5 found
  1.  19
    Structural Completeness in Substructural Logics.J. S. Olson, J. G. Raftery & C. J. Van Alten - 2008 - Logic Journal of the IGPL 16 (5):453-495.
    Hereditary structural completeness is established for a range of substructural logics, mainly without the weakening rule, including fragments of various relevant or many-valued logics. Also, structural completeness is disproved for a range of systems, settling some previously open questions.
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  2.  9
    An Algebraic Look at Filtrations in Modal Logic.W. Conradie, W. Morton & C. J. van Alten - 2013 - Logic Journal of the IGPL 21 (5):788-811.
  3.  33
    On Varieties of Biresiduation Algebras.C. J. van Alten - 2006 - Studia Logica 83 (1-3):425-445.
    A biresiduation algebra is a 〈/,\,1〉-subreduct of an integral residuated lattice. These algebras arise as algebraic models of the implicational fragment of the Full Lambek Calculus with weakening. We axiomatize the quasi-variety B of biresiduation algebras using a construction for integral residuated lattices. We define a filter of a biresiduation algebra and show that the lattice of filters is isomorphic to the lattice of B-congruences and that these lattices are distributive. We give a finite basis of terms for generating filters (...)
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  4.  1
    Embedding Theorems and Rule Separation in Logics Without Weakening.C. J. van Alten & J. G. Raftery - 2004 - Studia Logica 76 (2):241-274.
    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 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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  5.  13
    The Finite Model Property for Knotted Extensions of Propositional Linear Logic.C. J. van Alten - 2005 - Journal of Symbolic Logic 70 (1):84-98.
    The logics considered here are the propositional Linear Logic and propositional Intuitionistic Linear Logic extended by a knotted structural rule: γ, xn → y / γ, xm → y. It is proved that the class of algebraic models for such a logic has the finite embeddability property, meaning that every finite partial subalgebra of an algebra in the class can be embedded into a finite full algebra in the class. It follows that each such logic has the finite model property (...)
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