Solving Advanced Argumentation Problems with Answer Set Programming

TL;DR

This paper introduces efficient translations from advanced argumentation frameworks like ADFs and GRAPPA into Answer Set Programming, enabling effective computational reasoning for complex argumentation semantics.

Contribution

It presents novel reductions from ADFs and GRAPPA to ASP, matching their high complexity levels and supporting multiple semantics.

Findings

Reductions for five main ADF semantics implemented

Adaptations for GRAPPA semantics demonstrated

Complexity aligns with ASP for bounded predicate arity

Abstract

Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments, and the GRAPPA framework which allows argumentation scenarios to be represented as arbitrary edge-labelled graphs. The complexity of ADFs and GRAPPA is located beyond NP and ranges up to the third level of the polynomial hierarchy. The combined complexity of Answer Set Programming (ASP) exactly matches this complexity when programs are restricted to predicates of bounded arity. In this paper, we exploit this coincidence and present novel efficient translations from ADFs and GRAPPA to ASP. More specifically, we provide reductions for the five main ADF semantics of admissible, complete, preferred, grounded, and stable interpretations, and exemplify how these reductions need to be adapted for GRAPPA for the admissible, complete and preferred semantics. Under consideration in Theory and Practice of Logic Programming (TPLP).