Quantitative Method for Multi-Value Modal Logics

Abstract

在多值模态逻辑中构建了n-值模态模型及相应的语义理论,并指出这种语义是经典模态逻辑语义的推广.定义了〈W,R〉_n-型框架的概念,并在该框架下用归纳的方法构建了由模态公式诱导的局部化映射,给出公式的局部化真度的概念,并指出任意模态公式的局部化真度都可以转化为另一个不含模态词的公式在同一可能世界处的局部化真度.定义了模态公式的全局真度,并证明了当某模态公式不含模态词时,其全局真度与其在一般命题逻辑中的真度一致.;The concept of n-valued modal model for multi-value modal logics is introduced in this paper, and the corresponding semantics are constructed. The study points out this kind of semantics and generalizes the semantics for classical modal logics. The definition of 〈W,R〉_n-typed frame is presented, under which the localized mappings induced by modal formulae are constructed, and the concept of localized truth degree for modal formulae is introduced. It is obtained that the localized truth degree for any modal formula can be computed as the one for some modal formula without modalities in the same possible world. Based on these, the concept of global truth degree for modal formulae is introduced. It has been shown that whenever a modal formula contains no modalities, its global truth degree coincides with its truth degree in the common propositional logics.