数理逻辑中的数值化方法

数理逻辑的本质是形式推理而不是数值计算,非此即彼式的严谨性是其特征,因而在一定意义下它是"两极化"的.比如,(1)一个逻辑理论或者是相容的,或者是不相容的,不存在"半相容的"理论.(2)"逻辑公式A是假设集T的推论"或者成立,或者不成立,说它近似成立是无意义的.(3)逻辑公式中有重言式和矛盾式,但没有0.8重言式.本文的目的在于为上述基本概念提供程度化的版本,并从而建立一种近似推理理论.

Numerical Computations in Formalized Logic Theories

The essential character of mathematical logic is Formal Deduction rather than Computation.And logic rigour features a formalized theory where no equivocality exists. Hence basic logic Notions are polarized. For example, (1) a theory Γ is either consistent or inconsistent. (2) for anywff A,Γ|-A is either true or false and "Γ |-A is approximately true" is meaningless. etc.. (3) Moreover,the concepts of tautologics and contradications are introduced in propositional logic, they are wffs of absolutely true and absolute false propositions respectively while, say, no 3/4 tautologies are discussed in text books of mathematical logic. The aim of the present paper is to try to establish graded versions of basic logic notions mentioned above, and to provide approximate reasoning theories therefrom.