Semantic reasoning study for rough logic about n-ary formulas

Lin Yan, Sui-Hua Wang, Xue-Dong Zhang
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引用次数: 4

Abstract

We begin this paper with a discussion of constructing a kind of formulas which are called n-ary formulas in an approximate space of rough set theory. These formulas are an expansion of the formulas in Pawlak rough logic, so that the domains of the n-ary formulas are extended from subsets of U to subsets of U n (=U×U×…×U) . In subsequent discussions we define five rough logical values based on Pawlak rough logic for the n-ary formulas in n-dimensional space, and study rough logical reasoning in semantics through these rough logical value operations. Of course, we get some theorems which indicate that some forms of logical reasoning in classical logic are also true in rough logic for some rough logical values, but because 5-value rough logic is different from classical 2-value logic, we naturally obtain some new properties.
n元公式粗糙逻辑的语义推理研究
本文首先讨论在粗糙集理论的近似空间中构造一类称为n元公式的公式。这些公式是对Pawlak粗糙逻辑中公式的扩展,使得n元公式的定义域由U的子集扩展到U n的子集(=U×U×…×U)。在接下来的讨论中,我们基于Pawlak粗糙逻辑为n维空间中的n元公式定义了5个粗糙逻辑值,并通过这些粗糙逻辑值运算来研究语义上的粗糙逻辑推理。当然,我们得到了一些定理,表明经典逻辑中的某些形式的逻辑推理在粗糙逻辑中对某些粗糙逻辑值也是成立的,但是由于5值粗糙逻辑不同于经典的2值逻辑,我们自然得到了一些新的性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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