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Towards Constraints Handling by Conflict Tolerance in Abstract Argumentation Frameworks

In this paper we incorporate integrity constraints in Dung-style abstract argumentation frameworks. We show that even for constraints of a very simple form, standard conflict-free semantics for argumentation frameworks are not adequate as conflicts among arguments should sometimes be accepted and tolerated. For this, we use conflict-tolerant semantics and show how corresponding extensions may be represented in terms of propositional formulas. Introduction and Motivation Dung’s argumentation framework (1995) is a graph-style representation of what may be viewed as a dispute. It is instantiated by a set of abstract objects, called arguments, and a binary relation on this set that intuitively represents attacks between arguments. These structures have been found useful for modeling a range of formalisms for non-monotonic reasoning, including default logic (Reiter 1980), logic programming under stable model semantics (Gelfond and Lifschitz 1988), three-valued stable model semantics (Wu, Caminada, and Gabbay 2009) and well-founded model semantics (van Gelder, Ross, and Schlipf 1991), Nute’s defeasible logic (Governatori et al. 2004), and so on. Despite of their general nature, experience shows that in some cases argumentation frameworks lack sufficient expressivity for accurately capturing their domain, and some extra apparatus is needed to gain a more comprehensive representation. This observation motivated several works, like those of Amgoud and Cayrol (2002) and Modgil (2009), in which meta-knowledge, such as preferences relations among the arguments, is provided for refining the process of selecting the arguments that can collectively be accepted from the argumentation framework at hand. In this paper we formalize the additional knowledge that is linked to argumentation frameworks in terms of integrity constraints, that is, conditions that every accepted set of arguments must satisfy. We show that the satisfaction of such constraints (and even very simple ones) sometimes requires to abandon the conflict-freeness assumption behind standard argumentation semantics, so it might happen that accepted arguments attack each other. Such a case is considered next. Copyright c ⃝ 2013, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Example 1 The phenomena of interference on one hand and the photoelectric effect on the other hand may stand behind conflicting arguments about whether light is a particle or a wave. Any choice between such arguments would obviously be arbitrary, and the dismissal of one of them would unavoidably yield erroneous conclusions about the nature of light. For having a realistic theory it is therefore essential in this case to adopt an attitude that tolerates both conflicting arguments. To be able to capture situations like the one described in the example above we incorporate the conflicting-tolerant semantics described in (Arieli 2012). This also allows us to represent, using propositional languages, different kinds of semantics for argumentation frameworks, augmented with integrity constraints, and compute these semantics by offthe-shelf SAT-solvers. The rest of this paper is organized as follows: First, we review the main definitions pertaining to Dung’s theory of argumentation, then we show how integrity constrains can be added to this theory, and how four-valued labeling in the context of conflict-tolerant semantics can be incorporated for handling constrained argumentation. This is followed by a section in which we show that what is obtained is representable by signed theories whose models describe the intended semantics of the constrained argumentation frameworks. In the last section we conclude and consider some future work.