Inference from controversial arguments

International audienceWe present new careful semantics within Dung's theory of argumentation. Under such careful semantics, two arguments cannot belong to the same extension whenever one of them indirectly attacks a third argument while the other one indirectly defends the third.We argue that our semantics lead to a better handling of controversial arguments than Dung's ones in some settings. We compare the careful inference relations induced by our semantics w.r.t. cautiousness; we also compare them with the inference relations induced by Dung's semantic

Bridging the Gap between Abstract Argumentation Systems and Logic

International audienceDung’s argumentation system takes as input a set of arguments and a binary relation encoding attacks among these arguments, and returns different extensions of arguments. However, no indication is given on how to instantiate this setting, i.e. how to build arguments from a knowledge base and how to choose an appropriate attack relation. This leads in some cases to undesirable results like inconsistent extensions (i.e. the set of formulas forming an extension is inconsistent). This is due to the gap between the abstract setting and the knowledge base from which it is defined. The purpose of this paper is twofold: First it proposes to fill in this gap by extending Dung’s system. The idea is to consider all the ingredients involved in an argumentation problem. We start with an abstract monotonic logic which consists of a set of formulas and a consequence operator. We show how to build arguments from a knowledge base using the consequence operator of the logic. Second, we show that the choice of an attack relation is crucial for ensuring consistent results, and should not be arbitrary. In particular, we argue that an attack relation should be at least grounded on the minimal conflicts contained in the knowledge base. Moreover, due to the binary character of this relation, some attack relations may lead to unintended results. Namely, symmetric relations are not suitable when ternary (or more) minimal conflicts are in the knowledge base. We propose then the characteristics of attack relations that ensure sound results

Structural Properties for Deductive Argument Systems

There have been a number of proposals for using deductive arguments for instantiating abstract argumentation. These take a set of formulae as a knowledgebase, and generate a graph where each node is a logical argument and each arc is a logical attack. This then raises the question of whether for a specific logical argument system S, and for any graph G, there is a knowledgebase such that S generates G. If it holds, then it can be described as a kind of "structural" property of the system. If it fails then, it means that there are situations that cannot be captured by the system. In this paper, we explore some features, and the significance, of such structural properties. © 2013 Springer-Verlag Berlin Heidelberg

Symmetric argumentation frameworks

Abstract. This paper is centered on the family of Dung’s finite argumentation frameworks when the attacks relation is symmetric (and nonempty and irreflexive). We show that while this family does not contain any well-founded framework, every element of it is both coherent and relatively grounded. Then we focus on the acceptability problems for the various semantics introduced by Dung, yet generalized to sets of arguments. We show that only two distinct forms of acceptability are possible when the considered frameworks are symmetric. Those forms of acceptability are quite simple, but tractable; this contrasts with the general case for which all the forms of acceptability are intractable (except for the ones based on grounded or naive extensions).

Towards a Paradoxical Description Logic for the Semantic Web

As a vision for the future of the Web, the Semantic Web is an open, constantly changing and collaborative environment. Hence it is reasonable to expect that knowledge sources in the Semantic Web contain noise and inaccuracies. However, as the logical foundation of Ontology Web Language in the Semantic Web, description logics fail to tolerate inconsistent information. The study of inconsistency handling in description logics is an important issue in the Semantic Web. One major approach to inconsistency handling is based on so-called paraconsistent reasoning, in which standard semantics is refined so that inconsistencies can be tolerated. Four-valued description logics are not satisfactory for the Semantic Web in that its reasoning is a bit far from standard semantics. In this paper, we present a paraconsistent description logic called paradoxical description logic, which is based on a three-valued semantics. Compared to existing paraconsistent description logics, our approach is more suitable for dealing with inconsistent ontologies in that paraconsistent reasoning under our semantics provides a better approximation to the standard reasoning. An important result in this paper is that we propose a sound and complete tableau for paradoxical description logics. ? 2010 Springer Berlin Heidelberg.EI