Extended ASP tableaux and rule redundancy in normal logic programs

TL;DR

This paper introduces an extended tableau calculus for answer set programming, providing theoretical and empirical insights into proof complexity and the impact of rule redundancy on ASP solving efficiency.

Contribution

It extends ASP tableaux with an extension rule, demonstrating its superior proof efficiency and analyzing the effects of rule redundancy on ASP solver performance.

Findings

Extended ASP Tableaux have polynomial-length proofs for certain programs

Rule redundancy can significantly affect ASP solving efficiency

Extended ASP Tableaux outperform standard ASP Tableaux in proof length

Abstract

We introduce an extended tableau calculus for answer set programming (ASP). The proof system is based on the ASP tableaux defined in [Gebser&Schaub, ICLP 2006], with an added extension rule. We investigate the power of Extended ASP Tableaux both theoretically and empirically. We study the relationship of Extended ASP Tableaux with the Extended Resolution proof system defined by Tseitin for sets of clauses, and separate Extended ASP Tableaux from ASP Tableaux by giving a polynomial-length proof for a family of normal logic programs P_n for which ASP Tableaux has exponential-length minimal proofs with respect to n. Additionally, Extended ASP Tableaux imply interesting insight into the effect of program simplification on the lengths of proofs in ASP. Closely related to Extended ASP Tableaux, we empirically investigate the effect of redundant rules on the efficiency of ASP solving. To appear in Theory and Practice of Logic Programming (TPLP).