We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational investigations of various non-classical logics. We report some experiments using the higher-order automated theorem prover LEO-II.

Abstract. We investigate cut-elimination and cut-simulation in impredicative (higherorder) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -in our case a sequent calculus for classical type theory -is like adding cut. The phenomenon equally applies to prominent axioms like Boolean-and functional extensionality, induction, choice, and description. This calls for the development of calculi where these principles are built-in instead of being treated axiomatically.

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A converter from first-order modal logics to classical higherorder logic is presented. This tool enables the application of off-the-shelf higher-order theorem provers and model finders for reasoning within firstorder modal logics. The tool supports logics K, K4, D, D4, T, S4, and S5 with respect to constant, varying and cumulative domain semantics.

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