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Journal of Computer Science and Technology

, Volume 14, Issue 2, pp 135–139 | Cite as

Phase semantics for a pure noncommutative linear propositional logic

  • Ying Mingsheng 
Correspondence
  • 19 Downloads

Abstract

We use a many-sorted language to remove commutativity from phase semantics of linear logic and show that pure noncommutative intuitionistic linear propositional logic plus two classical rules enjoys the soundness and completeness with respect to completely noncommutative phase semantics.

Keywords

linear logic phase semantics noncommutativity 

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References

  1. [1]
    Girard J-Y. Linear logic.Theoretic Computer Sci., 1987, 50: 1–102.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Girard J-Y. Towards a geometry of interaction. InCategories in Computer Science and Logic. Contemporary Mathematics 92, American Mathematical Society, Providence, Rhode Island, 1989, pp.69–108.Google Scholar
  3. [3]
    Yetter D N. Quantales and (noncommutative) linear logic.J. Symbolic Logic, 1990, 55: 41–64.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Abrusci V M. Phase semantics and sequent calculus for pure noncommutative classical linear propositional logic.J. Symbolic Logic, 1991, 56: 1403–1451.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Abrusci V M. Noncommutative intuitionistic linear propositional logic.Zeitsch. f. Math. Logik und Grundlagen d. Math., 1990, 36: 297–318.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Abrusci V M. Sequent calculus for intuitionistic linear propositional logic.Mathematical Logic, P. P. Petkov (ed.), New York: Plenum Press, 1990, pp.223–242.Google Scholar
  7. [7]
    Abrusci V M. A comparison between Lambek syntactic calculus and intuitionistic linear logic.Zeitsch. f. Math. Logik und Grundlagen d. Math., 1990, 36: 11–15.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Science Press, Beijing China and Allerton Press Inc. 1999

Authors and Affiliations

  • Ying Mingsheng 
    • 1
  1. 1.Department of Computer Science and TechnologyTsinghua UniversityBeijingP.R. China

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