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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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29Alan Rose. Extensions of some theorems of Anderson and Belnap. The journal of symbolic logic, vol. 27 no. 4 , pp. 423–425 (review)Journal of Symbolic Logic 40 (3): 466-466. 1975.Review of the paper by Rose mentioned in the title.
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14Arthur Pap. Logic and the concept of entailment. The journal of philosophy, vol. 47 , pp. 378–387Journal of Symbolic Logic 40 (3): 466. 1975.Review of the paper mentioned in the title.
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30Brian F. Chellas. Modal logic. An introduction. Cambridge University Press, Cambridge etc. 1980, xii + 295 pp (review)Journal of Symbolic Logic 46 (3): 670-672. 1981.
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23Nicholas Rescher and Robert Brandom. The logic of inconsistency. A study in non-standard possible-world semantics and ontology. APQ library of philosophy. Basil Blackwell, Oxford, and Rowman and Littlefield, Totowa, N.J., © 1979, pub. 1980, x + 174 pp (review)Journal of Symbolic Logic 47 (1): 233-236. 1982.Review of the book mentioned in the title.
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29Lennart Åqvist. Deontic logic. Handbook of philosophical logic, Volume II, Extensions of classical logic, edited by D. Gabbay and F. Guenthner, Synthese library, vol. 165, D. Reidel Publishing Company, Dordrecht, Boston, and Lancaster, 1984, pp. 605–714 (review)Journal of Symbolic Logic 54 (4): 1481-1483. 1989.Review of the book mentioned in the title.
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62On an inferential semantics for classical logicLogic Journal of the IGPL 22 (1): 147-154. 2014.We seek a better understanding of why an inferential semantics devised by Tor Sandqvist yields full classical logic, by providing and analysing a direct proof via a suitable maximality construction
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13Advice to the relevantist policemanIn Vit Punochar & Petr Svarny (eds.), The Logica Yearbook 2012, College Publications. pp. 91-100. 2013.Relevance logic is ordinarily seen as a subsystem of classical logic under the translation that replaces arrows by horseshoes. If, however, we consider the arrow as an additional connective alongside the horseshoe and other classical connectives, another perspective emerges. Relevance logic, specifically the system R, may be seen as the output of a conservative extension of classical consequence into the language with arrow.
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7Vantagens e limitações da abordagem ajdukiewicziana da GramáticaDiscurso 4 (4): 155-166. 1973.Discusses the strong points and the limitations of Ajdukiewicz' approach to grammar.
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23Intelim rules for classical connectivesIn Sven Ove Hansson (ed.), David Makinson on Classical Methods for Non-Classical Problems, . 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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28Logical Friendliness and Sympathy in LogicIn J. Y. Beziau (ed.), Logica Universalis, Birkhäuser Verlog. pp. 191--205. 2005.Defines and examines a notion of logical friendliness, a broadening of the familiar notion of classical consequence. Also reviews familiar notions and operations with which friendliness makes contact, providing a new light in which they may be seen.
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28Relevance logic as a conservative extension of classical logicIn Sven Ove Hansson (ed.), David Makinson on Classical Methods for Non-Classical Problems. Series: Outstanding Contributions to Logic, Springer. 2014.Relevance logic is ordinarily seen as a subsystem of classical logic under the translation that replaces arrows by horseshoes. If, however, we consider the arrow as an additional connective alongside the horseshoe, then another perspective emerges: the theses of relevance logic, specifically the system R, may also be seen as the output of a conservative extension of the relation of classical consequence. We describe two ways in which this may be done. One is by defining a suitable closure relati…Read more
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53Completeness theorems, representation theorems: what's the difference?Hommage À Wlodek: Philosophical Papers Dedicated to Wlodek Rabinowicz, Ed. Rønnow-Rasmussen Et Al. 2007A discussion of the connections and differences between completeness and representation theorems in logic, with examples drawn from classical and modal logic, the logic of friendliness, and nonmonotonic reasoning.
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37Friendliness and sympathy in logicIn Jean-Yves Beziau (ed.), Logica Universalis, Birkhäuser Verlog. pp. 191-206. 2005.We define and examine a notion of logical friendliness, which is a broadening of the familiar notion of classical consequence. The concept is tudied first in its simplest form, and then in a syntax-independent version, which we call sympathy. We also draw attention to the surprising number of familiar notions and operations with which it makes contact, providing a new light in which they may be seen.
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31Friendliness for logiciansIn Sergei Artemov, H. Barringer, A. S. D'Avila Garcez, L. C. Lamb & J. Woods (eds.), We Will Show Them! Essays in Honour of Dov Gabbay, College Publications. pp. 259-292. 2005.We define and examine a notion of logical friendliness, which is a broadening of the familiar notion of classical consequence. The concept is studied first in its simplest form, and then in a syntax-independent version, which we call sympathy. We also draw attention to the surprising number of familiar notions and operations with which it makes contact, providing a new light in which they may be seen.
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57Parallel interpolation, splitting, and relevance in belief changeJournal of Symbolic Logic 72 (3): 994-1002. 2007.The splitting theorem says that any set of formulae has a finest representation as a family of letter-disjoint sets. Parikh formulated this for classical propositional logic, proved it in the finite case, used it to formulate a criterion for relevance in belief change, and showed that AGMpartial meet revision can fail the criterion. In this paper we make three further contributions. We begin by establishing a new version of the well-known interpolation theorem, which we call parallel interpolati…Read more
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47The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a very long time. But it began to take on a fresh life in 1999 when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh. First, the relation of relevance was considered modulo the belief set under consideration, Second, the belief set was put in a canonical form, known as its fine…Read more
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6Topics in modern logicMethuen; distributed by Harper & Row Publishers, inc., Barnes and Noble Import Division. 1973.
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84Permission from an Input/Output PerspectiveJournal of Philosophical Logic 32 (4). 2003.Input/output logics are abstract structures designed to represent conditional obligations and goals. In this paper we use them to study conditional permission. This perspective provides a clear separation of the familiar notion of negative permission from the more elusive one of positive permission. Moreover, it reveals that there are at least two kinds of positive permission. Although indistinguishable in the unconditional case, they are quite different in conditional contexts. One of them, whi…Read more
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4Remarks on the Concept of Distribution in Traditional LogicJournal of Symbolic Logic 40 (4): 608-609. 1975.
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301Input/output logicsJournal of Philosophical Logic 29 (4): 383-408. 2000.In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. Our purpose is to develop a theory of such input/output operations. Four are singled out: simple-minded, basic (making intelligent use of disjunctive inputs), simple-minded reusable (in which outputs ma…Read more
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15A Normal Modal Calculus Between T and S4 without the Finite Model PropertyJournal of Symbolic Logic 36 (4): 692-692. 1971.The first example of an intuitively meaningful propositional logic without the finite model property, and still the simplest one in the literature. The question of its decidability appears still to be open.
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28Input/Output LogicsJournal of Philosophical Logic 29 (4). 2000.In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. Our purpose is to develop a theory of such input/output operations. Four are singled out: simple-minded, basic (making intelligent use of disjunctive inputs), simple-minded reusable (in which outputs ma…Read more
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16Bridges from Classical to Nonmonotonic LogicCollege Publications. 2005.A textbook for graduate students of philosophy, computer science, and mathematics, on various approaches to nonmonotonic logic, with emphasis on they way in which they fall into an overall pattern.
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98Constraints for Input/Output LogicsJournal of Philosophical Logic 30 (2). 2001.In a previous paper we developed a general theory of input/output logics. These are operations resembling inference, but where inputs need not be included among outputs, and outputs need not be reusable as inputs. In the present paper we study what happens when they are constrained to render output consistent with input. This is of interest for deontic logic, where it provides a manner of handling contrary-to-duty obligations. Our procedure is to constrain the set of generators of the input/outp…Read more
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46How meaningful are modal operators?Australasian Journal of Philosophy 44 (3). 1966.A philosophical discussion of the intuitive meaning of the formalism of modal propositional logics.
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14Bull R. A.. A note on the modal calculi S4.2 and S4.3. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 10 , pp. 53–55.Bull R. A.. A class of extensions of the modal system S4 with the finite model property. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 11 , pp. 127–132.Bull R. A.. That all normal extensions of S4.3 have the finite model property. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 12 , pp. 341–344 (review)Journal of Symbolic Logic 33 (1): 136-136. 1968.Reviews of the papers mentioned in the title.
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1Review: R. A. Bull, A Note on the Modal Calculi S4.2 and S4.3; R. A. Bull, A Class of Extensions of the Modal System S4 with the Finite Model Property; R. A. Bull, That all Normal Extensions of S4.3 have the Finite Model Property (review)Journal of Symbolic Logic 33 (1): 136-136. 1968.
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10Review: Alan Ross Anderson, Nuel D. Belnap, Tautological Entailments (review)Journal of Symbolic Logic 33 (4): 608-608. 1968.
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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 |