7 found
  1.  79
    Constructive Logic with Strong Negation is a Substructural Logic. I.Matthew Spinks & Robert Veroff - 2008 - Studia Logica 88 (3):325-348.
    The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL ew of the substructural logic FL ew . In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL ew (namely, a certain variety of FL ew -algebras) are term equivalent. This answers a longstanding question of Nelson [30]. (...)
    Direct download (5 more)  
    Export citation  
    Bookmark   14 citations  
  2.  88
    Abelian Logic and the Logics of Pointed Lattice-Ordered Varieties.Francesco Paoli, Matthew Spinks & Robert Veroff - 2008 - Logica Universalis 2 (2):209-233.
    We consider the class of pointed varieties of algebras having a lattice term reduct and we show that each such variety gives rise in a natural way, and according to a regular pattern, to at least three interesting logics. Although the mentioned class includes several logically and algebraically significant examples (e.g. Boolean algebras, MV algebras, Boolean algebras with operators, residuated lattices and their subvarieties, algebras from quantum logic or from depth relevant logic), we consider here in greater detail Abelian ℓ-groups, (...)
    Direct download (6 more)  
    Export citation  
    Bookmark   11 citations  
  3.  6
    Nelson’s Logic ????Thiago Nascimento, Umberto Rivieccio, João Marcos & Matthew Spinks - 2020 - Logic Journal of the IGPL 28 (6):1182-1206.
    Besides the better-known Nelson logic and paraconsistent Nelson logic, in 1959 David Nelson introduced, with motivations of realizability and constructibility, a logic called $\mathcal{S}$. The logic $\mathcal{S}$ was originally presented by means of a calculus with infinitely many rule schemata and no semantics. We look here at the propositional fragment of $\mathcal{S}$, showing that it is algebraizable, in the sense of Blok and Pigozzi, with respect to a variety of three-potent involutive residuated lattices. We thus introduce the first known algebraic (...)
    Direct download (3 more)  
    Export citation  
    Bookmark   1 citation  
  4.  41
    Quasi-Subtractive Varieties.Tomasz Kowalski, Francesco Paoli & Matthew Spinks - 2011 - Journal of Symbolic Logic 76 (4):1261-1286.
    Varieties like groups, rings, or Boolean algebras have the property that, in any of their members, the lattice of congruences is isomorphic to a lattice of more manageable objects, for example normal subgroups of groups, two-sided ideals of rings, filters (or ideals) of Boolean algebras.algebraic logic can explain these phenomena at a rather satisfactory level of generality: in every member A of a τ-regular variety the lattice of congruences of A is isomorphic to the lattice of deductive filters on (...)
    Direct download (6 more)  
    Export citation  
    Bookmark   2 citations  
  5.  4
    Skew Lattices and Binary Operations on Functions.Karin Cvetko-Vah, Jonathan Leech & Matthew Spinks - 2013 - Journal of Applied Logic 11 (3):253-265.
  6.  61
    On a Homomorphism Property of Hoops.Robert Veroff & Matthew Spinks - 2004 - Bulletin of the Section of Logic 33 (3):135-142.
    Direct download  
    Export citation  
    Bookmark   1 citation  
  7.  6
    Discriminator Logics.Matthew Spinks, Robert Bignall & Robert Veroff - 2014 - Australasian Journal of Logic 11 (2).
    A discriminator logic is the 1 -assertional logic of a discriminator variety V having two constant terms 0 and 1 such that V ⊨ 0 1 iff every member of V is trivial. Examples of such logics abound in the literature. The main result of this research announcement asserts that a certain non-Fregean deductive system SBPC, which closely resembles the classical propositional calculus, is canonical for the class of discriminator logics in the sense that any discriminator logic S can be (...)
    Direct download (2 more)  
    Export citation