On Automatic Theorem Proving with ML

Abstract

In this paper, we describe the development of a series of automatic theorem provers for a variety of logics. Provers are developed from a functional approach. The first prover is for Classical Propositional Calculus (CPC), which is based on a constructive proof of Kalmar's Theorem. We also provide the implementation of a cut and contraction free sequent calculus for Intuitionistic Propositional Logic (IPC). Next, it is introduced a prover for ALCS4, which is the description logic ALC with transitive and reflexive roles only. This prover is also based on a cut and contraction free sequent calculus. We also provide a complexity analysis for each prover.