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Proof-Theoretic Functional Completeness for the Hybrid Logics of Everywhere and Elsewhere

Torben Braüner
Studia Logica: An International Journal for Symbolic Logic
Vol. 81, No. 2 (Nov., 2005), pp. 191-226
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016742
Page Count: 36
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Proof-Theoretic Functional Completeness for the Hybrid Logics of Everywhere and Elsewhere
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Abstract

A hybrid logic is obtained by adding to an ordinary modal logic further expressive power in the form of a second sort of propositional symbols called nominals and by adding so-called satisfaction operators. In this paper we consider hybridized versions of S5 ("the logic of everywhere") and the modal logic of inequality ("the logic of elsewhere"). We give natural deduction systems for the logics and we prove functional completeness results.

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