模糊Horn子句逻辑形式系统

A Formal System of Fuzzy Horn Clause Logic

简要回顾逻辑推理的发展历史,指出了经典数理逻辑中存在的一些问题。作者为每个传统的Horn子句赋予一个蕴涵强度f∈(0,1],从而得到模糊Horn子句及其Herbrand解释。进而,对传统Horn子句逻辑的语法和语义进行了拓展,建立了一个基于模糊Horn子句有限集合的逻辑推理系统,并证明了该系统的正确性和完备性。

By means of reviewing the history of logic resoning, in this paper, some shortcomings in the classical mathematical logic are point out. We associate with each Horn clause an implication strength f∈ （0,11, to obtain the fuzzy Horn clauses and their Herbrand interpretations. Moreover, we present an approach to generalizing the syntax and the semantics of the conventional Horn clause logic to establish the logical inference system based on the finite set of fuzzy Horn clauses, and we show that the correctness and the completeness of the system can be proved.