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14Ivan Efimovič Orlov’s paper “The calculus of the compatibility of propositions”, published in Russian in 1928, is fascinating for anyone interested in the early history of relevance, modal or intuitionistic logic. This is a guide that outlines Orlov's life and work, analyses the content of the paper, and relates it to work of his contemporaries and successors.
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19First-Order FriendlinessReview of Symbolic Logic 1-15. forthcoming.In this note we study a counterpart in predicate logic of the notion of logical friendliness, introduced into propositional logic in [15]. The result is a new consequence relation for predicate languages with equality using first-order models. While compactness, interpolation and axiomatizability fail dramatically, several other properties are preserved from the propositional case. Divergence is diminished when the language does not contain equality with its standard interpretation.
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41The Logic of Inconsistency. A Study in Non-Standard Possible-World Semantics and OntologyJournal of Symbolic Logic 47 (1): 233-236. 1979.
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149Intuitionistic Logic and Elementary RulesMind 120 (480): 1035-1051. 2011.The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results concerning intuitionistic propositional logic that bear on that perspective, and discuss their significance. First, for a range of connectives including both negation and the falsum, there are no classically or intuitionistically correct introduction rules. Second, irrespective of the choice of negation or the f…Read more
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6Doing the Best We Can. An Essay in Informal Deontic LogicJournal of Symbolic Logic 52 (4): 1050-1051. 1987.
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39Some embedding theorems for modal logicNotre Dame Journal of Formal Logic 12 (2): 252-254. 1971.Some results on the upper end of the lattice of all modal propositional logics.
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17Boole's indefinite symbols re-examinedAustralasian Journal of Logic 19 (5). 2022.We show how one can give a clear formal account of Boole’s notorious “indefinite" (or “auxiliary”) symbols by treating them as variables that range over functions from classes to classes rather than just over classes while, at the same time, following Hailperin’s proposal of binding them existentially.
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51Frege’s Ontological Diagram CompletedLogica Universalis 16 (3): 381-387. 2022.In a letter of 1891, Frege drew a diagram to illustrate his logical ontology. We observe that it omits features that play an important role in his thought on the matter, propose an extension of the diagram to include them, and compare with a diagram of the ontology of current first-order logic.
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8Relevance-Sensitive Truth-TreesIn Ivo Düntsch & Edwin Mares (eds.), Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs, Springer Verlag. pp. 23-65. 2021.Our goal is to articulate a clear rationale for relevance-sensitive propositional logic. The method: truth-trees. Familiar decomposition rules for truth-functional connectives, accompanied by novel ones for the for the arrow, together with a recursive rule, generate a set of ‘acceptable’ formulae that properly contains all theorems of the well-known system R and is closed under substitution, conjunction, and detachment. We conjecture that it satisfies the crucial letter-sharing condition.
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56Screened RevisionTheoria 63 (1-2): 14-23. 1997.Develops a concept of revision, akin in spirit to AGM partial meet revision, but in which the postulate of 'success' may fail. The basic idea is to see such an operation as composite, with a pre-processor using a priori considerations to resolve the question of whether to revise, following which another operation revises in a manner that protects the a priori material.
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11Intelim rules for classical connectivesIn Sven Ove Hansson (ed.), David Makinson on Classical Methods for Non-Classical Problems. Series: Outstanding Contributions to Logic, Springer. pp. 359-382. 2014.We investigate introduction and elimination rules for truth-functional connectives, focusing on the general questions of the existence, for a given connective, of at least one such rule that it satisfies, and the uniqueness of a connective with respect to the set of all of them. The answers are straightforward in the context of rules using general set/set sequents of formulae, but rather complex and asymmetric in the restricted (but more often used) context of set/formula sequents, as also in th…Read more
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16Floating conclusions and zombie paths: Two deep difficulties in the “directly skeptical” approach to defeasible inheritance netsArtificial Intelligence 48 (2): 199-209. 1991.
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15The Phenomenology of Second-Level Inference: Perfumes in The Deductive GardenBulletin of the Section of Logic 49 (4): 327-342. 2020.We comment on certain features that second-level inference rules commonly used in mathematical proof sometimes have, sometimes lack: suppositions, indirectness, goal-simplification, goal-preservation and premise-preservation. The emphasis is on the roles of these features, which we call 'perfumes', in mathematical practice rather than on the space of all formal possibilities, deployment in proof-theory, or conventions for display in systems of natural deduction.
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27Reviews of the papers mentioned in the title.
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19E. J. Lemmon. An extension algebra and the modal system T.Notre Dame Journal of formal logic, vol. 1 , pp. 3–12. - E. J. Lemmon. Algebraic semantics for modal logics.The journal of symbolic logic, vol. 31 , pp. 46–65; pp. 191–218 (review)Journal of Symbolic Logic 35 (1): 136-137. 1970.Review of the paper mentioned in the title.
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11Alan Ross Anderson and Nuel D. BelnapJr., Tautological entailments. Philosophical studies , vol. 13 , pp. 9–24Journal of Symbolic Logic 33 (4): 608. 1969.
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6F. R. Drake. On McKinsey's syntactical characterizations of systems of modal logic. The journal of symbolic logic, vol. 27 no. 4 , pp. 400–406 (review)Journal of Symbolic Logic 36 (4): 691-692. 1971.
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13M. H. Löb. Extensional interpretations of modal logics. The journal of symbolic logic, vol. 31 , pp. 23–45Journal of Symbolic Logic 36 (4): 692. 1971.Review of the paper mentioned in the title.
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21Charles F. Kielkopf. Kripke's axiomatization of S2. Notre Dame journal of formal logic, vol. 13 , pp. 379–380Journal of Symbolic Logic 38 (4): 661. 1973.Review of the paper mentioned in the title.
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17Jean Drabbe. Les S4-algèbres finies. Comptes rendus hehdomadaires des séances de l'Académic des Sciences, sér. A vol. 265 , p. 309 (review)Journal of Symbolic Logic 38 (2): 330. 1973.Review of paper mentioned in title.
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4Rolf George. Enthymematic consequence. American philosophical quarterly, vol. 9 , pp. 113–116Journal of Symbolic Logic 38 (2): 325. 1973.Review of the paper mentioned in the title.
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13Ralph C. Applebee and Biswambhar Pahi. Some results on generalized truth-tables. Notre Dame journal of formal logic, vol. 12 , pp. 435–440 (review)Journal of Symbolic Logic 38 (3): 521. 1973.Review of the paper mentioned in the title.
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17Gerald J. Massey. Four simple systems of modal propositional logic. Philosophy of science, vol. 32 , pp. 342–355Journal of Symbolic Logic 37 (4): 754. 1972.Review of the paper mentioned in the title.
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London School of EconomicsDepartment of Philosophy, Logic and Scientific MethodProfessor (Part-time)
Holborn, England, United Kingdom of Great Britain and Northern Ireland
Areas of Specialization
Science, Logic, and Mathematics |
Areas of Interest
Science, Logic, and Mathematics |