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20Generalized Galois Logics: Relational Semantics of Nonclassical Logical CalculiCenter for the Study of Language and Inf. 2008.Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. _Generalized Galois Logics_ develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and…Read more
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126Intuitive semantics for first-degree entailments and 'coupled trees'Philosophical Studies 29 (3): 149-168. 1976.
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247Conditional assertion and restricted quantification: Abstracts of commentsNoûs 4 (1): 13. 1970.
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13A guide to the Floridi keys: Luciano Floridi: The philosophy of information. Oxford: Oxford University Press, 2011, xx+405pp, £37.50 HB (review)Metascience 22 (1): 93-98. 2013.
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Relational semantics of nonclassical logical calculi. CSLI Lecture Notes, no. 188Bulletin of Symbolic Logic 16 (2): 277-278. 2010.
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23Generalized onrno negationIn Heinrich Wansing (ed.), Negation: a notion in focus, W. De Gruyter. pp. 7--3. 1996.
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51A sieve for entailmentsJournal of Philosophical Logic 9 (1). 1980.The validity of an entailment has nothing to do with whether or not the components are true, false, necessary, or impossible; it has to do solely with whether or not there is a necessary connection between antecedent and consequent. Hence it is a mistake (we feel) to try to build a sieve which will “strain out” entailments from the set of material or strict “implications” present in some system of truth-functions, or of truth-functions with modality. Anderson and Belnap (1962, p. 47)
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52A modification of Parry's analytic implicationNotre Dame Journal of Formal Logic 13 (2): 195-205. 1972.
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51Algebraic completeness results for r-Mingle and its extensionsJournal of Symbolic Logic 35 (1): 1-13. 1970.
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96Relevant predication 1: The formal theory (review)Journal of Philosophical Logic 16 (4): 347-381. 1987.
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47New Consecution Calculi for R→tNotre Dame Journal of Formal Logic 53 (4): 491-509. 2012.The implicational fragment of the logic of relevant implication, $R_{\to}$ is one of the oldest relevance logics and in 1959 was shown by Kripke to be decidable. The proof is based on $LR_{\to}$ , a Gentzen-style calculus. In this paper, we add the truth constant $\mathbf{t}$ to $LR_{\to}$ , but more importantly we show how to reshape the sequent calculus as a consecution calculus containing a binary structural connective, in which permutation is replaced by two structural rules that involve $\m…Read more
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83Negation in the Context of Gaggle TheoryStudia 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
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125Contradictory 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
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97A Kripke-style semantics for R-Mingle using a binary accessibility relationStudia Logica 35 (2). 1976.
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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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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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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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50A relational representation of quasi-Boolean algebrasNotre Dame Journal of Formal Logic 23 (4): 353-357. 1982.
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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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50Relevant Robinson's arithmeticStudia Logica 38 (4). 1979.In this paper two different formulations of Robinson's arithmetic based on relevant logic are examined. The formulation based on the natural numbers (including zero) is shown to collapse into classical Robinson's arithmetic, whereas the one based on the positive integers (excluding zero) is shown not to similarly collapse. Relations of these two formulations to R. K. Meyer's system R# of relevant Peano arithmetic are examined, and some remarks are made about the role of constant functions (e.g.,…Read more
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 |