ON SOME EXTENSIONS OF INTUITIONISTIC LOGIC
Rodolfo C. Ertola-Biraben · 2012
We prove that many extensions of Intuitionistic Sentential Calculus ISC with new intuitionistic connectives that are known to be conservative extensions of ISC are not conservative extensions of Intuitionistic Predicate Calculus because formulas such as Kuroda’s are derivable. We thus solve a problem posed by L opez-Escobar in 1985 and answer a question posed by Humberstone in 2001 regarding a connective called the strongest anticipator. In 1960 (see [12] and [13]) Smetanich introduced a new propositional intuitionistic constant connective we call and proved that the resulting extension ISC + of the Intuitionistic Sentential Calculus ISC is conservative. The logic ISC + may be given adding to any set of axiom schemas for ISC the following: