Natural deduction for first-order hybrid logic

This is a companion paper to Braüner (2004b, Journal of Logic and Computation 14, 329–353) 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
Gerhard Gentzen (1964). Investigations Into Logical Deduction. American Philosophical Quarterly 1 (4):288 - 306.

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Citations of this work BETA
Torben BraÜner (2005). Natural Deduction for First-Order Hybrid Logic. Journal of Logic, Language and Information 14 (2):173-198.

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