Giacomin, Massimiliano

Dealing with Generic Contrariness in Structured Argumentation

AAAI Conferences

The adoption of a generic contrariness notion in ASPIC+ substantially enhances its expressiveness with respect to other formalisms for structured argumentation. In particular, it opens the way to novel investigation directions, like the use of multivalued logics in the construction of arguments. This paper points out however that in the current version of ASPIC+ a serious technical difficulty related with generic contrariness is present. With the aim of preserving the same level of generality, the paper provides a solution based on a novel notion of closure of the contrariness relation at the level of sets of formulas and an abstract representation of conflicts between sets of arguments. The proposed solution is shown to satisfy the same rationality postulates as ASPIC+ and represents a starting point for further technical and conceptual developments in structured argumentation.

Computing Preferred Extensions in Abstract Argumentation: a SAT-based Approach Artificial Intelligence

This paper presents a novel SAT-based approach for the computation of extensions in abstract argumentation, with focus on preferred semantics, and an empirical evaluation of its performances. The approach is based on the idea of reducing the problem of computing complete extensions to a SAT problem and then using a depth-first search method to derive preferred extensions. The proposed approach has been tested using two distinct SAT solvers and compared with three state-of-the-art systems for preferred extension computation. It turns out that the proposed approach delivers significantly better performances in the large majority of the considered cases.

Computational Properties of Resolution-based Grounded Semantics

AAAI Conferences

In the context of Dung's theory of abstract argumentation frameworks, the recently introduced resolution-based grounded semantics features the unique property of fully complying with a set of general requirements, only partially satisfied by previous literature proposals. This paper contributes to the investigation of resolution-based grounded semantics by analyzing its computational properties with reference to a standard set of decision problems for abstract argumentation semantics: (a) checking the property of being an extension for a set of arguments; (b) checking agreement with traditional grounded semantics; (c) checking the existence of a non-empty extension; (d) checking credulous acceptance of an argument; (e) checking skeptical acceptance of an argument. It is shown that problems (a)-(c) admit polynomial time decision processes, while (d) is NP-complete and (e) coNP-complete.