α-ordered linear resolution method for lattice-valued logic system based on lattice implication algebra

An α-ordered linear resolution method for lattice-valued logic based on lattice implication algebra is proposed to provide an efficient resolution approach for resolution-based mechanical theorem proving. Firstly, some essential concepts for α-ordered linear resolution are given. The α-ordered linear resolution method for lattice-valued propositional logic system LP(X) based on lattice implication algebra is presented. Both soundness and weak completeness theorems are established. Secondly, the lifting lemma is established from LP(X) to LF(X), which is then used for obtaining the weak completeness theorem of α-ordered linear resolution method in LF(X) based on lattice implication algebra. Finally, an α-ordered linear resolution automated reasoning algorithm for lattice-valued logic system based on lattice implication algebra is designed.