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- Title
ON THE STRONG EQUIVALENCES FOR LP<sup>MLN</sup> PROGRAMS.
- Authors
BIN WANG; JUN SHEN; SHUTAO ZHANG; ZHIZHENG ZHANG
- Abstract
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. 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 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, which is expected to facilitate the applications of LPMLN.
- Subjects
NONMONOTONIC logic; LOGIC programming; KNOWLEDGE representation (Information theory); COMPUTATIONAL complexity; MATHEMATICAL equivalence
- Publication
Logical Methods in Computer Science (LMCS), 2021, Vol 17, Issue 1, p1
- ISSN
1860-5974
- Publication type
Article
- DOI
10.23638/LMCS-17(14)2021