Rule Separation and Embedding Theorems for Logics Without Weakening
- Cite this article as:
- Van Alten, C.J. & Raftery, J.G. Studia Logica (2004) 76: 241. doi:10.1023/B:STUD.0000032087.02579.e2
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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.