On Strong Equivalence Notions in Logic Programming and Abstract Argumentation

TL;DR

This paper investigates strong equivalence in logic programming and abstract argumentation, introducing a new notion that maintains compatibility across these formalisms in dynamic contexts.

Contribution

It proposes a novel strong equivalence concept for logic programs that preserves equivalence under translation to argumentation frameworks, addressing a key discrepancy.

Findings

The new notion of strong equivalence aligns logic programming and argumentation frameworks in dynamic settings.

It restores semantic compatibility between logic programs and argumentation frameworks during updates.

The approach ensures that equivalence is preserved across formalism translations in specific classes.

Abstract

Strong equivalence between knowledge bases ensures the possibility of replacing one with the other without affecting reasoning outcomes, in any given context. This makes it a crucial property in nonmonotonic formalisms. In particular, the fields of logic programming and abstract argumentation provide primary examples in which this property has been subject to vast investigations. However, while (classes of) logic programs and abstract argumentation frameworks are known to be semantically equivalent in static settings, this alignment breaks in dynamic contexts due to differing notions of update. As a result, strong equivalence does not always carry over from one formalism to the other. In this paper, we carefully investigate this discrepancy and introduce a new notion of strong equivalence for logic programs. Our approach preserves strong equivalence under translation between certain classes of logic programs and both Dung-style and claim-augmented argumentation frameworks, thus restoring compatibility across these formalisms.