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计量逻辑学(Ⅰ)
引用本文:王国俊.计量逻辑学(Ⅰ)[J].工程数学学报,2006,23(2):191-215.
作者姓名:王国俊
作者单位:陕西师范大学数学研究所,西安,710062;西安交通大学基础科学研究中心,西安,710049
摘    要:在多值命题逻辑系统中提出了公式的真度概念。基于此,提出了公式间的相似度与伪度量,研究了所得的逻辑度量空间的基本性质,提出并研究了逻辑理论的发散度与相容度概念,给出了三种近似推理的模式,初步建立了计量逻辑学理论。

关 键 词:真度  相似度  伪度量  发散度  相容度  计量逻辑
文章编号:1005-3085(2006)02-0191-25
收稿时间:2006-01-09
修稿时间:2006年1月9日

Quantitative Logic (Ⅰ)
WANG Guo-jun.Quantitative Logic (Ⅰ)[J].Chinese Journal of Engineering Mathematics,2006,23(2):191-215.
Authors:WANG Guo-jun
Abstract:The concept of truth degree of formulas in diverse propositional logic systems is proposed, and the concepts of similarity degree and pseudo-metric among formulas are introduced therefrom. Basic properties of the induced logic metric space are investigated, of which theories of divergency degree and consistency degree of a logic theory are developed, and three types of approximate reasoning models are proposed as well, and an elementary quantitative logic theory is hence established.
Keywords:truth degree  similarity degree  pseudo-metric  divergency degree  consistency degree  quantitative logic
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