Calculus similar degree and pseudometric in calculus semantics
Wu Hong · Journal of Shaanxi Normal University · 2000
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),e0, there exists a B∈ F(S) such that 1-eξ(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).