On semantics of L-valued first-order logic L-vfl
Many-valued logic system always plays a crucial role in artificial intelligence. Many researchers have paid considerable attention to lattice-valued logic with truth values in a lattice. In this paper. based on lattice implication algebras introduced by Xu (Journal of Southwest Jiaotong University (in Chinese), Sum. No. 89(1), 20-27, 1993, and L-valued propositional logic L-nu pl established by Xu et al. (Information Sciences, 114, 205-235, 1999a), the semantics of a L-type lattice-valued first-order logic L-nu fl with truth values in lattice implication algebras were investigated. Some basic concepts about semantics of L-nu fl such as the language and the interpretation etc. were given and some semantic properties also were discussed. Finally, a concept of g-Skolem standard form was introduced, and it was shown that the unsatisfiability of a given lattice-valued formula was equivalent to that of its g-Skolem standard form. II will become a foundation to investigate the resolution principle based on first-order logic L-nu fl.
l-valued first-order logic many-valued logic g-skolem standard form resolution principle semantics of l-vfl