, Volume 76, Issue 2, pp 241-274

Rule Separation and Embedding Theorems for Logics Without Weakening

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Abstract

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.