Modal translations in substructural logics

Journal of Philosophical Logic 21 (3):283 - 336 (1992)
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Substructural logics are logics obtained from a sequent formulation of intuitionistic or classical logic by rejecting some structural rules. The substructural logics considered here are linear logic, relevant logic and BCK logic. It is proved that first-order variants of these logics with an intuitionistic negation can be embedded by modal translations into S4-type extensions of these logics with a classical, involutive, negation. Related embeddings via translations like the double-negation translation are also considered. Embeddings into analogues of S4 are obtained with the help of cut elimination for sequent formulations of our substructural logics and their modal extensions. These results are proved for systems with equality too.



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The first axiomatization of relevant logic.Kosta Došen - 1992 - Journal of Philosophical Logic 21 (4):339 - 356.
Algebraic Study of Two Deductive Systems of Relevance Logic.Josep Maria Font & Gonzalo Rodríguez - 1994 - Notre Dame Journal of Formal Logic 35 (3):369-397.
Modal logic as metalogic.Kosta Došen - 1992 - Journal of Logic, Language and Information 1 (3):173-201.

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