  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.
