Tree-Sequent Methods for Subintuitionistic Predicate Logics

  • Ryo Ishigaki
  • Kentaro Kikuchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4548)


Subintuitionistic logics are a class of logics defined by using Kripke models with more general conditions than those for intuitionistic logic. In this paper we study predicate logics of this kind by the method of tree-sequent calculus (a special form of Labelled Deductive System). After proving the completeness with respect to some classes of Kripke models, we introduce Hilbert-style axiom systems and prove their completeness through a translation from the tree-sequent calculi. This gives a solution to the problem posed by Restall.


Modal Logic Inference Rule Predicate Logic Intuitionistic Logic Itionistic Logic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ryo Ishigaki
    • 1
  • Kentaro Kikuchi
    • 2
  1. 1.Department of Mathematical and Computing Sciences, Tokyo Institute of TechnologyJapan
  2. 2.Research Institute of Electrical Communication, Tohoku UniversityJapan

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