Translating Graded Modalities into Predicate Logic

Ohlbach, Hans Jürgen; Schmidt, Renate A.; Hustadt, Ullrich

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Translating Graded Modalities into Predicate Logic

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Ohlbach, Hans Jürgen
Programming Logics, MPI for Informatics, Max Planck Society;

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Schmidt, Renate A.
Programming Logics, MPI for Informatics, Max Planck Society;

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Hustadt, Ullrich
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Ohlbach, H. J., Schmidt, R. A., & Hustadt, U. (1996). Translating Graded Modalities into Predicate Logic. In H. Wansing (Ed.), Proof Theory of Modal Logic (pp. 253-291). Dordrecht, The Netherlands: Kluwer.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-AC23-6

Abstract

In the logic of graded modalities it is possible to talk about sets of finite cardinality. Various calculi exist for graded modal logics and all generate vast amounts of case distinctions. In this paper we present an optimized translation from graded modal logic into many-sorted predicate logic. This translation has the advantage that in contrast to known approaches our calculus enables us to reason with cardinalities of sets symbolically. In many cases the length of proofs for theorems of this calculus is independent of the cardinalities. The translation is sound and complete.