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

Abstract:

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
https://www.irit.fr/~Andreas.Herzig