集合代数是经典命题演算形式系统的语义解释

经典命题演算形式系统(CPC)中的公式只是一些形式符号,其意义是由具体的解释给出的.逻辑代数和集合代数都是布尔代数,都是CPC的解释.集合代数是CPC的集合语义,其中对联结词的解释就是集合运算;对形式公式的解释就是集合函数;对逻辑蕴涵.逻辑等价的解释就是集合包含和集合相等=.标准概率逻辑是在标准概率空间上建立的逻辑体系,命题表示随机事件,随机事件是集合,概率空间中的事件域是集合代数,概率逻辑就是CPC集合语义的实际应用.CPC完全适用于概率命题演算.

Set Algebra is Semantic Interpretation for Classical Formal System of Propositional Calculus

The well formed formulas(wffs) in classical formal system of propositional calculus(CPC) arc only some formal symbols,whose meanings are given by a interpretation. Both logic algebra and set algebra are Boolean algebra,and are interpretations for CPC. A set algebra is a set semantics for CPC, in which set operations are the interpretation for connectives, set functions arc the interpretation for wffs, the set inclusion is the interpretation for logical implication,and the set equality= is the interpretation for logical equivalence. Standard probabilistic logic is based on a standard probabilistic space, a proposition describes a random event which is a set, the event domain in a probabilistic space is a set algebra, probabilistic logic is j ust the practical application of the set semantics for CPC. We can perform event calculus instead of probability calculus in CPC. CPC is applicable to probabilistic propositional calculus completely.