Solving Quantified Modal Logic Problems by Translation to Classical Logics

TL;DR

This paper evaluates translating quantified modal logic problems into classical logics to leverage existing ATP systems, showing the embedding approach is reliable and versatile.

Contribution

It demonstrates that embedding modal logic into classical logic is effective and can outperform native modal ATP systems in certain tasks.

Findings

Embedding process is reliable with state-of-the-art ATP systems.

First-order and higher-order embeddings perform similarly.

Native modal ATP systems are outperformed by the embedding approach for disproving conjectures.

Abstract

This article describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to both typed first-order and higher-order logic in the TPTP language using an embedding approach, and solved using first-order resp. higher-order logic ATP systems and model finders. Additionally, the results from native modal logic ATP systems are considered, and compared with the results from the embedding approach. The findings are that the embedding process is reliable and successful when state-of-the-art ATP systems are used as backend reasoners, The first-order and higher-order embeddings perform similarly, native modal logic ATP systems have comparable performance to classical systems using the embedding for proving theorems, native modal logic ATP systems are outperformed by the embedding approach for disproving conjectures, and the embedding approach can cope with a wider range of modal logics than the native modal systems considered.