α-generalized linear resolution method based on lattice-valued propositional logic LP(X)

Abstract

The aim of this paper is to provide a more efficient approach for resolution-based automated reasoning in lattice-valued logic system. In the present paper, an a-generalized linear resolution method for lattice-valued propositional logic system LP(X) based on lattice implication algebra is established. Firstly, the properties of α-generalized resolution in lattice-valued propositional logic system are discussed. Secondly, some concepts for the α-generalized linear resolution method are presented. Both the soundness and weak completeness theorems for the α-generalized linear resolution method in LP(X) are investigated. The proposed approach efficiently deals with unsatisfiability under a truth-valued level α for a set of the general g-clauses in lattice-valued propositional logic system. This study can be expected to provide objective basis in order to design an applied automated reasoning program in the intelligent reasoning system.