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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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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