Recovering Intuition from Automated Formal Proofs using Tableaux with Superdeduction

TL;DR

This paper introduces a novel automated deduction method using tableaux and superdeduction principles to produce proofs that resemble human reasoning, applicable across various theories.

Contribution

The paper presents two implementations of a tableaux-based automated deduction method enriched with superdeduction, enhancing proof naturalness and applicability to multiple theories.

Findings

Generated more human-like proofs compared to traditional methods.

Successfully applied to set theory and other theories from the TPTP library.

Extended the Zenon theorem prover with new deduction rules.

Abstract

We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and uses the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. We present two implementations of this method, which consist of extensions of the Zenon automated theorem prover. The first implementation is a version dedicated to the set theory of the B formal method, while the second implementation is a generic version able to deal with any first order theory. We also provide several examples of problems, which can be handled by these tools and which come from different theories, such as the B set theory or theories of the TPTP library.