A Constructive Completeness Proof for Intuitionistic Propositional Calculus

http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR90-1179
unofficial copies [PDF], [PS]


by Judith Underwood

Cornell University Technical Report TR90-1179, 1990.

Abstract

This paper presents a constructive proof of completeness of Kripke models for the intuitionistic propositional calculus. The computational content of the proof is a form of the tableau decision procedure. If a formula is valid, the algorithm produces a proof of the formula in the form of an inhabitant of the corresponding type; if not, it produces a Kripke model and a state in the model such that the formula is not forced at that state in that model.