3值逻辑与经典2值逻辑关系探究

On Relation between Three Valued Logic and Classical Binary Logic

3值逻辑与经典2值逻辑的关系问题是逻辑哲学研究的基本问题之一,通常看法是:经典2值逻辑的某些推理规律在3值逻辑中不成立,3值逻辑是经典2值逻辑的变异。结合对这一观点来源的分析,在建立了一个函数完全的3值逻辑自然推演系统的基础上,从语形和语义两个方面证明:3值逻辑是经典2值逻辑的扩充,而不是变异。

The relation between three valued logic and classical binary logic is one of the basic problems of the logic philosophy research. The general idea on it is that some inference rules in classical binary logic are false in the three valued logic and the three valued logic is a variation of the binary logic. With the analysis on this idea, based on a three valued natural deduction system which is function complete, prove in terms of syntax and semantics： the three valued logic is an extension of the binary logic rather than a variation.