Summary: | 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 ...
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