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Internalization: The Case of Hybrid Logics

A sequent calculus for hybrid logics is developed from a calculus for classical predicat 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 unnattractive 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.