Combining Logics in Simple Type Theory

Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be elegantly embedded in simple type theory. Furthermore, simple type theory is sufficiently expressive to model combinations of embedded logics and it has a well understood semantics. Off-the-shelf reasoning systems for simple type theory exist that can be uniformly employed for reasoning within and about combinations of logics. Combinations of modal logics and other logics are particularly relevant for multi-agent systems.

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