1-minimal resolution principle based on lattice-valued propositional logic LP(X)

Abstract

Based on the academic ideas of resolution-based automated reasoning and the previously established research work on binary a-resolution based automated reasoning schemes in the framework of lattice-valued logic with truth-values in a lattice algebraic structure - lattice implication algebras (LIA), this paper is focused on investigating α-n(t)-ary resolution based dynamic automated reasoning system based on lattice-valued propositional logic LP(X) based in LIA. One of key issues for α-n(t) ary resolution automated reasoning for LP(X) is how to choose generalized literals. In this paper, the definition of α-minimal resolution principle which determines how to choose generalized literals in LP(X) is introduced. Then, its soundness and completeness are proved. These results lay the foundation for research of α-n(t) ary resolution automated reasoning.