Intuitionistic Existential Instantiation and Epsilon Symbol

Abstract

A natural deduction system for intuitionistic predicate logic with existential instantiation rule presented here uses Hilbert’s ϵ -symbol. It is conservative over intuitionistic predicate logic. We provide a completeness proof for a suitable Kripke semantics, sketch an approach to a normalization proof, survey related work and state some open problems. Our system extends intuitionistic systems with ϵ -symbol due to Dragalin and Maehara.