基于基底系统的双模态逻辑系统研究

双模态逻辑是多模态逻辑的一种,该逻辑系统可以同时处理两个初始模态算子。本文从多模态基底系统出发,给出双模态逻辑系统的一般理论,即分析双模态相互作用公理及相应的框架条件,给出双模态系统的基本构成以及双模态系统的极小基础。双模态逻辑系统的一般理论具有应用意义,它是具体的双模态系统的一般化概括;同时,双模态逻辑的研究方法是研究多模态逻辑一般理论的一个新视角,对于多模态逻辑一般理论的研究具有理论意义。

A Study of Bimodal Logics Based on Basilar Systems

Bimodal logics are one kind of multimodal logics, which can deal with two primitive modal operators. From the Basilar Systems of multimodal logics, this paper gave the general theory of bimodal logic systems, i. e analyzing the properties of the interaction axioms for bimodal logics, giving the structure of bimodal logics and the minimal basis of bimodal logics. The general theory of bimodal logic systems, which is a generalization of the specific systems, has significance in application. Meanwhile, the research method of bimodal logics, whic is a new perspective for studying the general theory of multimodal logics, has theoretical significance.