Operations on Propositions and Relations between Propositions in Probabilistic Propositional Logic

摘要

A probabilistic logic system is the logic description of a probabilistic space,a proposition describes a event,and the relations between propositions are the relations between the events described by the propositions. There are two layers of propositional equivalence,the equality of propositional truth values and the equality of propositional meanings. The connectives are essentially the operations on propositions,two valued logic system is homomorphic with the Boolean algebra <{0,1},-t,V,A>,so all connectives may be defined as the truth value functions on {0,1}. A probabilistic logic system is a Boolean algebra homomorphic with the event domain in a probabilistic space,so all connectives may be defined exactly by the set functions on an event domain instead of the truth value functions on {0,1/. The classical formal system of propositional calculus is also applicable to probabilistic propositions.