On bipolar argumentation frameworks and their equivalence with logic programming and SETAF

Abstract

Logic programming and abstract argumentation are closely connected paradigms suitable for representing incomplete, contradictory, and/or uncertain information. In Normal Logic Programs (NLPs), each claim is represented by an atom, which is considered true iff it can be derived by a set of logical rules. In Abstract Argumentation Frameworks (AAFs), claims are encoded as arguments and evaluated solely based on an attack relation, which determines how arguments (negatively) interact with each other. Different interactions give rise to distinct argumentation variants, such as Bipolar Argumentation Frameworks (BAFs) and Frameworks with Sets of Attacking Arguments (SETAFs), that additionally allow expressing the notions of support and collective attacks, respectively. For each variant, a evaluation criteria, called semantics, is needed to specify precisely which claims should be regarded as accepted, rejected, or neither (undecided). In this work, we study BAFs by both a semantic and a structural perspective. We propose new semantics for BAFs, called β-semantics, and employ them to find semantic-preserving translations between BAFs, SETAF, and NLPs. Moreover, our proposed translations preserve the structure of these formalisms when restricted to redundancy-free classes of them. The resulting translations are made accessible in the following website: https://web.archive.org/web/20260327154048/https://renpet-hhh.github.io/argnlp/static/.