Journal of Philosophical Logic 21 (3):283 - 336 (1992)
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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References found in this work BETA
Entailment: The Logic of Relevance and Neccessity, Vol. I.Alan R. Anderson & Nuel D. Belnap - 1975 - Princeton University Press.
Citations of this work BETA
The First Axiomatization of Relevant Logic.Kosta Došen - 1992 - Journal of Philosophical Logic 21 (4):339 - 356.
Modal Companions of Intermediate Propositional Logics.Alexander Chagrov & Michael Zakharyashchev - 1992 - Studia Logica 51 (1):49 - 82.
Modal Logic as Metalogic.Kosta Došen - 1992 - Journal of Logic, Language and Information 1 (3):173-201.
Cartesian Isomorphisms Are Symmetric Monoidal: A Justification of Linear Logic.Kosta Došen & Zoran Petrić - 1999 - Journal of Symbolic Logic 64 (1):227-242.
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