α-lock semantic resolution method based on lattice-valued first-order logic LF(X)

Abstract

In this paper, an α-resolution automated reasoning method is studied based on the multiary α-resolution principle in lattice-valued first-order logic system LF(X) with truth-value in lattice implication algebra. Concretely, α-lock semantic resolution method is presented in LF(X), its soundness and condition completeness theorems have also been proved. And then α-lock semantic resolution method is further analyzed in a special lattice-valued first-order logic system—linguistic truth-valued lattice-valued first-order logic ℒ V(n×2) F(X), and the conclusion that α-lock semantic resolution method in ℒ V(n×2) F(X) can be equivalently transformed into that for another more simple lattice-valued propositional logic system ℒ Vn P(X) under some conditions is also obtained.