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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关于 LPMLN 程序的强等价

LPMLN 是一种强大的知识表示和推理工具，它结合了答案集编程（ASP）的非单调推理能力和马尔可夫逻辑网络（MLN）的概率推理能力。在本文中，我们研究了 LPMLN 程序的强等效性，它是逻辑编程领域中程序重写和理论研究的重要工具。首先，我们提出了 LPMLN 的 p-强等价的概念，并提出了该概念的模型理论表征。我们研究了 p-强等价与 LPMLN 的其他现有强等价概念之间的关系。然后，我们从以下四个方面研究了 p-strong 等价的几个性质。首先，我们根据程序重写的实际场景研究了 p-strong 等价的两个宽松概念，并给出了这些概念的相应特征。其次，我们分析了确定 LPMLN 程序强等价的计算复杂性。第三，我们研究了 LPMLN 的强等价与 ASP 的两个扩展之间的关系：具有弱约束和有序析取的 ASP。最后，我们通过 p-strong 等价研究了 LPMLN 程序的简化，并提出了一些决定单个 LPMLN 规则和空程序之间 p-strong 等价的句法条件。论文的贡献如下。首先，本文提出的所有结果都提供了对 LPMLN 编程的更好理解，这有助于我们进一步探索 LPMLN 的特性。其次，强等价之间的关系为将一些逻辑形式的强等价翻译成LPLMN来研究强等价关系开辟了道路。第三，程序简化可用于增强 LPMLN 求解器的实现......