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51Completeness of relevant quantification theoriesNotre Dame Journal of Formal Logic 15 (1): 97-121. 1974.
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37Algebraic Completeness Results for Dummett's LC and Its ExtensionsMathematical Logic Quarterly 17 (1): 225-230. 1971.
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51A relational representation of quasi-Boolean algebrasNotre Dame Journal of Formal Logic 23 (4): 353-357. 1982.
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35On 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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86Partiality 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
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18Two 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 an…Read more
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19R-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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72A consecutive calculus for positive relevant implication with necessityJournal of Philosophical Logic 9 (4): 343-362. 1980.
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14Incompleteness of the bibinary semantics for RBulletin of the Section of Logic 16 (3): 107-109. 1987.
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105Canonical Extensions and Relational Completeness of Some Substructural LogicsJournal of Symbolic Logic 70 (3). 2005.In this paper we introduce canonical extensions of partially ordered sets and monotone maps and a corresponding discrete duality. We then use these to give a uniform treatment of completeness of relational semantics for various substructural logics with implication as the residual(s) of fusion
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155Relevance 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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100Positive 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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155Kripke 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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71Editors' 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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22Generalized 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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129Intuitive semantics for first-degree entailments and 'coupled trees'Philosophical Studies 29 (3): 149-168. 1976.
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 |