Natural deduction for first-order hybrid logic

Abstract
This is a companion paper to Braüner where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geometric theories. We prove soundness and completeness and we prove a normalisation theorem. Moreover, we give an axiom system first-order hybrid logic.
Keywords First-order hybrid logic  first-order modal logic  natural deduction
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DOI 10.1007/s10849-005-3927-y
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References found in this work BETA
Papers on Time and Tense.A. N. Prior - 1968 - Oxford University Press.
First-Order Modal Logic.Melvin Fitting, R. Mendelsohn & Roderic A. Girle - 2002 - Bulletin of Symbolic Logic 8 (3):429-430.
Ideas and Results in Proof Theory.Dag Prawitz & J. E. Fenstad - 1975 - Journal of Symbolic Logic 40 (2):232-234.

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Citations of this work BETA
Natural Deduction for First-Order Hybrid Logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic.Torben Braüner - 2006 - Journal of Logic, Language and Information 15 (3):179-194.
A Proof–Theoretic Study of the Correspondence of Hybrid Logic and Classical Logic.H. Kushida & M. Okada - 2006 - Journal of Logic, Language and Information 16 (1):35-61.

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