Theorem Provers for Every Normal Modal Logic

We present a procedure for algorithmically embedding problems formulated in higher- order modal logic into classical higher-order logic. The procedure was implemented as a stand-alone tool and can be used as a preprocessor for turning TPTP THF-compliant the- orem provers into provers for various modal logics. The choice of the concrete modal logic is thereby specified within the problem as a meta-logical statement. This specification for- mat as well as the underlying semantics parameters are discussed, and the implementation and the operation of the tool are outlined.
By combining our tool with one or more THF-compliant theorem provers we accomplish the most widely applicable modal logic theorem prover available to date, i.e. no other available prover covers more variants of propositional and quantified modal logics. Despite this generality, our approach remains competitive, at least for quantified modal logics, as our experiments demonstrate.