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97A Kripke-style semantics for R-Mingle using a binary accessibility relationStudia Logica 35 (2). 1976.
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67Symmetric generalized galois logicsLogica 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
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22The impossibility of certain higher-order non-classical logics with extensionalityIn D. F. Austin (ed.), Philosophical Analysis, Kluwer Academic Publishers. pp. 261--279. 1988.
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95Quantum MathematicsPSA: 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
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49Completeness of relevant quantification theoriesNotre Dame Journal of Formal Logic 15 (1): 97-121. 1974.
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71A theorem in 3-valued model theory with connections to number theory, type theory, and relevant logicStudia Logica 38 (2). 1979.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
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38Algebraic Completeness Results for Dummett's LC and Its ExtensionsMathematical Logic Quarterly 17 (1): 225-230. 1971.
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50A relational representation of quasi-Boolean algebrasNotre Dame Journal of Formal Logic 23 (4): 353-357. 1982.
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Computing and Information |
Areas of Interest
Philosophy of Mind |
Philosophy of Cognitive Science |
Philosophy of Mathematics |