Abstract
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.
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BraÜner, T. Natural Deduction for First-Order Hybrid Logic. J Logic Lang Inf 14, 173–198 (2005). https://doi.org/10.1007/s10849-005-3927-y
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DOI: https://doi.org/10.1007/s10849-005-3927-y