Luis Fariņas del Cerro and Andreas Herzig, Combining classical and intuitionistic logic, or: intuitionistic implication as a conditional

We study how a logic CJ conbining classical logic C and intuitionistic logic J can be defined. We show that its Hilbert axiomatization cannot be attained by simply extending the union of the axiomatizations of C and J by so called interaction axioms. (Such a logic would collapse into classical logic.) We solve that problem by by a suitable restriction on the axiomatics of C, and give a tableau calculus.
In: Baader, Franz and Schulz, Klaus U., eds., ``Frontiers in Combining Systems (Proc. Int. Workshop FroCoS'96)''. Kluwer Academic Publishers, Applied Logic Series 3, 1996, pages 93--102
Get Postscript