Combining Classical and Intuitionistic Implications

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.

• Type: Conference
• Year: 2007
• Where: FROCOS
• Authors: Carlos Caleiro, Jaime Ramos
• Keywords: FROCOS 2007, Intuitionistic Logics, Nice Complete Axiomatization, Simple Mixed Axioms