Solving QMLTP Problems by Translation to Higher-order Logic

This paper 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 higher-order logic in the TPTP languages using an embedding approach, and solved using higher-order logic ATP systems. Additionally, the results from native modal logic ATP systems are considered, and compared with those from the embedding approach. The conclusions are that (i) The embedding process is reliable and successful. (ii) The choice of backend ATP system can significantly impact the performance of the embedding approach. (iii) Native modal logic ATP systems outperform the embedding approach. (iv) The embedding approach can cope with a wider range modal logics than the native modal systems considered.