Dialectic semantics for argumentation frameworks

Abstract

We provide a formalism for the study of dialogues, where a dialogue is a two-person game, initiated by the proponent who defends a proposed thesis. We examine several different winning criteria and several different dialogue types, where a dialogue type is determined by a set of positions, an attack relation between positions and a legal-move function. We examine two proof theories, where a proof theory is determined by a dialogue type and a winning criterion. For each of the proof theories we supply a corresponding declarative semantics.

Proof Theories and Algorithms for Abstract Argumentation Frameworks

“…In this chapter we follow the approach of [8,13,15,17,25,27] and present the moving of arguments as 2-person dialogue games that provide a natural way in which to lay out and understand the algorithms that implement them. To be sure, the actual algorithms themselves, should, except for didactic purposes, not be implemented as dialogue games, but rather as monological procedures (or methods in OO-languages) that are called recursively.…”

“…Given a dispute tree T induced by a, the legal move function φ for a semantics s, prunes T to obtain the sub-tree T of T that we call the φ tree induced by a. T is the playing field of the game for semantics s. Thus, we define a φ -winning strategy for a [8,17] as a sub-tree of the φ dispute tree induced by a, in the same way as Definition 6, except that we replace 'for any x such that xRy' in condition 2, with 'for any x that OPP can φ legally move against y'. Intuitively, φ is defined such that a is in an admissible extension that conforms to the semantics s iff there is a φ -winning strategy for a in the φ tree induced by a, where the arguments moved by PRO in the φ -winning strategy are conflict free (recall that an admissible extension must contain no arguments that attack each other).…”

“…Section 3 then describes a framework for argument game based proof theories [8,15,17,27]. The inherently dialectical nature of argumentation naturally lends itself to the formulation of argument games in which a proponent starts with an initial argument to be tested, and then an opponent and the proponent successively attack each other's arguments.…”

A Two-Phase Dialogue Game for Skeptical Preferred Semantics

“…It has been argued that proof dialogues, while providing equivalent results to standard argumentation semantics, can decrease the gap between intuitive and formal accounts of argumentation [1,[11][12][13] , and have been used in human-computer interactions to aid understanding [16,6,4]. While the credulous acceptance problem under preferred semantics has been modelled using dialogue games in the past [16,7,12,3], the skeptical preferred semantics has received less attention.…”

Case-Based Argumentation in Agent Societies

“…The framework of Soh and Tsatsoulis does not interpret persuasion as most legal argumentation systems do [Jakobovits and Vermeir, 1999]. These perform a detailed study about the dialectical context of legal arguments and their condition of proposals, defenses, positions or attacks.…”