Natural deduction for first-order hybrid logic

Journal of Logic, Language and Information 14 (2):173-198 (2005)
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Abstract

This is a companion paper to Braüner 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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Citations of this work

Natural deduction for first-order hybrid logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
Axioms for classical, intuitionistic, and paraconsistent hybrid logic.Torben Braüner - 2006 - Journal of Logic, Language and Information 15 (3):179-194.
A proof–theoretic study of the correspondence of hybrid logic and classical logic.H. Kushida & M. Okada - 2006 - Journal of Logic, Language and Information 16 (1):35-61.

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References found in this work

Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
A New Introduction to Modal Logic.M. J. Cresswell & G. E. Hughes - 1996 - New York: Routledge. Edited by M. J. Cresswell.
Papers on time and tense.Arthur Norman Prior - 1968 - New York: Oxford University Press. Edited by Per F. V. Hasle.
First-Order Modal Logic.Melvin Fitting & Richard L. Mendelsohn - 1998 - Dordrecht, Netherland: Kluwer Academic Publishers.
Papers on time and tense.A. N. Prior - 1968 - Revue Philosophique de la France Et de l'Etranger 160:500-501.

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