Abstract
In this paper, we show the equivalence between the provability of a proof system of basic hybrid logic and that of translated formulas of the classical predicate logic with equality and explicit substitution by a purely proof–theoretic method. Then we show the equivalence of two groups of proof systems of hybrid logic: the group of labelled deduction systems and the group of modal logic-based systems.
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Kushida, H., Okada, M. A proof–theoretic study of the correspondence of hybrid logic and classical logic. JoLLI 16, 35–61 (2007). https://doi.org/10.1007/s10849-006-9023-0
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DOI: https://doi.org/10.1007/s10849-006-9023-0