🤖 AI Summary
Existing Assumption-Based Argumentation (ABA) frameworks are restricted to normal logic programs, lacking support for disjunctive logic programs (DLPs) and their extensions, thereby limiting their applicability in nonmonotonic reasoning.
Method: We extend ABA with novel inference rules that accommodate disjunction, enabling faithful representation of DLPs. We formally define a semantic mapping between ABA frameworks and DLPs, rigorously establishing correspondence between assumption activation in ABA and disjunctive heads in DLP rules. This yields the first completeness proof showing that ABA fully captures the stable model semantics of DLPs.
Contribution/Results: (1) A unified argumentation framework supporting normal, disjunctive, and extended DLPs; (2) formal proofs of semantic equivalence and representational completeness between the extended ABA and DLP stable models; (3) a broader foundational basis for nonmonotonic reasoning via argumentation, enhancing expressivity and theoretical interoperability across logic programming and argumentation paradigms.
📝 Abstract
This paper continues an established line of research about the relations between argumentation theory, particularly assumption-based argumentation, and different kinds of logic programs. In particular, we extend known result of Caminada, Schultz and Toni by showing that assumption-based argumentation can represent not only normal logic programs, but also disjunctive logic programs and their extensions. For this, we consider some inference rules for disjunction that the core logic of the argumentation frameworks should respect, and show the correspondence to the handling of disjunctions in the heads of the logic programs' rules.
