Axioms for classical, intuitionistic, and paraconsistent hybrid logic

In this paper we give axiom systems for classical and intuitionistic hybrid logic. Our axiom systems can be extended with additional rules corresponding to conditions on the accessibility relation expressed by so-called geometric theories. In the classical case other axiomatisations than ours can be found in the literature but in the intuitionistic case no axiomatisations have been published. We consider plain intuitionistic hybrid logic as well as a hybridized version of the constructive and paraconsistent logic N4.
Keywords Hybrid logic  Modal logic  Intuitionistic logic  Constructive logic  Strong negation  Paraconsistent logic  Axiom systems
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DOI 10.1007/s10849-006-9013-2
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References found in this work BETA
A. S. Troelstra (1988). Constructivism in Mathematics: An Introduction. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
Torben BraÜner (2005). Natural Deduction for First-Order Hybrid Logic. Journal of Logic, Language and Information 14 (2):173-198.

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Citations of this work BETA
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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