摘要
基于广义重言式理论,在四种重要的命题逻辑系统Lukasiewicz系统,L*系统,Godel系统和Π系统中,引入了公式的相对Γ-重言度概念,给出了相对Γ-重言度的若干性质。利用公式的相对Γ-重言度,定义了公式间的Γ-相似度,进而导出了命题集F(S)上的一种伪距离。最后讨论了命题集F(S)上统一的近似推理理论,得到了三种类型的近似推理模式之间的内在联系。
The concept of relativeΓ-tautology degree of formulas in four important propositional logics, Lukasiewicz logic, L＊ logic, Godel logic and product logic, has been proposed, and basic properties of it are obtained. TheΓ-similarity degree between formulas is defined by means of relativeΓ-tautology degrees, and a pseudo-metric between formulas is then introduced. Finally, an approximate reasoning theory is proposed, and inner relations of three patterns of approximate reasoning are also obtained.
出处
《工程数学学报》
CSCD
北大核心
2007年第4期598-610,共13页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(10331010)
关键词
命题逻辑
相对Γ-重言度
性质
Γ-相似度
伪距离
近似推理
propositional logic
relativeΓ-tautology degree
property
Γ-similarity degree
pseudo-metric
approximate reasoning
