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 alpha -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 alpha -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 alpha (i.e., alpha -false), is established, and the theorems of both soundness and completeness of this alpha -resolution principle are also proved. This will become the theoretical foundation for automated reasoning based on lattice-valued logical LP(X). (C) 2000 Elsevier Science Inc. All rights reserved.