Proof-theoretic functional completeness for the hybrid logics of everywhere and elsewhere

Studia Logica 81 (2):191 - 226 (2005)
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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Torben Braüner (2007). Why Does the Proof-Theory of Hybrid Logic Work so Well? Journal of Applied Non-Classical Logics 17 (4):521-543.
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