Strong Equivalence of Logic Programs with Counting

TL;DR

This paper extends the understanding of strong equivalence in answer set programming by including programs with #count aggregates, providing a method to establish equivalence through derivations.

Contribution

It introduces a novel approach to determine strong equivalence for programs with #count aggregates, expanding previous methods that excluded aggregates.

Findings

Extended the class of programs for which strong equivalence can be established

Provided a derivation-based method for programs with #count aggregates

Enhanced the theoretical framework of answer set programming

Abstract

In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. In some cases, strong equivalence of programs in the input language of the grounder gringo can be established by deriving rules of each program from rules of the other. The possibility of such proofs has been demonstrated for a subset of that language that includes comparisons, arithmetic operations, and simple choice rules, but not aggregates. This method is extended here to a class of programs in which some uses of the #count aggregate are allowed. This paper is under consideration for acceptance in TPLP.