On the Strong Equivalences for LPMLN Programs

LPMLN is a powerful knowledge representation and reasoning tool that combines the non-monotonic reasoning ability of Answer Set Programming (ASP) and the probabilistic reasoning ability of Markov Logic Networks (MLN). In this paper, we study the strong equivalence for LPMLN programs, which is an important tool for program rewriting and theoretical investigations in the field of logic programming. First of all, we present the notion of p-strong equivalence for LPMLN and present a model-theoretical characterization for the notion. And we investigate the relationships among the p-strong equivalence and other existing notions of strong equivalences for LPMLN. Then, we investigate several properties of the p-strong equivalence from the following four aspects. Firstly, we investigate two relaxed notions of the p-strong equivalence according to practical scenarios of program rewriting, and present corresponding characterizations for the notions. Secondly, we analyze the computational complexities of deciding strong equivalences for LPMLN programs. Thirdly, we investigate the relationships among the strong equivalences of LPMLN and two extensions of ASP: ASP with weak constraints and ordered disjunctions. Finally, we investigate LPMLN program simplification via the p-strong equivalence and present some syntactic conditions that decide the p-strong equivalence between a single LPMLN rule and the empty program. The contributions of the paper are as follows. Firstly, all of the results presented in this paper provide a better understanding of LPMLN programming, which helps us further explore the properties of LPMLN. Secondly, the relationships among the strong equivalences open a way to study the strong equivalences for some logic formalisms by translating into LPMLN. Thirdly, the program simplification can be used to enhance the implementations of the LPMLN solvers ..

On the Strong Equivalences for LPMLN Programs

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 ..