•  96
    Relevant predication 1: The formal theory (review)
    Journal of Philosophical Logic 16 (4): 347-381. 1987.
  •  58
    Negation in the Context of Gaggle Theory
    Studia Logica 80 (2): 235-264. 2005.
    We study an application of gaggle theory to unary negative modal operators. First we treat negation as impossibility and get a minimal logic system Ki that has a perp semantics. Dunn 's kite of different negations can be dealt with in the extensions of this basic logic Ki. Next we treat negation as “unnecessity” and use a characteristic semantics for different negations in a kite which is dual to Dunn 's original one. Ku is the minimal logic that has a characteristic semantics. We also show that…Read more
  •  125
    Contradictory Information: Too Much of a Good Thing (review)
    Journal of Philosophical Logic 39 (4). 2010.
    Both I and Belnap, motivated the "Belnap-Dunn 4-valued Logic" by talk of the reasoner being simply "told true" (T) and simply "told false" (F), which leaves the options of being neither "told true" nor "told false" (N), and being both "told true" and "told false" (B). Belnap motivated these notions by consideration of unstructured databases that allow for negative information as well as positive information (even when they conflict). We now experience this on a daily basis with the Web. But the …Read more
  •  161
    Curry’s Paradox
    with Robert K. Meyer and Richard Routley
    Analysis 39 (3). 1979.
  •  69
    Symmetric generalized galois logics
    Logica Universalis 3 (1): 125-152. 2009.
    Symmetric generalized Galois logics (i.e., symmetric gGl s) are distributive gGl s that include weak distributivity laws between some operations such as fusion and fission. Motivations for considering distribution between such operations include the provability of cut for binary consequence relations, abstract algebraic considerations and modeling linguistic phenomena in categorial grammars. We represent symmetric gGl s by models on topological relational structures. On the other hand, topologic…Read more
  •  2
    Entailment: The Logic of Relevance and Necessity, Vol. II
    with Alan Ross Anderson and Nuel D. Belnap
    Princeton University Press. 1992.
  •  96
    Quantum Mathematics
    PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980. 1980.
    This paper explores the development of mathematics on a quantum logical base when mathematical postulates are taken as necessary truths. First it is shown that first-order Peano arithmetic formulated with quantum logic has the same theorems as classical first-order Peano arithmetic. Distribution for first-order arithmetical formulas is a theorem not of quantum logic but rather of arithmetic. Second, it is shown that distribution fails for second-order Peano arithmetic without extensionality. Thi…Read more
  •  45
    Is Existence a (Relevant) Predicate?
    Philosophical Topics 24 (1): 1-34. 1996.
  •  71
    Given classical (2 valued) structures and and a homomorphism h of onto , it is shown how to construct a (non-degenerate) 3-valued counterpart of . Classical sentences that are true in are non-false in . Applications to number theory and type theory (with axiom of infinity) produce finite 3-valued models in which all classically true sentences of these theories are non-false. Connections to relevant logic give absolute consistency proofs for versions of these theories formulated in relevant logic…Read more
  •  51
    Completeness of relevant quantification theories
    with Robert K. Meyer and Hugues Leblanc
    Notre Dame Journal of Formal Logic 15 (1): 97-121. 1974.
  •  37
    Algebraic Completeness Results for Dummett's LC and Its Extensions
    with Robert K. Meyer
    Mathematical Logic Quarterly 17 (1): 225-230. 1971.
  •  51