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

In the present paper, resolution-based automated reasoning theory in an L-type fuzzy logic is focused. Concretely, the α-resolution principle, which is based on lattice-valued propositional logic LP(X) with truth-value in a logical algebra - lattice implication algebra, is investigated. Finally, an α-resolution principle that can be used to judge if a lattice-valued logical formula in LP(X) is always false at a truth-valued level α (i.e., α-false), is established, and the theorems of both soundness and completeness of this α-resolution principle are also proved. This will become the theoretical foundation for automated reasoning based on lattice-valued logical LP(X).