α-Satisfiability and α-Lock Resolution for a Lattice-Valued Logic LP(X)

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


This paper focuses on some automated reasoning issues for a kind of lattice-valued logic LP(X) based on lattice-valued algebra. Firstly some extended strategies from classical logic to LP(X) are investigated in order to verify the α-satisfiability of formulae in LP(X) while the main focus is given on the role of constant formula played in LP(X) in order to simply the verification procedure in the semantic level. Then, an α-lock resolution method in LP(X) is proposed and the weak completeness of this method is proved. The work will provide a support for the more efficient resolution based automated reasoning in LP(X).


lattice-valued logic α-resolution principle α-satisfiability α-lock resolution method 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Xingxing He
    • 1
  • Yang Xu
    • 1
  • Yingfang Li
    • 2
  • Jun Liu
    • 3
  • Luis Martinez
    • 4
  • Da Ruan
    • 5
  1. 1.Intelligent Control Development CenterSouthwest Jiaotong UniversityChengduPR China
  2. 2.Department of MathematicsSouthwest Jiaotong UniversityChengduPR China
  3. 3.School of Computing and MathematicsUniversity of UlsterNorthern Ireland, UK
  4. 4.Department of ComputingUniversity of JaénJaénSpain
  5. 5.Belgian Nuclear Research Centre (SCK∘CEN)Mol, and Ghent UniversityBelgium

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