A Syntactic Approach to Studying Strongly Equivalent Logic Programs

TL;DR

This paper introduces a new syntactic approach to analyze strong equivalence in logic programs, providing automated methods to identify and simplify conditions that preserve equivalence in ASP and LPMLN.

Contribution

It presents a novel syntactic framework, including transformations and algorithms, for studying and discovering strong equivalence conditions in logic programming.

Findings

Developed five types of syntactic transformations for logic programs.

Created an automatic algorithm to find strong equivalence-preserving conditions.

Simplified SE-conditions for various LPMLN programs.

Abstract

In the field of Answer Set Programming (ASP), two logic programs are strongly equivalent if they are ordinarily equivalent under any extensions. This property provides a theoretical foundation for studying many aspects of logic programs such as program simplification and transformation etc. Therefore, strong equivalence has been investigated extensively for ASP and its extensions such as LPMLN. In this paper, we present a syntactic approach to studying the strong equivalence of logic programs, which provides several interesting results and would help us understand the strong equivalence from a new perspective. Firstly, we present the notions of independent sets and five kinds of syntactic transformations (S-* transformations) for logic programs. And we investigate the strong equivalence (SE) and non-strong equivalence (NSE) preserving properties of the S-* transformations in the contexts of ASP and LPMLN. Secondly, based on the properties of the S-* transformations, we present a fully automatic algorithm to discover syntactic conditions that preserve strong equivalences (SE-conditions) of ASP and LPMLN programs. To discover the SE-conditions efficiently, we present four kinds of approaches to improve the algorithm. Thirdly, we present a preliminary method to simplify the discovered SE-conditions and report the simplified SE-conditions of several kinds of LPMLN programs. After that, we present a discussion on the discovered SE-conditions and some existing problems. Finally, we present a comparison between SE-conditions discovering approaches in this paper and in the related work.