Solving Set Optimization Problems by Cardinality Optimization via Weak Constraints with an Application to Argumentation

TL;DR

This paper introduces a method for efficiently finding subset-optimal solutions in AI tasks by leveraging cardinality optimization techniques like MaxSAT and ASP, demonstrated through argumentation frameworks.

Contribution

It presents a novel approach that uses weak constraints to compute all subset-optimal solutions via iterative cardinality optimization in logic programming.

Findings

Effective method for subset-optimal solution computation

Application to argumentation frameworks

Leverages existing logic programming constructs

Abstract

Optimization - minimization or maximization - in the lattice of subsets is a frequent operation in Artificial Intelligence tasks. Examples are subset-minimal model-based diagnosis, nonmonotonic reasoning by means of circumscription, or preferred extensions in abstract argumentation. Finding the optimum among many admissible solutions is often harder than finding admissible solutions with respect to both computational complexity and methodology. This paper addresses the former issue by means of an effective method for finding subset-optimal solutions. It is based on the relationship between cardinality-optimal and subset-optimal solutions, and the fact that many logic-based declarative programming systems provide constructs for finding cardinality-optimal solutions, for example maximum satisfiability (MaxSAT) or weak constraints in Answer Set Programming (ASP). Clearly each cardinality-optimal solution is also a subset-optimal one, and if the language also allows for the addition of particular restricting constructs (both MaxSAT and ASP do) then all subset-optimal solutions can be found by an iterative computation of cardinality-optimal solutions. As a showcase, the computation of preferred extensions of abstract argumentation frameworks using the proposed method is studied.