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Logic of belief revision

Stanford Encyclopedia of Philosophy (2008)

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  1. Conditional Probability in the Light of Qualitative Belief Change.David C. Makinson - 2011 - Journal of Philosophical Logic 40 (2):121 - 153.
    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 explain how recent work on (...)
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  • System of Spheres-Based Multiple Contractions.Eduardo Fermé & Maurício D. L. Reis - 2012 - Journal of Philosophical Logic 41 (1):29-52.
    We propose a new class of multiple contraction operations — the system of spheres-based multiple contractions — which are a generalization of Grove’s system of spheres-based (singleton) contractions to the case of contractions by (possibly non-singleton) sets of sentences. Furthermore, we show that this new class of functions is a subclass of the class of the partial meet multiple contractions.
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  • Severe Withdrawal (and Recovery).Hans Rott & Maurice Pagnucco - 1999 - Journal of Philosophical Logic 28 (5):501-547.
    The problem of how to remove information from an agent's stock of beliefs is of paramount concern in the belief change literature. An inquiring agent may remove beliefs for a variety of reasons: a belief may be called into doubt or the agent may simply wish to entertain other possibilities. In the prominent AGM framework for belief change, upon which the work here is based, one of the three central operations, contraction, addresses this concern (the other two deal with the (...)
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  • A Note on Partial Meet Package Contraction.Jun Li - 1998 - Journal of Logic, Language and Information 7 (2):139-142.
    It was shown that finite P-recovery holds for partial meet package contraction in Furhmann and Hansson (1994). However, it is not known if recovery holds for partial meet package contraction in the infinite case. In this paper, I show that recovery does not hold for partial meet package contraction in the infinite case.
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  • Global and Iterated Contraction and Revision: An Exploration of Uniform and Semi-Uniform Approaches. [REVIEW]Sven Ove Hansson - 2012 - Journal of Philosophical Logic 41 (1):143-172.
    In order to clarify the problems of iterated (global) belief change it is useful to study simple cases, in particular consecutive contractions by sentences that are both logically and epistemically independent. Models in which the selection mechanism is kept constant are much more plausible in this case than what they are in general. One such model, namely uniform specified meet contraction, has the advantage of being closely connected with the AGM model. Its properties seem fairly adequate for the intended type (...)
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  • Iterated Belief Change Based on Epistemic Entrenchment.Abhaya C. Nayak - 1994 - Erkenntnis 41 (3):353-390.
    In this paper it is argued that, in order to solve the problem of iterated belief change, both the belief state and its input should be represented as epistemic entrenchment (EE) relations. A belief revision operation is constructed that updates a given EE relation to a new one in light of an evidential EE relation. It is shown that the operation in question satisfies generalized versions of the Gärdenfors revision postulates. The account offered is motivated by Spohn's ordinal conditionalization functions, (...)
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  • Changes in Preference.Sven Ove Hansson - 1995 - Theory and Decision 38 (1):1-28.
  • Iterated Belief Revision, Reliability, and Inductive Amnesia.Kevin T. Kelly - 1999 - Erkenntnis 50 (1):11-58.
    Belief revision theory concerns methods for reformulating an agent's epistemic state when the agent's beliefs are refuted by new information. The usual guiding principle in the design of such methods is to preserve as much of the agent's epistemic state as possible when the state is revised. Learning theoretic research focuses, instead, on a learning method's reliability or ability to converge to true, informative beliefs over a wide range of possible environments. This paper bridges the two perspectives by assessing the (...)
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  • Notes on the History of Ideas Behind AGM.Peter Gärdenfors - 2011 - Journal of Philosophical Logic 40 (2):115 - 120.
  • Theory Contraction Through Base Contraction.André Fuhrmann - 1991 - Journal of Philosophical Logic 20 (2):175 - 203.
  • Ifs, Though, and Because.Hans Rott - 1986 - Erkenntnis 25 (3):345-370.
    The paper proposes a unified analysis of the natural language connectives 'if', 'if … might', 'even if' (all of them with indicative and subjunctive mood), 'because' and 'though'. They are all interpreted as instances of universal (pro)conditionals, unconditionals, or counterconditionals. The paper imports the notion of relevance into the meaning of conditionals, viewing conditionals as close in meaning to explanations and statements about causal relations. The antecedent of a conditional is interpreted as being relevant for its consequent, thus avoiding the (...)
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  • Subjunctives, Dispositions and Chances.Isaac Levi - 1977 - Synthese 34 (4):423 - 455.
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  • Iteration of Conditionals and the Ramsey Test.Isaac Levi - 1988 - Synthese 76 (1):49 - 81.
  • A Survey of Multiple Contractions.André Fuhrmann & Sven Ove Hansson - 1994 - Journal of Logic, Language and Information 3 (1):39-75.
    The AGM theory of belief contraction is extended tomultiple contraction, i.e. to contraction by a set of sentences rather than by a single sentence. There are two major variants: Inpackage contraction all the sentences must be removed from the belief set, whereas inchoice contraction it is sufficient that at least one of them is removed. Constructions of both types of multiple contraction are offered and axiomatically characterized. Neither package nor choice contraction can in general be reduced to contractions by single (...)
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  • A Theory of Conditionals.Robert C. Stalnaker - 1968 - In Nicholas Rescher (ed.), Studies in Logical Theory (American Philosophical Quarterly Monographs 2). Oxford: Blackwell. pp. 98-112.
  • The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability, and Chance.Isaac Levi - 1980 - MIT Press.
    This major work challenges some widely held positions in epistemology - those of Peirce and Popper on the one hand and those of Quine and Kuhn on the other.
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  • A Textbook of Belief Dynamics. Theory Change and Database Updating.S. O. Hansson - 1999 - Kluwer Academic Publishers.
    SUGGESTED COURSES Introductory level A (Requires very little background in logic .): 4: -9 - - -7 -2 Introductory level B: -9,:+-+ -,2:+,2: -,3:20+-22+ -7 -2 ...
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  • Probability and the Logic of Rational Belief.Henry Ely Kyburg - 1961 - Middletown, Conn., Wesleyan University Press.
  • The Fixation of Belief and its Undoing: Changing Beliefs Through Inquiry.Isaac Levi - 1991 - Cambridge University Press.
    Isaac Levi's new book is concerned with how one can justify changing one's beliefs. The discussion is deeply informed by the belief-doubt model advocated by C. S. Peirce and John Dewey, of which the book provides a substantial analysis. Professor Levi then addresses the conceptual framework of potential changes available to an inquirer. A structural approach to propositional attitudes is proposed, which rejects the conventional view that a propositional attitude involves a relation between an agent and either a linguistic entity (...)
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  • Mild Contraction: Evaluating Loss of Information Due to Loss of Belief.Isaac Levi - 2004 - Oxford University Press.
    Isaac Levi's new book develops further his pioneering work in formal epistemology, focusing on the problem of belief contraction, or how rationally to relinquish old beliefs. Levi offers the most penetrating analysis to date of this key question in epistemology, offering a completely new solution and explaining its relation to his earlier proposals. He mounts an argument in favor of the thesis that contracting a state of belief by giving up specific beliefs is to be evaluated in terms of the (...)
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  • The Paradox of the Preface.David C. Makinson - 1965 - Analysis 25 (6):205.
    By means of an example, shows the possibility of beliefs that are separately rational whilst together inconsistent.
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  • Screened Revision.David Makinson - 1997 - Theoria 63 (1-2):14-23.
    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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  • Shielded Contraction.E. Fermé & S. O. Hansson - 2001 - In M. Williams & Hans Rott (eds.), Fronties of Belief Revision. Kluwer Academic Publishers. pp. 85-107.
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  • A Truth Maintenance System.Jon Doyle - 1979 - Artificial Intelligence 12 (3):231-272.
  • Belief Revisions and the Ramsey Test for Conditionals.Peter Gardenfors - 1986 - Philosophical Review 95 (1):81-93.
  • Revision by Comparison.Eduardo Fermé & Hans Rott - 2004 - Artificial Intelligence 157 (1):5-47.
    Since the early 1980s, logical theories of belief revision have offered formal methods for the transformation of knowledge bases or “corpora” of data and beliefs. Early models have dealt with unconditional acceptance and integration of potentially belief-contravening pieces of information into the existing corpus. More recently, models of “non-prioritized” revision were proposed that allow the agent rationally to refuse to accept the new information. This paper introduces a refined method for changing beliefs by specifying constraints on the relative plausibility of (...)
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  • On the Logic of Iterated Belief Revision.Adnan Darwiche & Judea Pearl - 1997 - Artificial Intelligence 89 (1-2):1-29.
    We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a (...)
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  • Two Modellings for Theory Change.Adam Grove - 1988 - Journal of Philosophical Logic 17 (2):157-170.
  • Logic Based Merging.Sébastien Konieczny & Ramón Pino Pérez - 2011 - Journal of Philosophical Logic 40 (2):239-270.
    Belief merging aims at combining several pieces of information coming from different sources. In this paper we review the works on belief merging of propositional bases. We discuss the relationship between merging, revision, update and confluence, and some links between belief merging and social choice theory. Finally we mention the main generalizations of these works in other logical frameworks.
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  • Rational Conceptual Change.William L. Harper - 1976 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1976:462 - 494.
  • Shifting Priorities: Simple Representations for Twenty-Seven Iterated Theory Change Operators.Hans Rott - 2006 - In David Makinson, Jacek Malinowski & Heinrich Wansing (eds.), Towards Mathematical Philosophy. Dordrecht: Springer. pp. 269–296.
    Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of belief (...)
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  • Changing Legal Systems: Legal Abrogations and Annulments in Defeasible Logic.Guido Governatori & Antonino Rotolo - 2010 - Logic Journal of the IGPL 18 (1):157-194.
    In this paper we investigate how to represent and reason about legal abrogations and annulments in Defeasible Logic. We examine some options that embed in this setting, and in similar rule-based systems, ideas from belief and base revision. In both cases, our conclusion is negative, which suggests to adopt a different logical model. This model expresses temporal aspects of legal rules, and distinguishes between two main timelines, one internal to a given temporal version of the legal system, and another relative (...)
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  • Hierarchies of Regulations and Their Logic.Carlos E. Alchourrón & David Makinson - 1981 - In Risto Hilpinen (ed.), New Studies in Deontic Logic. Dordrecht: Reidel. pp. 125--148.
    Investigates the resolution of contradictions and ambiguous derogations in a code, by means of the imposition of partial orderings.
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  • Epistemic Entrenchment with Incomparabilities and Relational Belief Revision.Sten Lindström & Wlodek Rabinowicz - 1991 - In André Fuhrmann & Michael Morreau (eds.), The Logic of Theory Change. Springer. pp. 93--126.
    In earlier papers (Lindström & Rabinowicz, 1989. 1990), we proposed a generalization of the AGM approach to belief revision. Our proposal was to view belief revision as a relation rather thanas a function on theories (or belief sets). The idea was to allow for there being several equally reasonable revisions of a theory with a given proposition. In the present paper, we show that the relational approach is the natural result of generalizing in a certain way an approach to belief (...)
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  • Knowledge and Belief: An Introduction to the Logic of the Two Notions.Jaakko Hintikka - 1962 - Studia Logica 16:119-122.
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  • Descriptor Revision.Sven Ove Hansson - 2014 - Studia Logica 102 (5):955-980.
    A descriptor is a set of sentences that are truth-functional combinations of expressions of the form \ , where \ is a metalinguistic belief predicate and p a sentence in the object language in which beliefs are expressed. Descriptor revision ) is an operation of belief change that takes us from a belief set K to a new belief set \ where \ is a descriptor representing the success condition. Previously studied operations of belief change are special cases of descriptor (...)
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  • Multiple and Iterated Contraction Reduced to Single-Step Single-Sentence Contraction.Sven Ove Hansson - 2010 - Synthese 173 (2):153-177.
    Multiple contraction (simultaneous contraction by several sentences) and iterated contraction are investigated in the framework of specified meet contraction (s.m.c.) that is extended for this purpose. Multiple contraction is axiomatized, and so is finitely multiple contraction (contraction by a finite set of sentences). Two ways to reduce finitely multiple contraction to contraction by single sentences are introduced. The reduced operations are axiomatically characterized and their properties are investigated. Furthermore, it is shown how iterated contraction can be reduced to single-step, single-sentence (...)
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  • AGM 25 Years: Twenty-Five Years of Research in Belief Change.Eduardo Fermé & Sven Ove Hansson - 2011 - Journal of Philosophical Logic 40 (2):295-331.
    The 1985 paper by Carlos Alchourrón, Peter Gärdenfors, and David Makinson, “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions” was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twenty-five years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original (...)
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  • Logics of Public Communications.Jan Plaza - 2007 - Synthese 158 (2):165 - 179.
    Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain (...)
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  • Variations on the Ramsey Test: More Triviality Results.Peter Gärdenfors - 1987 - Studia Logica 46 (4):319-325.
    The purpose of this note is to formulate some weaker versions of the so called Ramsey test that do not entail the following unacceptable consequenceIf A and C are already accepted in K, then if A, then C is also accepted in K. and to show that these versions still lead to the same triviality result when combined with a preservation criterion.
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  • Multiple Kernel Contraction.Eduardo Fermé, Karina Saez & Pablo Sanz - 2003 - Studia Logica 73 (2):183 - 195.
    This paper focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson presented an axiomatic for Multiple Contraction and a construction based on the AGM Partial Meet Contraction. We propose for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of Kernel Contraction, proposed by Hansson [Han94] to construct classical AGM contractions and belief base contractions. This construction (...)
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  • Dynamic Doxastic Logic: Why, How, and Where To?Hannes Leitgeb & Krister Segerberg - 2007 - Synthese 155 (2):167-190.
    We investigate the research programme of dynamic doxastic logic (DDL) and analyze its underlying methodology. The Ramsey test for conditionals is used to characterize the logical and philosophical differences between two paradigmatic systems, AGM and KGM, which we develop and compare axiomatically and semantically. The importance of Gärdenfors’s impossibility result on the Ramsey test is highlighted by a comparison with Arrow’s impossibility result on social choice. We end with an outlook on the prospects and the future of DDL.
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  • Credibility Limited Revision.Sven Hansson, Eduardo Ferme, John Cantwell & Marcelo Falappa - 2001 - Journal of Symbolic Logic 66 (4):1581-1596.
    Five types of constructions are introduced for non-prioritized belief revision, i.e., belief revision in which the input sentence is not always accepted. These constructions include generalizations of entrenchment-based and sphere-based revision. Axiomatic characterizations are provided, and close interconnections are shown to hold between the different constructions.
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  • Knowledge in Flux. Modeling the Dynamics of Epistemic States.Peter Gärdenfors - 1988 - Studia Logica 49 (3):421-424.
     
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  • On the Logic of Theory Change: Partial Meet Contraction and Revision Functions.Carlos E. Alchourrón, Peter Gärdenfors & David Makinson - 1985 - Journal of Symbolic Logic 50 (2):510-530.
    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 (...)
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  • Belief Revision From the Point of View of Doxastic Logic.Krister Segerberg - 1995 - Logic Journal of the IGPL 3 (4):535-553.
    In 1985 Alchourrón, Gärdenfors and Makinson presented their now classic theory of theory change . In 1988 Adam Grove, generalizing David Lewis's theory of counterfactuals, presented a model theory suitable for the AGM theory. Although AGM and Grove mentioned object languages, neither used them. But recently, Maarten de Rijke has shown how object languages can be brought into the picture. In the present paper we take de Rijke's idea further, addressing the question whether there is a particular doxastic or epistemic (...)
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  • Change, Choice and Inference. A Study of Belief Revision and Nonmonotonic Reasoning.Hans Rott - 2001 - Studia Logica 77 (1):145-147.
     
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  • On the Logic of Small Changes in Hypertheories.John Cantwell - 1997 - Theoria 63 (1-2):54-89.
  • On the Difference Between Updating a Knowledge Base and Revising It.H. Katsuno & A. O. Mendelzon - 1992 - In Belief Revision. Cambridge University Press. pp. 183-203.
     
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  • Ten Philosophical Problems in Belief Revision.Sven Ove Hansson - 2003
    The paper introduces ten open problems in belief revision theory, related to the representation of the belief state, to different notions of degrees of belief, and to the nature of change operations. It is argued that these problems are all issues in philosopical logic, in the strong sense of requiring inputs from both logic and philosophy for their solution.
     
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