Strong equivalence for LP^MLN programs
Strong equivalence is a well-studied and important concept in answer set programming (ASP). LP^MLN is a probabilistic extension of answer set programs with the weight scheme adapted from Markov Logic. Because of the semantic differences, strong equivalence for ASP does not simply carry over to LP^MLN. I study the concept of strong equivalence in LP^MLN with the goal of extending strong equivalence to LP^MLN programs. My study shows that the verification of strong equivalence in LP^MLN can be reduced to equivalence checking in classical logic plus weight consideration.The result allows us to leverage an answer set solver for checking strong equivalence in LP^MLN. Furthermore, this study also suggests us a few reformulations of the LP^MLN semantics using choice rules, logic of here and there, and the second-order logic. I will present my work result of strong equivalence for LP^MLN and talk about my next steps for research: one is approximately strong equivalence, and another is the integration of fuzzy logic with neural network.
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