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175Partiality 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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351Conditional assertion and restricted quantification: Abstracts of commentsNoûs 4 (1): 13. 1970.
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114Completeness of relevant quantification theoriesNotre Dame Journal of Formal Logic 15 (1): 97-121. 1974.
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113On 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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78R-mingle and beneath. Extensions of the Routley-Meyer semantics for RNotre Dame Journal of Formal Logic 20 (n/a): 369. 1979.
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44Incompleteness of the bibinary semantics for RBulletin of the Section of Logic 16 (3): 107-109. 1987.
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111A sieve for entailmentsJournal of Philosophical Logic 9 (1): 41-57. 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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46Two extensions of the structurally free logic LCLogic Journal of the IGPL 6 (3): 403-424. 1998.The paper considers certain extensions of the system LC introduced in Dunn & Meyer 1997. LC is a structurally free system, but it has combinators as formulas in the place of structural rules. We consider two ways to extend LC with conjunction and disjunction depending on whether they distribute over each other or not. We prove the elimination theorem for the systems. At the end of the paper we give a Routley-Meyer style semantics for the distributive extension, including some new definitions and…Read more
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135A consecutive calculus for positive relevant implication with necessityJournal of Philosophical Logic 9 (4): 343-362. 1980.
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151Positive modal logicStudia Logica 55 (2): 301-317. 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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177Contradictory Information: Too Much of a Good Thing (review)Journal of Philosophical Logic 39 (4): 425-452. 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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166A Kripke-style semantics for R-Mingle using a binary accessibility relationStudia Logica 35 (2): 163-172. 1976.
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233Relevance 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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119A modification of Parry's analytic implicationNotre Dame Journal of Formal Logic 13 (2): 195-205. 1972.
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170Relevant predication 1: The formal theory (review)Journal of Philosophical Logic 16 (4): 347-381. 1987.
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225Intuitive semantics for first-degree entailments and 'coupled trees'Philosophical Studies 29 (3): 149-168. 1976.
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160A theorem in 3-valued model theory with connections to number theory, type theory, and relevant logicStudia Logica 38 (2): 149-169. 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 (t…Read more
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121Axiomatizing Belnap's conditional assertionJournal of Philosophical Logic 4 (4): 383-397. 1975.
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60Generalized 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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49The 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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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 |