Rule separation and embedding theorems for logics without weakening

Studia Logica 76 (2):241-274 (2004)
A full separation theorem for the derivable rules of intuitionistic linear logic without bounds, 0 and exponentials is proved. Several structural consequences of this theorem for subreducts of (commutative) residuated lattices are obtained. The theorem is then extended to the logic LR + and its proof is extended to obtain the finite embeddability property for the class of square increasing residuated lattices.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/B:STUD.0000032087.02579.e2
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James G. Raftery (2013). Order algebraizable logics. Annals of Pure and Applied Logic 164 (3):251-283.

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