Internalization: The case of hybrid logics. (English) Zbl 0991.03024

Seligman, Jeremy

J. Log. Comput. 11, No. 5, 671-689 (2001).

The author presents a method of internalization for hybrid logic. It works in three steps. First the semantic theory of hybrid logic is formalized in a sequent calculus of predicate logic with additional axioms. In a second step a refined calculus with the subformula property is introduced which, however, is not fully internalized. This is solved in a third step by another calculus which uses a hybrid operator. In the final paragraph the author claims that the given strategy can be applied to a wide range of logical operations but that the exact limits of the method are still open.

Reviewer: Reinhard Kahle (Tübingen)

MSC:

03B45	Modal logic (including the logic of norms)
03F05	Cut-elimination and normal-form theorems

Keywords:

internalization; hybrid logic; sequent calculus