现代模态逻辑的形式分析初步——魔态羽翼的跨世界逃逸与“刑师”分析下的在劫难逃

Formal Analyzing the Form of Modern Modal Logic

现代模态逻辑其实是按一阶逻辑公理和规则对经典真值函数做分类研究。模态命题逻辑中任一个可能世界集W仅表示与某一公理模式相应的一组二真值函数,相应的可能世界间的关系R就是这组真值函数共有的一种集合性质。任一公理模式在一框架内有效,就是将属于W的每个真值函数式按K-2分别依次代入该公理模式中的每一个"□",使得形成一组经典定理。

Modern modal logic,in fact,is a kind of classifying study on classical two truth-values function in terms of first order logical axioms and rules.In modal propositional logic,any set of possible worlds W only means a set of a truth-function with two variables,and the corresponding relation between possible worlds R is a set property which the set of truth-functions have in common.And the validity of any axiom schema in a framework is just that every truth-functional formula with two variables belonging to W is,in turn,substituted in each □ of the axiom schema respectively such that a set of classical theorems are formulated.