Defining defense and defeat in abstract argumentation from scratch – A generalizing approach

Abstract

We propose a general framework to investigate semantics of Dung-style argumentation frameworks (AFs) by means of a generic defeat notion formalized by refute operators.The main idea underlying our approach is that, given a refute operator δ, counter-parts to all classical semantics can be deduced in a natural way. We demonstrate how classical as well as recent proposals can be captured by our approach when utilizing suitable refute operators. In addition, we showcase how our general scheme can be employed to propose novel semantics in a systematic manner. This results in what we call cooperative semantics which stem from a novel refute operator we will introduce. We perform an in-depth investigation of basic properties of refute operators and to which extent the induced semantics inherit desirable properties from it. Among others, we show under which conditions i) a counterpart to Dung’s fundamental lemma can be inferred, ii) the generalized version of the grounded extension is unique, or iii) the generalized version of stable semantics does not collapse. Moreover, we contribute to a principle-based study of AF semantics by discussing properties tailored to assess the behavior of different refute operators. This includes an investigation of means to compare refute operators in terms of their aggressiveness. Finally, we conclude the study by reporting computational complexity results for basic reasoning tasks which hold in our general framework.