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Journal of Logic and Computation 2004 14(3):329-353; doi:10.1093/logcom/14.3.329
© 2004 by Oxford University Press
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Original Article

Natural Deduction for Hybrid Logic

Torben Braüner

Department of Computer Science, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark. E-mail: torben{at}ruc.dk

In this paper we give a natural deduction formulation of hybrid logic. Our natural deduction system can be extended with additional inference rules corresponding to conditions on the accessibility relations expressed by so-called geometric theories. Thus, we give natural deduction systems in a uniform way for a wide class of hybrid logics which appears to be impossible in the context of ordinary modal logic. We prove soundness and completeness and we prove a normalization theorem. We finally prove a result which says that normal derivations in the natural deduction system correspond to derivations in a cut-free Gentzen system.

Keywords: Hybrid logic, modal logic, natural deduction, Gentzen systems

Received 16 August 2001.


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