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Functional Completenes for a Natural Deduction Formulation of Hybridized S5

In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 31-49 (1998)

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  1. Why does the proof-theory of hybrid logic work so well?Torben Braüner - 2007 - Journal of Applied Non-Classical Logics 17 (4):521-543.
    This is primarily a conceptual paper. The goal of the paper is to put into perspective the proof-theory of hybrid logic and in particular, try to give an answer to the following question: Why does the proof-theory of hybrid logic work so well compared to the proof-theory of ordinary modal logic?Roughly, there are two different kinds of proof systems for modal logic: Systems where the formulas involved in the rules are formulas of the object language, that is, ordinary modal-logical formulas, (...)
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  • A Deep Inference System for the Modal Logic S5.Phiniki Stouppa - 2007 - Studia Logica 85 (2):199-214.
    We present a cut-admissible system for the modal logic S5 in a formalism that makes explicit and intensive use of deep inference. Deep inference is induced by the methods applied so far in conceptually pure systems for this logic. The system enjoys systematicity and modularity, two important properties that should be satisfied by modal systems. Furthermore, it enjoys a simple and direct design: the rules are few and the modal rules are in exact correspondence to the modal axioms.
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  • Proof-Theoretic Functional Completeness for the Hybrid Logics of Everywhere and Elsewhere.Torben Braüner - 2005 - Studia Logica 81 (2):191-226.
    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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