Certification of Prefixed Tableau Proofs for Modal Logic

TL;DR

This paper introduces a unified certification method for modal logic proofs across various formats by translating them into a common first-order polarized language and verifying with a focused sequent calculus kernel.

Contribution

It presents a novel translation and certification framework that supports multiple modal proof formats, enhancing proof verification consistency and extensibility.

Findings

Successfully certified modal proofs in labeled sequent calculi and tableaux formats

Implemented a Prolog-like checker for the logic K

Discussed extension possibilities to other modal logics

Abstract

Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the general project of establishing a common specification language in order to certify proofs given in a wide range of deductive formalisms. In particular, by using a translation from the modal language into a first-order polarized language and a checker whose small kernel is based on a classical focused sequent calculus, we are able to certify modal proofs given in labeled sequent calculi, prefixed tableaux and free-variable prefixed tableaux. We describe the general method for the logic K, present its implementation in a prolog-like language, provide some examples and discuss how to extend the approach to other normal modal logics