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Natural Deduction for First-Order Hybrid Logic
Authors:Torben?Braüner  author-information"  >  author-information__contact u-icon-before"  >  mailto:torben@ruc.dk"   title="  torben@ruc.dk"   itemprop="  email"   data-track="  click"   data-track-action="  Email author"   data-track-label="  "  >Email author
Affiliation:(1) Department of Computer Science, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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.
Keywords:First-order hybrid logic  first-order modal logic  natural deduction
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