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Journal of Logic and Computation 2001 11(5):671-689; doi:10.1093/logcom/11.5.671
© 2001 by Oxford University Press
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Internalization: The Case of Hybrid Logics

Jeremy Seligman1

1 Department of Philosophy, The University of Auckland, Private Bag 92019, Auckland, New Zealand. E-mail: j.seligman@auckland.ac.nz

A sequent calculus for hybrid logics is developed from a calculus for classical predicate logic by a series of transformations. We formalize the semantic theory of hybrid logic using a sequent calculus for predicate logic plus axioms. This works, but it is ugly. The unattractive features are removed one-by-one, until the final vestiges of the metalanguage can be set aside to reveal a fully internalized calculus. The techniques are quite general and can be applied to a wide range of hybrid and modal logics.

Keywords: Proof theory; cut-; elimination; internalization; hybrid logic; modal logic; subformula property; sequent calculus


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