Rule Separation and Embedding Theorems for Logics Without Weakening |
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| Authors: | Van Alten Clint J. Raftery James G. |
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| Affiliation: | (1) School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, 2050, Johannesburg, South Africa |
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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. |
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| Keywords: | linear logic separation theorem residuated lattice finite embeddability property Lattice-R |
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