In the field of Answer Set Programming (ASP), two logic programs are strongly equivalent if they are ordinarily equivalent under any extensions. This property provides a theoretical foundation for studying many aspects of logic programs such as program simplification and transformation etc. Therefore, strong equivalence has been investigated extensively for ASP and its extensions such as LPMLN. In this paper, we present a syntactic approach to studying the strong equivalence of logic programs, which provides several interesting results and would help us understand the strong equivalence from a new perspective. Firstly, we present the notions of independent sets and five kinds of syntactic transformations (S-* transformations) for logic programs. And we investigate the strong equivalence (SE) and non-strong equivalence (NSE) preserving properties of the S-* transformations in the contexts of ASP and LPMLN. Secondly, based on the properties of the S-* transformations, we present a fully automatic algorithm to discover syntactic conditions that preserve strong equivalences (SE-conditions) of ASP and LPMLN programs. To discover the SE-conditions efficiently, we present four kinds of approaches to improve the algorithm. Thirdly, we present a preliminary method to simplify the discovered SE-conditions and report the simplified SE-conditions of several kinds of LPMLN programs. After that, we present a discussion on the discovered SE-conditions and some existing problems. Finally, we present a comparison between SE-conditions discovering approaches in this paper and in the related work.
翻译:在“答案设置”编程(ASP)领域,两个逻辑程序如果在任何扩展中通常等效(ASP),则两个逻辑程序是相当的。这一属性为研究逻辑程序的许多方面,例如程序简化和变换等,提供了一个理论基础。因此,对ASP及其扩展(LPMLN)进行了广泛调查,对ASP及其扩展(LPMLN)进行了强有力的等同性。在本文中,我们提出了一个研究逻辑程序强烈等同性的综合方法,它提供了几个有趣的结果,并将帮助我们从新的角度理解强烈等同性。首先,我们介绍了独立成套和五种合成转换(S-*变换)的概念,为逻辑程序提供了理论基础。我们研究了强等等(SES)和非等等等等等(NSE)在ASP和LPMN背景下维护S*变换的特性。第二,根据S-*转换的特性,我们提出了一个完全自动的算法,以发现从新的角度来保持亚SP和LPMN方案的强等同性(SE-M)的等同性条件(SE-M)概念,我们提出了四种比较方法,我们在SEE-SE-L最后的文件中发现了一些变现后,我们发现了一些SE-rismacrodrodrodrodrodrodrop(SE-s),我们提出了一种初步方法。我们提出了一种方法。