Verifying the Modal Logic Cube Is an Easy Task (For Higher-Order Automated Reasoners)

Prominent logics, including quantified multimodal logics, can be elegantly embedded in simple type theory (classical higher-order logic). Furthermore, off-the-shelf reasoning systems for simple type type theory exist that can be uniformly employed for reasoning within and about embedded logics. In this paper we focus on reasoning about modal logics and exploit our framework for the automated verification of inclusion and equivalence relations between them. Related work has applied first-order automated theorem provers for the task. Our solution achieves significant improvements, most notably, with respect to elegance and simplicity of the problem encodings as well as with respect to automation performance.