α-group Semantic Resolution Method Based on Lattice-valued Propositional Logic System LP(X)

摘要

On the basis of α -group resolution principle, an a -group resolution automated reasoning method for lattice-valued prepositional logic system LP(X) based on lattice implication algebra is proposed in the present paper. Firstly, α -group semantic resolution method is established in LP(X), as well as its soundness and condition completeness. Secondly, α -group semantic resolution in lattice-valued propositional logic [L_n×L_2)P(X) is equivalently transformed into that in lattice-valued propositional logic L_n P(X) under certain conditions. Finally, as product lattice implication algebra L_n × L_2 and linguistic truth-valued lattice implication algebra L_(V(n×2)) have the same structure, the conclusion that α -group semantic resolution in linguistic truth-valued lattice-valued propositional logic L_(V(n×2)) P(X) is equivalent to that in lattice-valued propositional logic L_(Vn)P_(X) is also obtained.