Proof-finding Algorithms for Classical and Subclassical Propositional Logics

Abstract

The formulas-as-types isomorphism tells us that every proof and theorem, in the intuitionistic implicational logic $H_{\to }$, corresponds to a lambda term or combinator and its type. The algorithms of Bunder very efficiently find a lambda term inhabitant, if any, of any given type of $H_{\to }$ and of many of its subsystems. In most cases the search procedure has a simple bound based roughly on the length of the formula involved. Computer implementations of some of these procedures were done in Dekker. In this paper we extend these methods to full classical propositional logic as well as to its various subsystems. This extension has partly been implemented by Oostdijk.