Preferred extensions as stable models

Abstract

AbstractGiven an argumentation frameworkAF, we introduce a mapping function that constructs a disjunctive logic programP, such that the preferred extensions ofAFcorrespond to the stable models ofP, after intersecting each stable model with the relevant atoms. The given mapping function is of polynomial size w.r.t.AF.In particular, we identify that there is a direct relationship between the minimal models of a propositional formula and the preferred extensions of an argumentation framework by working on representing the defeated arguments. Then we show how to infer the preferred extensions of an argumentation framework by using UNSAT algorithms and disjunctive stable model solvers. The relevance of this result is that we define a direct relationship between one of the most satisfactory argumentation semantics and one of the most successful approach of nonmonotonic reasoning i.e., logic programming with the stable model semantics.