Determination of α -Resolution for Lattice-Valued First-Order Logic Based on Lattice Implication Algebra

As a continuation of our research work on resolutionbased automated reasoning approaches for latticevalued logic systems with truth-values in a latticevalued logical algebraic structure – lattice implication algebra (LIA), in the present paper, we prove thatα resolution for lattice-valued first-order logic ( ) LF X based on LIA can be equivalently transformed into that for lattice-valued propositional logic ( ) LP X based on LIA, and then prove that α -resolution for latticevalued propositional logic 2 ( ) n L P X which is linguistic truth-valued propositional logic based on a lattice implication algebra based on LIA can be equivalently transformed into α -resolution for lattice-valued propositional logic ( ) n L P X based on another linguistic-valued LIA. Finally, the determination table of α -resolution of any two generalized literals under 49 cases for lattice-valued propositional logic ( ) LP X is given so that the determination ofα -resolution for lattice-valued first-order logic ( ) LF X as a key issue, can be accordingly resolved, which, at the same time, provide the key support for α -resolution automated reasoning algorithms in linguistic truth-valued logic based on LIA.