积分语义学中的积分相似度与伪距离

Calculus similar degree and pseudometric in calculus semantics

研究了积分语义学理论的相似度与伪距离 ,对特殊公式In=p1∧p2 ∧…∧pn,Un=p1∨ p2 ∨…∨ pn 的真度值进行了计算 ,给出了F(S)中的积分相似度和F(S)上的伪距离的一些性质 .得到了 :( 1 )在任何一个逻辑系统中τ(In) =1n + 1 ,τ(Un) =nn + 1 ;( 2 )在Lukasiewicz逻辑系统中 ,对公式A和正数ε ,存在公式B ,使得1 -ε<ξ(A ,B) <1 ;( 3)在Lukasiewicz逻辑系统中 ,(ⅰ )设C为矛盾式 ,则 ρ(A→C ,B→C) =ρ( A , B) ,(ⅱ ) ρ( (A→B)→B ,(C→D)→D) =ρ(A∨B ,C∨D) .

The calculus similar degree and pseudometric in the theory of calculus semantics has been studied. The true value degree of special formulas I n=p 1∧…∧p n,U n=p 1∨…∨p n has been computed and some properties of calculus similar degree and pseudometric in calculus semantics have been given. The main results are: (1) In each logic system, τ(I n)=1n+1, τ(U n) =nn+1; (2) In Lukasiewicz logic system, for any A∈F(S),ε>0, there exists a B∈ F(S) such that 1-ε<ξ(A,B)<1; (3) In Lukasiewicz logic system, (ⅰ) ρ(A→B)→B,((C→D)→D)=ρ(A∨B,C∨D) ,(ⅱ) Let C be a contradiction formula, then ρ(A→C,B→C) =ρ(A,B).