Results for 'Belief functions'

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  1. Scientific and Religious Belief.Paul Weingartner, Elena Klevakina-Uljanov, Gerhard Schurz & International Conference on Scientific and Religious Belief - 1994
     
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  2. Coherence in the Aggregate: A Betting Method for Belief Functions on Many-Valued Events.Tommaso Flaminio, Lluis Godo & Hykel Hosni - unknown
    Betting methods, of which de Finetti's Dutch Book is by far the most well-known, are uncertainty modelling devices which accomplish a twofold aim. Whilst providing an interpretation of the relevant measure of uncertainty, they also provide a formal definition of coherence. The main purpose of this paper is to put forward a betting method for belief functions on MV-algebras of many-valued events which allows us to isolate the corresponding coherence criterion, which we term coherence in the aggregate. Our (...)
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  3. Objective Belief Functions as Induced Measures.Yutaka Nakamura - 2003 - Theory and Decision 55 (1):71-83.
    Given a belief function ? on the set of all subsets of prizes, how should ? values be understood as a decision alternative? This paper presents and characterizes an induced-measure interpretation of belief functions.
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  4.  39
    Coherent Bets Under Partially Resolving Uncertainty and Belief Functions.Jean-Yves Jaffray - 1989 - Theory and Decision 26 (2):99-105.
  5.  40
    Consensus for Belief Functions and Related Uncertainty Measures.Carl G. Wagner - 1989 - Theory and Decision 26 (3):295-304.
  6.  63
    Connecting Dempster–Shafer Belief Functions with Likelihood-Based Inference.Mikel Aickin - 2000 - Synthese 123 (3):347-364.
    The Dempster–Shafer approach to expressing beliefabout a parameter in a statistical model is notconsistent with the likelihood principle. Thisinconsistency has been recognized for some time, andmanifests itself as a non-commutativity, in which theorder of operations (combining belief, combininglikelihood) makes a difference. It is proposed herethat requiring the expression of belief to be committed to the model (and to certain of itssubmodels) makes likelihood inference very nearly aspecial case of the Dempster–Shafer theory.
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  7. Belief Functions and Default Reasoning.Salem Benferhat, Alessandro Saffiotti & Philippe Smets - 2000 - Artificial Intelligence 122 (1--2):1--69.
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  8.  28
    Second-Order Probabilities and Belief Functions.Jonathan Baron - 1987 - Theory and Decision 23 (1):25-36.
  9. Reasoning with Belief Functions: An Analysis of Compatibility.Judea Pearl - 1990 - International Journal of Approximate Reasoning 4:363--389.
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  10.  23
    Statistical Evidence and Belief Functions.Teddy Seidenfeld - 1978 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:478 - 489.
    PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1978, Volume Two: Symposia and Invited Papers. (1978), pp. 478-489.
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  11.  14
    Probability of Provability and Belief Functions.Philippe Smets - 1991 - Logique Et Analyse 133 (134):177-195.
  12.  8
    A Study of Probabilities and Belief Functions Under Conflicting Evidence: Comparisons and New Methods.Mary Deutsch-McLeish - 1991 - In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. pp. 41--49.
  13.  3
    Propagating Belief Functions Through Constraints Systems.Jürg Kohlas & Paul-André Monney - 1991 - In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. pp. 50--57.
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  14. Rejoinder to Comments on ``Reasoning with Belief Functions: An Analysis of Compatibility.Judea Pearl - 1992 - International Journal of Approximate Reasoning 6 (3):425--443.
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  15. Comments on Shafer's``Perspectives on the Theory and Practice of Belief Functions''.Larry Wasserman - 1992 - International Journal of Approximate Reasoning 6 (2):367--375.
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  16.  67
    The Dynamics of Belief: Contractions and Revisions of Probability Functions.Peter Gärdenfors - 1986 - Topoi 5 (1):29-37.
    Using probability functions defined over a simple language as models of states of belief, my goal in this article has been to analyse contractions and revisions of beliefs. My first strategy was to formulate postulates for these processes. Close parallels between the postulates for contractions and the postulates for revisions have been established - the results in Section 5 show that contractions and revisions are interchangeable. As a second strategy, some suggestions for more or less explicit constructive definitions (...)
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  17.  43
    On Belief: Aims, Norms, and Functions.C. J. Atkinson - 2018 - Dissertation, Lingnan University
    In this dissertation, I explore whether teleological, normative, and functional theories of belief each have the resources to answer three central questions about the nature and normativity of belief. These questions are: (i) what are beliefs, (ii), why do we have them, and (iii) how should we interpret doxastic correctness--the principle that it is correct to believe that p if and only if p? -/- I argue that teleological and normative theories fail to adequately address these questions, and (...)
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  18.  93
    Rational Belief Change, Popper Functions and Counterfactuals.William L. Harper - 1975 - Synthese 30 (1-2):221 - 262.
    This paper uses Popper's treatment of probability and an epistemic constraint on probability assignments to conditionals to extend the Bayesian representation of rational belief so that revision of previously accepted evidence is allowed for. Results of this extension include an epistemic semantics for Lewis' theory of counterfactual conditionals and a representation for one kind of conceptual change.
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  19.  65
    Frege On Shared Belief and Total Functions.Patricia A. Blanchette - 2012 - Journal of Philosophy 109 (1-2):9-39.
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  20.  16
    A Computational Model of the Belief System Under the Scope of Social Communication.María Teresa Signes Pont, Higinio Mora Mora, Gregorio De Miguel Casado & David Gil Méndez - 2016 - Foundations of Science 21 (1):215-223.
    This paper presents an approach to the belief system based on a computational framework in three levels: first, the logic level with the definition of binary local rules, second, the arithmetic level with the definition of recursive functions and finally the behavioural level with the definition of a recursive construction pattern. Social communication is achieved when different beliefs are expressed, modified, propagated and shared through social nets. This approach is useful to mimic the belief system because the (...)
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  21. Some Connections Between Epistemic Logic and the Theory of Nonadditive Probability.Philippe Mongin - 1992 - In Paul Humphreys (ed.), Patrick Suppes: Scientific Philosopher. Dordrecht: Kluwer. pp. 135-171.
    This paper is concerned with representations of belief by means of nonadditive probabilities of the Dempster-Shafer (DS) type. After surveying some foundational issues and results in the D.S. theory, including Suppes's related contributions, the paper proceeds to analyze the connection of the D.S. theory with some of the work currently pursued in epistemic logic. A preliminary investigation of the modal logic of belief functions à la Shafer is made. There it is shown that the Alchourrron-Gärdenfors-Makinson (A.G.M.) logic (...)
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  22. Nash Equilibrium with Lower Probabilities.Ebbe Groes, Hans Jørgen Jacobsen, Birgitte Sloth & Torben Tranaes - 1998 - Theory and Decision 44 (1):37-66.
    We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible (...)
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  23.  43
    Explaining Modulation of Reasoning by Belief.Vinod Goel & Raymond J. Dolan - 2003 - Cognition 87 (1):B11-B22.
    Although deductive reasoning is a closed system, one's beliefs about the world can influence validity judgements. To understand the associated functional neuroanatomy of this belief-bias we studied 14 volunteers using event-related fMRI, as they performed reasoning tasks under neutral, facilitatory and inhibitory belief conditions. We found evidence for the engagement of a left temporal lobe system during belief-based reasoning and a bilateral parietal lobe system during belief-neutral reasoning. Activation of right lateral prefrontal cortex was evident when (...)
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  24. Probabilistic Dynamic Belief Revision.Alexandru Baltag & Sonja Smets - 2008 - Synthese 165 (2):179 - 202.
    We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge (...)
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  25.  65
    A Semantic Approach to Nonmonotonic Reasoning: Inference Operations and Choice, Uppsala Prints and Preprints in Philosophy, 1994, No 10.Sten Lindström - manuscript
    This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premises. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred ones. (...)
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  26. Tensed Belief.Vasilis Tsompanidis - 2011 - Dissertation, University of California Santa Barbara
    Human beings seem to capture time and the temporal properties of events and things in thought by having beliefs usually expressed with statements using tense, or notions such as ‘now’, ‘past’ or ‘future’. Tensed beliefs like these seem indispensable for correct reasoning and timely action. For instance, my belief that my root canal is over seems inexpressible with a statement that does not use tense or a temporal indexical. However, the dominant view on the nature of time is that (...)
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  27.  39
    Belief System Foundations of Backward Induction.Antonio Quesada - 2002 - Theory and Decision 53 (4):393-403.
    Two justifications of backward induction (BI) in generic perfect information games are formulated using Bonanno's (1992; Theory and Decision 33, 153) belief systems. The first justification concerns the BI strategy profile and is based on selecting a set of rational belief systems from which players have to choose their belief functions. The second justification concerns the BI path of play and is based on a sequential deletion of nodes that are inconsistent with the choice of rational (...)
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  28. Functions, Warrant, History.Peter J. Graham - 2014 - In Abrol Fairweather & Owen Flanagan (eds.), Naturalizing Epistemic Virtue. Cambridge University Press. pp. 15-35.
    I hold that epistemic warrant consists in the normal functioning of the belief-forming process when the process has forming true beliefs reliably as an etiological function. Evolution by natural selection is the central source of etiological functions. This leads many to think that on my view warrant requires a history of natural selection. What then about learning? What then about Swampman? Though functions require history, natural selection is not the only source. Self-repair and trial-and-error learning are both (...)
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  29.  62
    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 (...)
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  30.  66
    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 (1931–1996), Peter Gärdenfors, and David Makinson (AGM), "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 twentyfive years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators (...)
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  31.  36
    Bridging Ranking Theory and the Stability Theory of Belief.Eric Raidl & Niels Skovgaard-Olsen - 2017 - Journal of Philosophical Logic 46 (6):577-609.
    In this paper we compare Leitgeb’s stability theory of belief and Spohn’s ranking-theoretic account of belief. We discuss the two theories as solutions to the lottery paradox. To compare the two theories, we introduce a novel translation between ranking functions and probability functions. We draw some crucial consequences from this translation, in particular a new probabilistic belief notion. Based on this, we explore the logical relation between the two belief theories, showing that models of (...)
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  32.  63
    Coherence and Conservatism in the Dynamics of Belief Part I: Finding the Right Framework.Hans Rott - 1999 - Erkenntnis 50 (2-3):387-412.
    In this paper I discuss the foundations of a formal theory of coherent and conservative belief change that is suitable to be used as a method for constructing iterated changes of belief, sensitive to the history of earlier belief changes, and independent of any form of dispositional coherence. I review various ways to conceive the relationship between the beliefs actually held by an agent and her belief change strategies, show the problems they suffer from, and suggest (...)
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  33.  25
    Coherence and Conservatism in the Dynamics of Belief. Part II: Iterated Belief Change Without Dispositional Coherence.Hans Rott - 2003 - Journal of Logic and Computation 13 (1):111-145.
    This paper studies the idea of conservatism with respect to belief change strategies in the setting of unary, iterated belief revision functions (based on the conclusions of Rott, ‘Coherence and Conservatism in the Dynamics of Belief, Part I: Finding the Right Framework’, Erkenntnis 50, 1999, 387–412). Special attention is paid to the case of ‘basic belief change’ where neither the (weak) AGM postulates concerning conservatism with respect to beliefs nor the (stong) supplementary AGM postulates concerning (...)
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  34.  78
    Belief From the Past.Andrew Naylor - 2012 - European Journal of Philosophy 20 (4):598-620.
    Abstract: A person who remembers having done something has a belief that she did it from having done it. To have a belief that one did something from having done it is to believe that one did the action on the (causal) basis of having done it, where this belief (in order for one to have it) need not be (causally) based even in part on any contributor to the belief other than doing the action. The (...)
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  35. Belief and Contextual Acceptance.Eleonora Cresto - 2010 - Synthese 177 (1):41-66.
    I develop a strategy for representing epistemic states and epistemic changes that seeks to be sensitive to the difference between voluntary and involuntary aspects of our epistemic life, as well as to the role of pragmatic factors in epistemology. The model relies on a particular understanding of the distinction between full belief and acceptance , which makes room for the idea that our reasoning on both practical and theoretical matters typically proceeds in a contextual way. Within this framework, I (...)
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  36. Defining Ontological Categories in an Expansion of Belief Dynamics.Jan Westerhoff - 2002 - Logic and Logical Analysis 10 (3):199-210.
    There have been attempts to get some logic out of belief dynamics, i.e. attempts to define the constants of propositional logic in terms of functions from sets of beliefs to sets of beliefs. It is interesting to see whether something similar can be done for ontological categories, i.e. ontological constants. The theory presented here will be a (modest) expansion of belief dynamics: it will not only incorporate beliefs, but also parts of beliefs, so called belief fragments. (...)
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  37.  39
    Bounded Revision: Two-Dimensional Belief Change Between Conservative and Moderate Revision.Hans Rott - 2012 - Journal of Philosophical Logic 41 (1):173-200.
    This paper presents the model of ‘bounded revision’ that is based on two-dimensional revision functions taking as arguments pairs consisting of an input sentence and a reference sentence. The key idea is that the input sentence is accepted as far as (and just a little further than) the reference sentence is ‘cotenable’ with it. Bounded revision satisfies the AGM axioms as well as the Same Beliefs Condition (SBC) saying that the set of beliefs accepted after the revision does not (...)
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  38.  63
    AGM-Like Paraconsistent Belief Change.Rafael R. Testa, Marcelo E. Coniglio & Marcio M. Ribeiro - 2017 - Logic Journal of the IGPL 25 (4):632-672.
    Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three (...)
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  39.  78
    Belief Change in Branching Time: AGM-Consistency and Iterated Revision. [REVIEW]Giacomo Bonanno - 2012 - Journal of Philosophical Logic 41 (1):201-236.
    We study belief change in the branching-time structures introduced in Bonanno (Artif Intell 171:144–160, 2007 ). First, we identify a property of branching-time frames that is equivalent (when the set of states is finite) to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the AGM (...)
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  40.  18
    A General Family of Preferential Belief Removal Operators.Richard Booth, Thomas Meyer & Chattrakul Sombattheera - 2012 - Journal of Philosophical Logic 41 (4):711 - 733.
    Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in Booth et al. (Artif Intell 174:1339-1368, 2010). However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of Booth et al. (Artif Intell 174: 1339-1368, (...)
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  41. Ordinal Conditional Functions. A Dynamic Theory of Epistemic States.Wolfgang Spohn - 1988 - In W. L. Harper & B. Skyrms (eds.), Causation in Decision, Belief Change, and Statistics, vol. II. Kluwer Academic Publishers.
    It is natural and important to have a formal representation of plain belief, according to which propositions are held true, or held false, or neither. (In the paper this is called a deterministic representation of epistemic states). And it is of great philosophical importance to have a dynamic account of plain belief. AGM belief revision theory seems to provide such an account, but it founders at the problem of iterated belief revision, since it can generally account (...)
     
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  42.  71
    Jaffray’s Ideas on Ambiguity.Peter P. Wakker - 2011 - Theory and Decision 71 (1):11-22.
    This paper discusses Jean-Yves Jaffray’s ideas on ambiguity and the views underlying his ideas. His models, developed 20 years ago, provide the most tractable separation of risk attitudes, ambiguity attitudes, and ambiguity beliefs available in the literature today.
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  43.  41
    Foundations of the Theory of Evidence: Resolving Conflict Among Schemata.Bonnie K. Ray & David H. Krantz - 1996 - Theory and Decision 40 (3):215-234.
  44. 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 (...)
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  45. The Evolutionary Paths to Collective Rituals: An Interdisciplinary Perspective on the Origins and Functions of the Basic Social Act.Martin Lang - 2019 - Archive for the Psychology of Religion 41 (3):224-252.
    The present article is an elaborated and upgraded version of the Early Career Award talk that I delivered at the IAPR 2019 conference in Gdańsk, Poland. In line with the conference’s thematic focus on new trends and neglected themes in psychology of religion, I argue that psychology of religion should strive for firmer integration with evolutionary theory and its associated methodological toolkit. Employing evolutionary theory enables to systematize findings from individual psychological studies within a broader framework that could resolve lingering (...)
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  46. Imprecise Bayesianism and Global Belief Inertia.Aron Vallinder - 2018 - British Journal for the Philosophy of Science 69 (4):1205-1230.
    Traditional Bayesianism requires that an agent’s degrees of belief be represented by a real-valued, probabilistic credence function. However, in many cases it seems that our evidence is not rich enough to warrant such precision. In light of this, some have proposed that we instead represent an agent’s degrees of belief as a set of credence functions. This way, we can respect the evidence by requiring that the set, often called the agent’s credal state, includes all credence (...) that are in some sense compatible with the evidence. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In this article I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid it without compromising the initial evidentialist motivation. _1_ Introduction _2_ Precision and Its Problems _3_ Imprecise Bayesianism and Respecting Ambiguous Evidence _4_ Local Belief Inertia _5_ From Local to Global Belief Inertia _6_ Responding to Global Belief Inertia _7_ Conclusion. (shrink)
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  47.  62
    Measuring the Overall Incoherence of Credence Functions.Julia Staffel - 2015 - Synthese 192 (5):1467-1493.
    Many philosophers hold that the probability axioms constitute norms of rationality governing degrees of belief. This view, known as subjective Bayesianism, has been widely criticized for being too idealized. It is claimed that the norms on degrees of belief postulated by subjective Bayesianism cannot be followed by human agents, and hence have no normative force for beings like us. This problem is especially pressing since the standard framework of subjective Bayesianism only allows us to distinguish between two kinds (...)
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  48.  51
    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 (...)
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  49.  27
    Intention, Belief, and Intentional Action.Alfred R. Mele - 1989 - American Philosophical Quarterly 26 (1):19 - 30.
    Ordinary usage supports both a relatively strong belief requirement on intention and a tight conceptual connection between intention and intentional action. More specifically, it speaks in favor both of the view that "S intends to A" entails "S believes that he (probably) will A" and of the thesis that "S intentionally A-ed" entails "S intended to A." So, at least, proponents of these ideas often claim or assume, and with appreciable justification. The conjunction of these two ideas, however, has (...)
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  50.  83
    Ranking Functions, AGM Style.Wolfgang Spohn - 1999 - Internet Festschrift for Peter Gärdenfors.
    First, ranking functions are argued to be superior to AGM belief revision theory in two crucial respects. Second, it is shown how ranking functions are uniquely reflected in iterated belief change. More precisely, conditions on threefold contractions are specified which suffice for representing contractions by a ranking function uniquely up to multiplication by a positive integer. Thus, an important advantage AGM theory seemed to have over ranking functions proves to be spurious.
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