On the Strong Equivalences of LPMLN Programs

TL;DR

This paper investigates strong equivalences in LPMLN programs, combining ASP and MLN, providing new notions, characterizations, and conditions to simplify and understand LPMLN logic programs.

Contribution

It introduces p-strong and w-strong equivalences for LPMLN, generalizes SE-models from ASP, and offers syntactic conditions for strong equivalence in LPMLN.

Findings

Defined p-strong and w-strong equivalences for LPMLN.

Generalized SE-model approach to LPMLN.

Provided syntactic conditions for program simplification.

Abstract

By incorporating the methods of Answer Set Programming (ASP) and Markov Logic Networks (MLN), LPMLN becomes a powerful tool for non-monotonic, inconsistent and uncertain knowledge representation and reasoning. To facilitate the applications and extend the understandings of LPMLN, we investigate the strong equivalences between LPMLN programs in this paper, which is regarded as an important property in the field of logic programming. In the field of ASP, two programs P and Q are strongly equivalent, iff for any ASP program R, the programs P and Q extended by R have the same stable models. In other words, an ASP program can be replaced by one of its strong equivalent without considering its context, which helps us to simplify logic programs, enhance inference engines, construct human-friendly knowledge bases etc. Since LPMLN is a combination of ASP and MLN, the notions of strong equivalences in LPMLN is quite different from that in ASP. Firstly, we present the notions of p-strong and w-strong equivalences between LPMLN programs. Secondly, we present a characterization of the notions by generalizing the SE-model approach in ASP. Finally, we show the use of strong equivalences in simplifying LPMLN programs, and present a sufficient and necessary syntactic condition that guarantees the strong equivalence between a single LPMLN rule and the empty program.