On the Strong Equivalences of LPMLN Programs

Abstract

By incorporating the methods of Answer Set Programming (ASP) and Markov Logic Networks (MLN), LP MLN becomes a powerful tool for non-monotonic, inconsistent and uncertain knowledge representation and reasoning. To facilitate the applications and extend the understandings of LP MLN , we investigate the strong equivalences between LP MLN 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 ∪ R and Q ∪ 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 LP MLN is a combination of ASP and MLN, the notions of strong equivalences in LP MLN is quite different from that in ASP. Firstly, we present the notions of p-strong and w-strong equivalences between LP MLN 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 LP MLN programs, and present a sufficient and necessary syntactic condition that guarantees the strong equivalence between a single LP MLN rule and the empty program.