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151Relevance logics and relation algebrasReview of Symbolic Logic 2 (1): 102-131. 2009.Relevance logics are known to be sound and complete for relational semantics with a ternary accessibility relation. This paper investigates the problem of adequacy with respect to special kinds of dynamic semantics (i.e., proper relation algebras and relevant families of relations). We prove several soundness results here. We also prove the completeness of a certain positive fragment of R as well as of the first-degree fragment of relevance logics. These results show that some core ideas are sha…Read more
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148Kripke models for linear logicJournal of Symbolic Logic 58 (2): 514-545. 1993.We present a Kripke model for Girard's Linear Logic (without exponentials) in a conservative fashion where the logical functors beyond the basic lattice operations may be added one by one without recourse to such things as negation. You can either have some logical functors or not as you choose. Commutatively and associatively are isolated in such a way that the base Kripke model is a model for noncommutative, nonassociative Linear Logic. We also extend the logic by adding a coimplication operat…Read more
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99Positive modal logicStudia Logica 55 (2). 1995.We give a set of postulates for the minimal normal modal logicK + without negation or any kind of implication. The connectives are simply , , , . The postulates (and theorems) are all deducibility statements . The only postulates that might not be obvious are.
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68Editors' Introduction: The Third Life of Quantum Logic: Quantum Logic Inspired by Quantum Computing (review)Journal of Philosophical Logic 42 (3): 443-459. 2013.
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5Review: Hugues LeBlanc, Truth-Value Semantics (review)Journal of Symbolic Logic 43 (2): 376-377. 1978.
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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
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 |