Abstract: 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.

Key words: CPC, Probabilistic propositional logic, Probabilistic space, Set algebra, Homomorphism