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6PrefaceIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. 2017.
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11Chapter VI. the theory of entailmentIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 1-69. 2017.
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24Chapter VIII. Ackermann's strenge implikationIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 129-141. 2017.
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6Analytical table of contentsIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. 2017.
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21Chapter X. proof theory and decidabilityIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 267-391. 2017.
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14AcknowledgmentsIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. 2017.
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10Special symbolsIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 747-749. 2017.
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9ContentsIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. 2017.
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12Index of subjectsIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 719-746. 2017.
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16Entailment, Vol. Ii: The Logic of Relevance and NecessityPrinceton University Press. 2017.In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in the…Read more
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69Relevant predication 3: essential propertiesIn J. Dunn & A. Gupta (eds.), Truth or Consequences: Essays in Honor of Nuel Belnap, Kluwer Academic Publishers. pp. 77--95. 1990.
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10A logical framework for the notion of natural propertyIn John Earman & John Norton (eds.), The Cosmos of Science, University of Pittsburgh Press. pp. 6--458. 1997.
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140Dualling: A critique of an argument of Popper and MillerBritish Journal for the Philosophy of Science 37 (2): 220-223. 1986.
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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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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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49Completeness of relevant quantification theoriesNotre Dame Journal of Formal Logic 15 (1): 97-121. 1974.
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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.
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32On the decidability of implicational ticket entailmentJournal of Symbolic Logic 78 (1): 214-236. 2013.The implicational fragment of the logic of relevant implication, $R_\to$ is known to be decidable. We show that the implicational fragment of the logic of ticket entailment, $T_\to$ is decidable. Our proof is based on the consecution calculus that we introduced specifically to solve this 50-year old open problem. We reduce the decidability problem of $T_\to$ to the decidability problem of $R_\to$. The decidability of $T_\to$ is equivalent to the decidability of the inhabitation problem of implic…Read more
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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
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85Partiality and its dualStudia Logica 66 (1): 5-40. 2000.This paper explores allowing truth value assignments to be undetermined or "partial" and overdetermined or "inconsistent", thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dun…Read more
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72Algebraic Methods in Philosophical LogicOxford University Press. 2001.This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects
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 |