正则模型存在性、唯一性和数量的图条件
Graphical Conditions for the Existence, Unicity and Number of Regular Models
AI总结：
本文针对有限基正常逻辑程序的依赖图提出图条件，推广现有结果得到非平凡正则模型存在的必要条件、正则模型唯一性的充分条件，及基于正反馈顶点集的数量上界，关键是建立其与布尔网络理论的联系。
摘要：
正常逻辑程序的正则模型是一类特殊的部分（即三值）模型，对应具有最小未定义性的稳定部分模型。本文针对有限基正常逻辑程序的依赖图，探索图条件以分析其正则模型的存在性、唯一性和数量。我们展示了三个主要结果：1）非平凡（即非二值）正则模型存在的必要条件；2）正则模型唯一性的充分条件；3）基于正反馈顶点集的正则模型数量的两个上界。前两个条件推广了You和Yuan（1994）针对具有良基分层的正常逻辑程序所获两个现有结果的有限情形。据我们所知，第三个结果也是新的。我们证明的关键是建立有限基正常逻辑程序与布尔网络理论之间的联系。
英文摘要：
The regular models of a normal logic program are a particular type of partial (i.e. 3-valued) models which correspond to stable partial models with minimal undefinedness. In this paper, we explore graphical conditions on the dependency graph of a finite ground normal logic program to analyze the existence, unicity and number of regular models for the program. We show three main results: 1) a necessary condition for the existence of non-trivial (i.e. non-2-valued) regular models, 2) a sufficient condition for the unicity of regular models, and 3) two upper bounds for the number of regular models based on positive feedback vertex sets. The first two conditions generalize the finite cases of the two existing results obtained by You and Yuan (1994) for normal logic programs with well-founded stratification. The third result is also new to the best of our knowledge. Key to our proofs is a connection that we establish between finite ground normal logic programs and Boolean network theory.
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