Studia Logica

, Volume 76, Issue 2, pp 241–274

Rule Separation and Embedding Theorems for Logics Without Weakening

  • Clint J. Van Alten
  • James G. Raftery

DOI: 10.1023/B:STUD.0000032087.02579.e2

Cite this article as:
Van Alten, C.J. & Raftery, J.G. Studia Logica (2004) 76: 241. doi:10.1023/B:STUD.0000032087.02579.e2


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.

linear logic separation theorem residuated lattice finite embeddability property Lattice-R 

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Clint J. Van Alten
    • 1
  • James G. Raftery
    • 1
  1. 1.School of MathematicsUniversity of the WitwatersrandSouth Africa

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