模态逻辑公理的粗糙真语义分析

Semantic Analyses of Rough Truth for Axioms in Modal Logic

粗糙真是Pawlak粗糙逻辑的5个逻辑值之一,介于真与假之间.通过对论域Un上所有近似空间相互关系的讨论,构造了一类代数结构——格,这类格形成了特殊的克里普克语义模型.其目的就是要在这种模型中,对模态逻辑形式推理系统的公理进行语义分析.这种分析不限于真与假的二值讨论,而主要对粗糙真进行重点研究.最终的结果表明模态逻辑形式系统的公理在这类特殊语义模型中基本都粗糙真有效.从而也得到了利用某些公理进行粗糙真形式推理的可靠性.

Rough truth which lies between truth and falsity is onc of the five logic values logic. Through considering relations between any two approximate spaces among all of U^n, a lattice is constructed, which is a kind of algebraic structure, and just using the in Pawlak rough them on domain lattice, a special Kripke model is developed. Within this model, semantic analyses are discussed for axioms of the formal reasoning system in modal logic. Instead of discussing only two values of truth and falsity, the discussions mainly focus on the analyses of rough truth. The conclusions show that the axioms of the formal reasoning system in modal logic are almost rough truth validity within the special Kripke model. Thus soundness would be gained when using some of the axioms to make formal reasoning.