Linguistic truth-valued lattice-valued propositional logic system lP(X) based on linguistic truth-valued lattice implication algebra

  • Authors:

  • Jiajun Lai;Yang Xu

  • Affiliations:

  • Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, P.R. China and School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, P ...;Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, P.R. China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2010

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Abstract

In the semantics of natural language, quantification may have received more attention than any other subject, and syllogistic reasoning is one of the main topics in many-valued logic studies on inference. Particularly, lattice-valued logic, a kind of important non-classical logic, can be applied to describe and treat incomparability by the incomparable elements in its truth-valued set. In this paper, we first focus on some properties of linguistic truth-valued lattice implication algebra. Secondly, we introduce some concepts of linguistic truth-valued lattice-valued propositional logic system @?P(X), whose truth-valued domain is a linguistic truth-valued lattice implication algebra. Then we investigate the semantic problem of @?P(X). Finally, we further probe into the syntax of linguistic truth-valued lattice-valued propositional logic system @?P(X), and prove the soundness theorem, deduction theorem and consistency theorem.