Vincent Risch

Argumentation frameworks with necessities

In this paper, we introduce argumentation frameworks with necessities (AFNs), an extension of Dungs argumentation frameworks (AFs) taking into account a necessity relation as a kind of support relation between arguments (an argument is necessary for another). We redefine the acceptability semantics for these extended frameworks and we show how the necessity relation allows a direct and easy correspondence between a fragment of logic programs (LPs) and AFNs. We introduce then a further generalization of AFNs that extends the necessity relation to deal with sets of arguments. We give a natural adaptation of the acceptability semantics to this new context and show that the generalized frameworks allow to encode arbitrary logic programs.

Bipolar Argumentation Frameworks with Specialized Supports

We generalize in this paper the Dung’s abstract argumentation theory in order to represent, in addition to the attack relation, a particular kind of support relation which captures knowledge of the form : “argument a is necessary to obtain argument b”. Unlike a general unspecified support, the necessity relation has the advantage to ensure that its interaction with direct attacks generates new (indirect) attacks having exactly the same nature of the direct ones. We discuss the advantageous consequences of this specialization of the support relation on the acceptability semantics of the underlying bipolar framework. Then, we show a suitable translation of any such bipolar framework into a logic program without passing by a preliminary translation into the classical framework of Dung.

A Tableau-Based Characterisation for Default Logic

This paper has two objectives: We first give a necessary and sufficient criterion for the existence of extension of default theories in the general case. Second, we present a new, efficient and clear method for computing extensions and deriving formulae of default theory in the general case. It is based on the semantic tableaux method [Smullyan 1968] and works for default theories with a finite set of defaults that are formulated over a decidable subset of first-order logic. We prove that all extensions (if any) of a default theory can be produced by constructing the semantic tableau of one formula built from the general laws and the default consequences.

Toward a logical tool for generating new arguments in an argumentation based framework

Following the framework proposed by Besnard and Hunter for argumentation, this paper aims to propose a logical tool for the generation of new arguments when two formal agents have to face their respective knowledge. The following notions are addressed: the behaviour of an agent facing an argument, the answer of an agent in front of a set of formulas, and relations among arguments. X-logics, a nonmonotonic extension of classical propositional logic proposed by Siegel and Forget, is used as the background formalism for representing the reasoning of the agents on arguments

Comparing a Pair-Wise Compatibility Heuristic and Relaxed Stratification: Some Preliminary Results

An extension-building heuristic is developed and a preliminary investigation of its computational properties is given by comparing its run times to those of DeReS which uses relaxed stratification, another extension-building heuristic. Heuristics which can take advantage of the structural properties of a default theory may provide the information about the theory so that divide-and-conquer-like techniques may be applied on those problems which exhibit appropriate structural properties. Structural properties of a default theory are defined in terms of properties of graphs that represent important features of default theories. Unlike the syntax-dependent heuristics used in previous extension-building algorithms, the heuristic developed here is consistency-based.

Managing Deceitful Arguments with X-Logics

In most works on negotiation dialogues, agents are supposed to be ideally honest. However, there are many situations where such a behaviour cannot always be expected from the agents (e.g. advertising, political negotiation, etc.). The aim of this paper is to reconsider the role of deceitful arguments in argumentation frameworks. We propose a logical tool for representing and handling deceitful arguments in a dialogue between two formal agents having to face their respective knowledge and trying to convince each other. X-logics, a nonmonotonic extension of classical propositional logics, is used as the background formalism for representing the reasoning of the agents on arguments. Starting from a previous work dedicated to the generation of new arguments, we propose to define the notion of lie as a new kind of possible agents answer. Finally, we describe the way an agent may trick and how the other agent may detect it