On Semantics of L-Valued First-Order Logice Lvft

Y Xu, J Liu, Qin KY, Song ZM

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


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, the semantics of a L-type lattice-valued first-order logic Lvfl with truth values in lattice implication algebras were investigated. Some basic concepts about semantics of Lvfl 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. It will become a foundation to investigate the resolution principle based on first-order logic Lvfl.

Original languageEnglish
Pages (from-to)53-79
Number of pages27
JournalInternational Journal of General Systems
Issue number1
Publication statusPublished (in print/issue) - 2000


  • many-valued logic
  • L-valued first-order logic
  • semantics of L-vfl
  • g-Skolem standard form
  • resolution principle


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