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It is known that intuitionistic Kripke semantics can be generalized so thatit can treat arbitrary propositional connectives characterized by truthfunctions. We extend this generalized Kripke semantics to first-order logic,and study how the choice of connectives changes the relation betweenintuitionistic predicate logic and the logic of constant domains in terms ofvalidity of sequents. Our main result gives a simple necessary and sufficientcondition for the set of valid sequents in intuitionistic predicate logic tocoincide with the set of valid sequents in the logic of constant domains.

What Kinds of Connectives Cause the Difference between Intuitionistic Predicate Logic and the Logic of Constant Domains?