The General Representation And Application Of Formulas In Two-valued Proposition Logic In The Meaning Of Equivalence

Through development of a long period of time,classical two-valued propositional logic is rather recipe and is extensively applied in some fields including computer science and artificial intelligence.In spite of this,some problems in two-valued propositional logic are still unsolved.It is still in development.This paper discusses three problems and acquires some new conclusions.First,the concept of truth degree of a formulas was given in conference[1].For two formulas in F(S_n),if they are provably equivalent,then they have the same truth degree.On the contrary,it is not true.This article gives the relation between the two concepts.Second,This paper gives the general representation of formulas in F(S_n) in the meaning of provable equivalence.Some preparatory work has been done in Chapter 2, then the conclusion is acquired.The concept of truth degree is used in this process.Third,In the meaning of provable equivalence between two formulas,for the setГof formulas in F(S_n),this paper provides the structure of D(Г) which consists of allГ-conclusion.In chapter 3,using the result of the general representation of formulas in the meaning of provable equivalence,through making a special mapping, the operations of∧,∨,(?),among formulas change into operations of∩,∪,' on a special set in the meaning of provable equivalence.This makes the foundation to discuss the structure of D(Г).Moreover,in Chapter 3,for a given setГof formulas in F(S_n),according to the concept of distance between two formulas given in reference[1],in the meaning of provable equivalence,the formulas which is the nearest one in D(Г) to the given formulas of F(S_n) is found.For two subsetsГ₁ andГ₂ of F(S_n),some relations between D(Г₁) and D(Г₂) are given.