Abstract
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 Jiaolong University (in Chinese), Sum. No. 89(1), 20-27, 1993, and L-valued propositional logic vft, established by Xu et al. (Information Sciences, 114, 20S-235, 1999a), the semantics of a L-type lattice-valued first-order logic Lvft, with truth values in lattice implication algebras were investigated. Some basic concepts about semantics of Lvftsuch 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. It will become a foundation to investigate the resolution principle based on first-order logic Lvft
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