Rule Separation and Embedding Theorems for Logics without Weakening

Studia Logica 76 (2):241 - 274 (2004)
Abstract
A full separation theorem for the derivable rules of intuitionistic linear logic without bounds, 0 and exponemtials 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.
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