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arXiv 0712.0948cs.AIcs.LO
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关于集合规划中强等价、一致等价和其它等价概念的一般观点

A Common View on Strong, Uniform, and Other Notions of Equivalence in Answer-Set Programming

Technische Universität Wien(维也纳工业大学)

Stefan Woltran

摘要:

如今,在答案集语义下的逻辑编程处理了许多不同的程序等价概念。这是因为替代等价(称为强等价)和普通等价是不同的概念。前者成立,给定程序P和Q,当且仅当P在任何上下文R内都可以被Q忠实地替换;后者成立当且仅当P和Q提供相同的输出,即它们具有相同的答案集。强等价和普通等价之间的概念被引入作为比较不完整程序的理论工具,并且通过限制所考虑的上下文程序R的句法结构或通过限制允许在R中出现的原子的集合A(相对化等价)来定义。然而,对于前一种方法,结果是对R的任何“合理”的句法限制都与普通的、强的或一致的等价一致。在本文中,我们提出了一个参数化的等价概念,同时照顾到这两种限制的范围内,一方面,允许发生在规则头的上下文中的原子,另一方面,允许发生在规则机构的上下文中的原子。我们介绍了一个一般的语义特征,其中包括已知的SE模型(强等价)或UE模型(一致等价)作为特殊情况。此外,我们提供的问题的复杂性界限,并勾勒出一个可能的实现方法。逻辑程序设计理论与实践(Theory and Practice of Logic Programming,TPLP)

英文摘要:

Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are different concepts. The former holds, given programs P and Q, iff P can be faithfully replaced by Q within any context R, while the latter holds iff P and Q provide the same output, that is, they have the same answer sets. Notions in between strong and ordinary equivalence have been introduced as theoretical tools to compare incomplete programs and are defined by either restricting the syntactic structure of the considered context programs R or by bounding the set A of atoms allowed to occur in R (relativized equivalence).For the latter approach, different A yield properly different equivalence notions, in general. For the former approach, however, it turned out that any ``reasonable'' syntactic restriction to R coincides with either ordinary, strong, or uniform equivalence. In this paper, we propose a parameterization for equivalence notions which takes care of both such kinds of restrictions simultaneously by bounding, on the one hand, the atoms which are allowed to occur in the rule heads of the context and, on the other hand, the atoms which are allowed to occur in the rule bodies of the context. We introduce a general semantical characterization which includes known ones as SE-models (for strong equivalence) or UE-models (for uniform equivalence) as special cases. Moreover,we provide complexity bounds for the problem in question and sketch a possible implementation method. To appear in Theory and Practice of Logic Programming (TPLP).

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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