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Combining Classical and Intuitionistic Implications

  • Carlos Caleiro
  • Jaime Ramos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4720)

Abstract

We present a simple logic that combines, in a conservative way, the implicative fragments of both classical and intuitionistic logics, thus settling a problem posed by Dov Gabbay in [5]. We also show that the logic can be given a nice complete axiomatization by adding four simple mixed axioms to the usual axiomatizations of classical and intuitionistic implications.

Keywords

Combine Model Intuitionistic Logic Kripke Model Philosophical Logic Conservative Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Carlos Caleiro
    • 1
  • Jaime Ramos
    • 1
  1. 1.SQIG-IT and CLC, Department of Mathematics, IST, TU LisbonPortugal

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