Natural Deduction for First-Order Hybrid Logic

Authors:
Torben Braüner
Affiliations:
Department of Computer Science, Roskilde University, Roskilde, Denmark DK-4000
Venue:
Journal of Logic, Language and Information
Year:
2005

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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.