The Well-Founded Semantics Coincides with the Three-Valued Stable Semantics
The Well-Founded Semantics Coincides with the Three-Valued Stable Semantics
复制标题
有根语义与三值稳定语义一致
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
Teodor C. Przymusinski
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文献类型：
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作者：
Teodor C. Przymusinski
我们引入了3-值稳定模型，它是标准（2-值）稳定模型的自然推广。我们证明了每个逻辑程序P至少有一个3值稳定模型，并且任何程序P的良基模型与P的最小3值稳定模型一致.我们得出结论，任意逻辑程序的良基语义与3值稳定模型语义一致.三值稳定语义与人工智能中的非单调形式主义密切相关。也就是说，每一个程序P都可以被翻译成一个合适的自认知（或默认）理论^ P，使得P的3值稳定语义与（3值）自认知（分别）一致。缺省）语义。对于限定和CWA也有类似的结果。此外，它可以表明，三值稳定语义有一个自然的推广到所有的析取逻辑程序和演绎数据库的类。[1]最后，根据Gelfond和Lifschitz最近提出的方法，我们把我们的所有结果推广到更一般的逻辑程序，这些程序除了把否定作为失败使用之外，还允许使用经典否定。
We introduce 3-valued stable models which are a natural generalization of standard (2-valued) stable models. We show that every logic program P has at least one 3-valued stable model and that the well-founded model of any program P VGRS90] coincides with the smallest 3-valued stable model of P. We conclude that the well-founded semantics of an arbitrary logic program coincides with the 3-valued stable model semantics. The 3-valued stable semantics is closely related to non-monotonic formalisms in AI. Namely, every program P can be translated into a suitable autoepistemic (resp. default) theory ^ P so that the 3-valued stable semantics of P coincides with the (3-valued) autoepistemic (resp. default) semantics of ^ P. Similar results hold for circumscrip-tion and CWA. Moreover, it can be shown that the 3-valued stable semantics has a natural extension to the class of all disjunctive logic programs and deductive databases. 1 Finally, following upon the recent approach developed by Gelfond and Lifschitz, we extend all of our results to more general logic programs which, in addition to the use of negation as failure, permit the use of classical negation.