Probabilistic logic system is Boolean algebra homomorphic with set algebra

Abstract-The connectives are essentially the logical operations on propositions, two valued logic system is homomorphic with the Boolean algebra <;{0,1},-i,v,λ>;, so all connectives may be defined by the truth value functions on {0,1}. In probabilistic logic, any function on [0,1] isn´t true of all propositions because of propositional meanings. A probabilistic logic system is the logical description of a probabilistic space, the event domain in a probabilistic space is a set algebra, and probabilistic logic system is a Boolean algebra homomorphic with set algebra. All connectives can be defined exactly by set functions on event domain instead of the truth value functions on [0,1]. The classical formal system of propositional calculus is applicable to probabilistic propositions completely.