Solving Advanced Argumentation Problems with Answer Set Programming
This work addresses computational bottlenecks in formal argumentation for AI researchers, though it is incremental as it adapts existing ASP methods to specific frameworks.
The paper tackles the high computational complexity of abstract dialectical frameworks (ADFs) and GRAPPA in argumentation by developing efficient translations to Answer Set Programming (ASP), leveraging their matching complexity levels to enable solving advanced argumentation problems.
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).