Combining Classical and Intuitionistic Implications

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


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.


Combine Model Intuitionistic Logic Kripke Model Philosophical Logic Conservative Extension 
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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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