摘要：LPMLN is a powerful knowledge representation and reasoning tool that combinesthe non-monotonic reasoning ability of Answer Set Programming (ASP) and theprobabilistic reasoning ability of Markov Logic Networks (MLN). In this paper,we study the strong equivalence for LPMLN programs, which is an important toolfor program rewriting and theoretical investigations in the field of logicprogramming. First of all, we present the notion of p-strong equivalence forLPMLN and present a model-theoretical characterization for the notion. And weinvestigate the relationships among the p-strong equivalence and other existingnotions of strong equivalences for LPMLN. Then, we investigate severalproperties of the p-strong equivalence from the following four aspects.Firstly, we investigate two relaxed notions of the p-strong equivalenceaccording to practical scenarios of program rewriting, and presentcorresponding characterizations for the notions. Secondly, we analyze thecomputational complexities of deciding strong equivalences for LPMLN programs.Thirdly, we investigate the relationships among the strong equivalences ofLPMLN and two extensions of ASP: ASP with weak constraints and ordereddisjunctions. Finally, we investigate LPMLN program simplification via thep-strong equivalence and present some syntactic conditions that decide thep-strong equivalence between a single LPMLN rule and the empty program. Thecontributions of the paper are as follows. Firstly, all of the resultspresented in this paper provide a better understanding of LPMLN programming,which helps us further explore the properties of LPMLN. Secondly, therelationships among the strong equivalences open a way to study the strongequivalences for some logic formalisms by translating into LPMLN. Thirdly, theprogram simplification can be used to enhance the implementations of the LPMLNsolvers of theLP MLN solvers, which is expected to facilitate the applications of LP MLN .
关键词：Computer Science - Logic in Computer Science; D.1.6
