Proof Search in the Intuitionistic Sequent Calculus

The use of Ilerbrand functions (sometimes called Skolemization) plays an important role in classical theorem proving and logic programming. We define a notion of Herbrand functions for the full intuitionistic predicate calculus. This definition is based on the view that the proof-theoretic role of Herbrand functions (to replace universal quantifiers), and of unification (to find instances corresponding to existential quantifiers), is to ensure the eigenvariable conditions on a sequent proof. The propositional impermutabilities that arise in the intuitionistic but not the classical sequent calculus motivate a generalization of the classical notion of Ilerbrand functions. This generalization of Herbrand functions also applies to the sequent calculus formalizations of logics other than intuitionistic predicate calculus.

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