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.
This work was partially supported by FCT and EU FEDER, namely via the recently approved KLog project PTDC/MAT/68723/2006 of SQIG-IT, and also the QuantLog project POCI/MAT/55796/2004 of CLC.
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Caleiro, C., Ramos, J. (2007). Combining Classical and Intuitionistic Implications. In: Konev, B., Wolter, F. (eds) Frontiers of Combining Systems. FroCoS 2007. Lecture Notes in Computer Science(), vol 4720. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74621-8_8
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DOI: https://doi.org/10.1007/978-3-540-74621-8_8
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