Shedding new light on the foundations of abstract argumentation: Modularization and weak admissibility

Abstract

In his seminal 1995 paper, Dung laid the foundations of abstract argumentation, a by now major research area in knowledge representation. He pointed out that there is a problematic issue with self-defeating arguments underlying all traditional semantics. A self-defeat occurs if an argument attacks itself either directly or indirectly via an odd attack loop, unless the loop is broken up by some argument attacking the loop from outside. Motivated by the fact that such arguments represent self-contradictory or paradoxical arguments, he asked for reasonable semantics which overcome the problem that such arguments may indeed invalidate any argument they attack.This paper provides a solution to this problem. More precisely, we introduce alternative foundations for abstract argumentation, namely weak admissibility and weak defense. After showing that these key concepts are compatible as in the classical case we introduce new versions of the classical Dung-style semantics including complete, preferred and grounded semantics. We provide a rigorous study of these new concepts including interrelationships as well as the relations to their Dung-style counterparts. We also conduct an analysis of the relationship of our concepts with similar concepts found in the literature. We show that weak admissibility, although defined in entirely different terms, is in fact equivalent to a notion of acceptability which was defined by Kakas and Mancarella yet never studied in depth.The new semantics presented here overcome the issue with self-defeating arguments, and they are semantically insensitive to syntactic deletions of self-attacking arguments, a special case of self-defeat.1