7 found
  1.  36
    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.  8
    Rule Separation and Embedding Theorems for 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 (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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  3.  25
    Computational complexity for bounded distributive lattices with negation.Dmitry Shkatov & C. J. Van Alten - 2021 - Annals of Pure and Applied Logic 172 (7):102962.
    We study the computational complexity of the universal and quasi-equational theories of classes of bounded distributive lattices with a negation operation, i.e., a unary operation satisfying a subset of the properties of the Boolean negation. The upper bounds are obtained through the use of partial algebras. The lower bounds are either inherited from the equational theory of bounded distributive lattices or obtained through a reduction of a global satisfiability problem for a suitable system of propositional modal logic.
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  4.  15
    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.
  5.  38
    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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  6.  31
    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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  7.  13
    Complexity of the Universal Theory of Residuated Ordered Groupoids.Dmitry Shkatov & C. J. Van Alten - 2023 - Journal of Logic, Language and Information 32 (3):489-510.
    We study the computational complexity of the universal theory of residuated ordered groupoids, which are algebraic structures corresponding to Nonassociative Lambek Calculus. We prove that the universal theory is co $$\textsf {NP}$$ -complete which, as we observe, is the lowest possible complexity for a universal theory of a non-trivial class of structures. The universal theories of the classes of unital and integral residuated ordered groupoids are also shown to be co $$\textsf {NP}$$ -complete. We also prove the co $$\textsf {NP}$$ (...)
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