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On Compactness and Consistency in Finite Lattice-Valued Propositional Logic

  • Xiaodong Pan
  • Yang Xu
  • Luis Martinez
  • Da Ruan
  • Jun Liu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6077)

Abstract

In this paper, we investigate the semantical theory of finite lattice-valued propositional logic based on finite lattice implication algebras. Based on the fuzzy set theory on a set of formulas, some propositions analogous to those in the classical logic are proved, and using the semantical consequence operation, the consistence and compactness is investigated.

Keywords

Lattice-valued logic Consequence operation Compactness Fuzzy theory Consistency 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Xiaodong Pan
    • 1
  • Yang Xu
    • 1
  • Luis Martinez
    • 2
  • Da Ruan
    • 3
  • Jun Liu
    • 4
  1. 1.Intelligent Control Development CenterSouthwest Jiaotong University, ChengduSichuanPR China
  2. 2.Department of ComputingUniversity of JaénJaénSpain
  3. 3.Belgian Nuclear Research Centre (SCK·CEN)Mol, and Ghent UniversityBelgium
  4. 4.School of Computing and MathematicsUniversity of UlsterNorthern Ireland, UK

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