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85Maps between some different kinds of contraction function: The finite caseStudia Logica 45 (2). 1986.In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial me…Read more
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23Feldman Fred. Doing the best we can. An essay in informal deontic logic. Philosophical studies series in philosophy, vol. 35. D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, and Tokyo, 1986, xiv + 244 pp (review)Journal of Symbolic Logic 52 (4): 1050-1051. 1987.
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2Review: Fred Feldman, Doing the Best We Can. An Essay in Informal Deontic Logic (review)Journal of Symbolic Logic 52 (4): 1050-1051. 1987.
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44On the status of the postulate of recovery in the logic of theory changeJournal of Philosophical Logic 16 (4). 1987.Describes and discusses the rather special behaviour of one of the postulates in the AGM account of theory change.
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12Review: Lennart Aqvist, Deontic Logic (review)Journal of Symbolic Logic 54 (4): 1481-1483. 1989.
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28On attributing rights to all peoples: Some logical questions (review)Law and Philosophy 8 (1). 1989.
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43The gärdenfors impossibility theorem in non-monotonic contextsStudia Logica 49 (1). 1990.Gärdenfors' impossibility theorem draws attention to certain formal difficulties in defining a conditional connective from a notion of theory revision, via the Ramsey test. We show that these difficulties are not avoided by taking the background inference operation to be non-monotonic.
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38Relations between the logic of theory change and nonmonotonic logicIn André Fuhrmann & Michael Morreau (eds.), The Logic of Theory Change: Workshop, Konstanz, FRG, October 13-15, 1989, Proceedings, Springer. pp. 183--205. 1991.Examines the link between nonmonotonic inference relations and theory revision operations, focusing on the correspondence between abstract properties which each may satisfy.
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74The relationship between KLM and MAK models for nonmonotonic inference operationsJournal of Logic, Language and Information 1 (2): 131-140. 1992.The purpose of this note is to make quite clear the relationship between two variants of the general notion of a preferential model for nonmonotonic inference: the models of Kraus, Lehmann and Magidor (KLM models) and those of Makinson (MAK models).On the one hand, we introduce the notion of the core of a KLM model, which suffices to fully determine the associated nonmonotonic inference relation. On the other hand, we slightly amplify MAK models with a monotonic consequence operation as addition…Read more
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75Five faces of minimalityStudia Logica 52 (3). 1993.We discuss similarities and residual differences, within the general semantic framework of minimality, between defeasible inference, belief revision, counterfactual conditionals, updating — and also conditional obligation in deontic logic. Our purpose is not to establish new results, but to bring together existing material to form a clear overall picture.
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3General Patterns in Nonmonotonic ReasoningIn Handbook of Logic in Artificial Intelligence Nad Logic Programming, Vol. Iii, Clarendon Press. pp. 35-110. 1994.An extended review of what is known about the formal behaviour of nonmonotonic inference operations, including those generated by the principal systems in the artificial intelligence literature. Directed towards computer scientists and others with some background in logic.
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16In memoriam carlos eduardo alchourronNordic Journal of Philosophical Logic 1 (1): 3-10. 1996.Obituary notice with overview of the work of Carlos Alchourrón, focussing on his contributions to the logic of theory change.
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64Combinatorial versus decision-theoretic components of impossibility theoremsTheory and Decision 40 (2): 181-189. 1996.Separates the purely combinatorial component of Arrow's impossibility theorem in the theory of collective preference from its decision-theoretic part, and likewise for the closely related Blair/Bordes/Kelly/Suzumura theorem. Such a separation provides a particularly elegant proof of Arrow's result, via a new 'splitting theorem'.
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27Bridges from Classical to Nonmonotonic LogicKing's College Publications. 2005.An graduate level introduction to nonmonotonic reasoning, emphasizing structures and spirit common to different formulations, with exercises.
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69Respecting relevance in belief changeAnálisis Filosófico 26 (1): 53-61. 2006.In this paper dedicated to Carlos Alchourrón, we review an issue that emerged only after his death in 1996, but would have been of great interest to him: To what extent do the formal operations of AGM belief change respect criteria of relevance? A natural criterion was proposed in 1999 by Rohit Parikh, who observed that the AGM model does not always respect it. We discuss the pros and cons of this criterion, and explain how the AGM account may be refined, if we so desire, so that it is always re…Read more
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62The Quantitative/Qualitative Watershed for Rules of Uncertain InferenceStudia Logica 86 (2): 247-297. 2007.We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness pro…Read more
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23Propositional relevance through letter-sharingJournal of Applied Logic 7 (4): 377-387. 2009.The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a long time. But it began to take on a fresh life in the late 1990s 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: the relation of relevance was considered modulo the choice of a background belief set, and the belief set was put into a canonical form, called its finest …Read more
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39Levels of Belief in Nonmonotonic ReasoningIn Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of belief, Springer. pp. 341--354. 2009.Reviews the connections between different kinds of nonmonotonic logic and the general idea of varying degrees of belief.
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110Conditional Probability in the Light of Qualitative Belief ChangeJournal of Philosophical Logic 40 (2). 2011.We explore ways in which purely qualitative belief change in the AGM tradition throws light on options in the treatment of conditional probability. First, by helping see why it can be useful to go beyond the ratio rule defining conditional from one-place probability. Second, by clarifying what is at stake in different ways of doing that. Third, by suggesting novel forms of conditional probability corresponding to familiar variants of qualitative belief change, and conversely. Likewise, we explai…Read more
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11Dov M. Gabbay and Karl Schlechta , Conditionals and Modularity in General Logics . Reviewed by (review)Philosophy in Review 32 (5): 376-378. 2012.Review of the book mentioned in the title.
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222Logical questions behind the lottery and preface paradoxes: lossy rules for uncertain inferenceSynthese 186 (2): 511-529. 2012.We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A second lesson is …Read more
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13Cresswell M. J.. A Henkin completeness theorem for T. Notre Dame journal of formal logic, vol. 8 no. 3 , pp. 186–190.Cresswell M. J.. Alternative completeness theorems for modal systems. Notre Dame journal of formal logic, vol. 8 no. 4 , pp. 339–345.Cresswell M. J.. Some proofs of relative completeness in modal logic. Notre Dame journal of formal logic, vol. 9 no. 1 , pp. 62–66 (review)Journal of Symbolic Logic 35 (4): 581-582. 1970.Reviews of the papers referred to in the title.
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1Review: Jean Drabbe, Les S4-Algebres Finies (review)Journal of Symbolic Logic 38 (2): 330-330. 1973.
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131On the logic of theory change: Contraction functions and their associated revision functionsTheoria 48 (1): 14-37. 1982.A study in the logic of theory change, examining the properties of maxichoice contraction and revision operations.
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81On the logic of theory change: Safe contractionStudia Logica 44 (4). 1985.This paper is concerned with formal aspects of the logic of theory change, and in particular with the process of shrinking or contracting a theory to eliminate a proposition. It continues work in the area by the authors and Peter Gärdenfors. The paper defines a notion of safe contraction of a set of propositions, shows that it satisfies the Gärdenfors postulates for contraction and thus can be represented as a partial meet contraction, and studies its properties both in general and under various…Read more
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460On the logic of theory change: Partial meet contraction and revision functionsJournal of Symbolic Logic 50 (2): 510-530. 1985.This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of…Read more
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29Local and global metrics for the semantics of counterfactual conditionalsJournal of Applied Non-Classical Logics 4 (2): 129-140. 1994.No aConsiders the question of how far the different ‘closeness’ relations, indexed by worlds, in a given model for counterfactual conditionals may be derived from a common source. Counterbalancing some well-known negative observations, we show that there is also a strong positive answer.
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29Bridges between Classical and Nonmonotonic LogicLogic Journal of the IGPL 11 (1): 69-96. 2003.The purpose of this paper is to take some of the mystery out of what is known as nonmonotonic logic, by showing that it is not as unfamiliar as may at first sight appear. In fact, it is easily accessible to anybody with a background in classical propositional logic, provided that certain misunderstandings are avoided and a tenacious habit is put aside. In effect, there are logics that act as natural bridges between classical consequence and the principal kinds of nonmonotonic logic to be found i…Read more
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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 |