命题逻辑系统Ｌn中公式相对于有限理论的∑Γ－模糊真度理论

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命题逻辑系统Ｌ_n中公式相对于有限理论的∑_Γ^－模糊真度理论

吴洪博¹,乔希民^1,2

1. 陕西师范大学数学与信息科学学院, 陕西西安 710062; 2. 商洛学院数学系，陕西商洛 726000

收稿日期:2008-03-17 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 吴洪博

The ∑_Γ^－fuzzy truth degree of formula relative to the finite theory in propositional logic system Ln

WU Hong-bo¹, QIAO Xi-min^1,2

1. Instititue of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China;2. Department of Mathematics, Shangluo 726000, Shaanxi, China

Received:2008-03-17 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: WU Hong-bo

摘要/Abstract

摘要： 将模糊命题逻辑系统中的∑-(α-重言式)理论与计量逻辑学中的真度理论相结合,在n-值Lukasievicz模糊命题逻辑系统Ln中引入了公式相对于有限理论的∑_Γ^－模糊真度理论,讨论了其中的主要性质。特别地证明了真度关系:τ_Γ(A)+τ_Γ(A→B)≤1+τ_Γ(B),并利用这一关系在模糊命题演算系统Ln中的公式集F(S)上引入相对于有限理论的Γ-伪距离, 从而为在模糊命题逻辑系统Ln中建立相对于有限理论的近似推理框架奠定了基础。

关键词: 多值逻辑, Γ-伪距离, ∑_Γ^－模糊真度, 有限理论, 逻辑系统Ln

Abstract: Abstract: The theory of ∑-α-tautologies of fuzzy propositional logic was combined with the theory of truth degree in metrology of logic introduced by professor G.J.Wang, and the theory of ∑_Γ^－fuzzy truth degrees of formula relative to the finite theory in propositional logic system n was introduced. By employing the theory of ∑_Γ^－fuzzy truth degree, the concepts of Γ-pseudometric on F(S) was proposed in the propositional logic system Ln. The results obtained can complement and enhance the original theory of metrology of logic, and can give a new frame for fuzzy reasoning study.

Key words: Γ-pseudometric

, ∑_Γ^－fuzzy truth degree, finite theory, logic system Ln, many valued logic

中图分类号:

O141.1

吴洪博,乔希民, . 命题逻辑系统Ｌ_n中公式相对于有限理论的∑_Γ^－模糊真度理论[J]. J4, 2008, 43(6): 1-8 .

WU Hong-bo,QIAO Xi-min, . The ∑_Γ^－fuzzy truth degree of formula relative to the finite theory in propositional logic system Ln[J]. J4, 2008, 43(6): 1-8 .

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