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Fuzzy logic programming reduced to reasoning with attribute implications

机译：模糊逻辑编程简化为具有属性含义的推理

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摘要

We present a link between two types of logic systems for reasoning with graded if-then rules: the system of fuzzy logic programming (FLP) in sense of Vojtas and the system of fuzzy attribute logic (FAL) in sense of Belohlavek and Vychodil. We show that each finite theory consisting of formulas of FAL can be represented by a definite program so that the semantic entailment in FAL can be characterized by correct answers for the program. Conversely, we show that for each definite program there is a collection of formulas of FAL so that the correct answers can be represented by the entailment in FAL. Using the link, we can transport results from FAL to FLP and vice versa which gives us, e.g., a syntactic characterization of correct answers based on Pavelka-style Armstrong-like axiomatization of FAL. We further show that entailment in FLP is reducible to reasoning with Boolean attribute implications and elaborate on related issues including properties of least models.
机译：我们提出了两种使用分级的if-then规则进行推理的逻辑系统之间的链接：就Vojtas而言的模糊逻辑编程（FLP）系统和就Belohlavek和Vychodil而言的模糊属性逻辑（FAL）系统。我们表明，由FAL公式组成的每个有限理论都可以用一个确定的程序表示，这样FAL中的语义蕴涵可以通过对该程序的正确答案来表征。相反，我们表明，对于每个确定的程序，都有FAL公式的集合，因此正确的答案可以用FAL中的蕴涵表示。使用链接，我们可以将结果从FAL传输到FLP，反之亦然，这可以为我们提供基于FAL的Pavelka式阿姆斯特朗式公理化的正确答案的句法表征。我们进一步表明，FLP中的蕴含可简化为具有布尔属性含义的推理，并详细说明了相关问题，包括最小模型的属性。

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