A formal concept view of argumentation

International audienceThe paper presents a parallel between two important theories for the treatment of information which address questions that are apparently unrelated and that are studied by different research communities: an enriched view of formal concept analysis and abstract argumentation. Both theories exploit a binary relation (expressing object-property links, attacks between arguments). We show that when an argumentation framework rather considers the complementary relation does not attack, then its stable extensions can be seen as the exact counterparts of formal concepts. This leads to a cube of oppositions, a generalization of the well-known square of oppositions, between eight remarkable sets of arguments. This provides a richer view for argumentation in cases of bi-valued attack relations and fuzzy ones

A QBF-based Formalization of Abstract Argumentation Semantics

Supported by the National Research Fund, Luxembourg (LAAMI project) and by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant ref. EP/J012084/1 (SAsSY project).Peer reviewedPostprin

Studying the grounded semantics by using a suitable codification

One of the most representative semantics of Dung's approach is the grounded semantics. This semantics captures a skeptical approach, this means that given an argumentation framework the grounded semantics always identifies a single set of arguments, called grounded extension. It worth mentioning that the grounded semantics approach is one of the most useful argumentation approaches in real argumentation-based systems As argumentation can be abstractly defined as the interaction of arguments for and against some conclusion, a reasoning based on an abstract argumentation semantics for describing the interaction arguments is as important as to find an extension of an argumentation framework. In this paper, we introduce a novel formal argumentation method based on normal programs and rewriting systems which is able to - describe the interaction of arguments during the process of inferring an extension, and -define extensions of the grounded semantics based on specific rewriting rules which perform particular kind of reasoning as in reasoning by cases. Moreover, we point out that our codification of an argumentation framework as a normal program is a suitable codification for studying other abstract argumentation semantics as are the stable semantics and the preferred semantics.Postprint (author's final draft

Approximating Operators and Semantics for Abstract Dialectical Frameworks

We provide a systematic in-depth study of the semantics of abstract dialectical frameworks (ADFs), a recent generalisation of Dung\''s abstract argumentation frameworks. This is done by associating with an ADF its characteristic one-step consequence operator and defining various semantics for ADFs as different fixpoints of this operator. We first show that several existing semantical notions are faithfully captured by our definition, then proceed to define new ADF semantics and show that they are proper generalisations of existing argumentation semantics from the literature. Most remarkably, this operator-based approach allows us to compare ADFs to related nonmonotonic formalisms like Dung argumentation frameworks and propositional logic programs. We use polynomial, faithful and modular translations to relate the formalisms, and our results show that both abstract argumentation frameworks and abstract dialectical frameworks are at most as expressive as propositional normal logic programs