun, hito 'human being,' satisfies the type required by the classifier, -nin, because both the source and target types are human (cf. (15a)) 8 . The same is true for (18b), in which both the source and target types are event (cf. (15d)).
(18) a. san-nin-no hito-ga iru. 3-CL-GEN human-NOM be.PRES 'There are three men.' b. san-kai-no ensoo-ga owat-ta. 3-CL-GEN performance-NOM end-PST '(lit.) Three performances were over.' Second, we will show an example of Accommodation Subtyping (AS). As shown in (19), tsubame 'swallow' is counted by both -wa and -hiki. It is assumed that the TM applies when it is quantified by -wa (15c), because the Formal role of tsubame is typed as bird. The AS takes place, however, when it is counted by -hiki (15b), because the type bird is a subtype of the type animal (bird ⊆ animal). Actually, all the nouns counted by -wa can also be counted by -hiki, but not vice versa. type requirement of the classifier mechanism -wa: bird→t TM -hiki: animal→t AS Table 1. Compositional mechanisms of tsubame Third, we will see cases where coercion takes place. Dango 'rice dumpling,' for example, is an artificial type, and its type structure is considered to be "food⊗ T eat." It is not necessarily skewered, but it is interpreted to be skewered when counted by -kushi as in (20). As -kushi is of type "food⊗ C skewer→t" (16a), Coercion by Qualia Introduction (CI-Q) applies to dango, adding the Constitutive value skewer 9 .
Lastly, we will show a case in which Coercion by Introduction (CI) takes place. As shown in (23a), supiichi can also be counted by -mai which selects for a type phys (2D).
2-CL-quantity-GEN '(I) tore two speeches.' The CI is considered to apply to supiichi (e⋅i) here, resulting in the noun being a type phys. This is confirmed in (23a), because it can be the argument of the predicate, yaburu 'tear,' which selects for phys. This is impossible when it is counted by -kai and -hon, as shown in (23b). It follows from what has been shown in this section that all four mechanisms are observed when classifiers select their arguments.

Conclusion
By using the Generative Lexicon Theory, this paper suggests the formalization of semantic requirements of classifiers in Japanese. It is also shown that all four compositional mechanisms in (17) are observed between classifiers and the quantified nouns. It is reasonable to say that the Generative Lexicon approach can propose a new analysis of classifiers.
It needs further investigation, however. As space is limited, we have concentrated on limited classifiers, but the lexical structures of other classifiers should be examined. In addition to this, I have not addressed the issues of the quantifier floating. Their syntactic structures should be more carefully examined.