5 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]. (...)
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  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, (...)
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  3.  57
    Double-Negation Elimination in Some Propositional Logics.Michael Beeson, Robert Veroff & Larry Wos - 2005 - Studia Logica 80 (2-3):195-234.
    This article answers two questions (posed in the literature), each concerning the guaranteed existence of proofs free of double negation. A proof is free of double negation if none of its deduced steps contains a term of the formn(n(t)) for some term t, where n denotes negation. The first question asks for conditions on the hypotheses that, if satisfied, guarantee the existence of a double-negation-free proof when the conclusion is free of double negation. The second question asks about the existence (...)
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  4.  61
    On a Homomorphism Property of Hoops.Robert Veroff & Matthew Spinks - 2004 - Bulletin of the Section of Logic 33 (3):135-142.
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  5.  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 (...)
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