On the Strong Equivalences of LPMLN Programs

Bin Wang
(Southeast University, China)
Jun Shen
(Southeast University, China)
Shutao Zhang
(Southeast University, China)
Zhizheng Zhang
(Southeast University, China)

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.

In Bart Bogaerts, Esra Erdem, Paul Fodor, Andrea Formisano, Giovambattista Ianni, Daniela Inclezan, German Vidal, Alicia Villanueva, Marina De Vos and Fangkai Yang: Proceedings 35th International Conference on Logic Programming (Technical Communications) (ICLP 2019), Las Cruces, NM, USA, September 20-25, 2019, Electronic Proceedings in Theoretical Computer Science 306, pp. 114–125.
Published: 19th September 2019.

ArXived at: https://dx.doi.org/10.4204/EPTCS.306.18 bibtex PDF
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