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  1. Elementary Iterated Revision and the Levi Identity.Jake Chandler & Richard Booth - forthcoming - In Proceedings of the 7th International Conference on Logic, Rationality and Interaction (LORI 2019).
    Recent work has considered the problem of extending to the case of iterated belief change the so-called `Harper Identity' (HI), which defines single-shot contraction in terms of single-shot revision. The present paper considers the prospects of providing a similar extension of the Levi Identity (LI), in which the direction of definition runs the other way. We restrict our attention here to the three classic iterated revision operators--natural, restrained and lexicographic, for which we provide here the first collective characterisation in the (...)
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  2. Degrees of Assertability.Sam Carter - 2020 - Philosophy and Phenomenological Research 104 (1):19-49.
    Philosophy and Phenomenological Research, Volume 104, Issue 1, Page 19-49, January 2022.
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  3. The logic of epistemic justification.Martin Smith - 2018 - Synthese 195 (9):3857-3875.
    Theories of epistemic justification are commonly assessed by exploring their predictions about particular hypothetical cases – predictions as to whether justification is present or absent in this or that case. With a few exceptions, it is much less common for theories of epistemic justification to be assessed by exploring their predictions about logical principles. The exceptions are a handful of ‘closure’ principles, which have received a lot of attention, and which certain theories of justification are well known to invalidate. But (...)
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  4. Why follow the royal rule?Franz Huber - 2017 - Synthese 194 (5).
    This note is a sequel to Huber. It is shown that obeying a normative principle relating counterfactual conditionals and conditional beliefs, viz. the royal rule, is a necessary and sufficient means to attaining a cognitive end that relates true beliefs in purely factual, non-modal propositions and true beliefs in purely modal propositions. Along the way I will sketch my idealism about alethic or metaphysical modality.
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  5. The Laws of Belief: Ranking Theory & its Philosophical Applications, by Wolfgang Spohn.A. C. Paseau - 2017 - Mind 126 (501):273-278.
    The Laws of Belief: Ranking Theory & its Philosophical Applications, by SpohnWolfgang. New York: Oxford University Press, 2012. Pp. xv + 598.
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  6. "If Oswald had not killed Kennedy" – Spohn on Counterfactuals.Hans Rott - 2016 - In Wolfgang Freitag, Hans Rott, Holger Sturm & Alexandra Zinke (eds.), Von Rang und Namen. Philosophical Essays in Honour of Wolfgang Spohn. Münster, Germany: Mentis. pp. 379–399.
    Wolfgang Spohn's theory of ranking functions is an elegant and powerful theory of the structure and dynamics of doxastic states. In two recent papers, Spohn has applied it to the analysis of conditionals, claiming to have presented a unified account of indicative and subjunctive (counterfactual) conditionals. I argue that his analysis fails to account for counterfactuals that refer to indirect causes. The strategy of taking the transitive closure that Spohn employs in the theory of causation is not available for counterfactuals. (...)
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  7. Between Probability and Certainty: What Justifies Belief.Martin Smith - 2016 - Oxford, GB: Oxford University Press UK.
    This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...)
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  8. Updating, Undermining, and Independence.Jonathan Weisberg - 2015 - British Journal for the Philosophy of Science 66 (1):121-159.
    Sometimes appearances provide epistemic support that gets undercut later. In an earlier paper I argued that standard Bayesian update rules are at odds with this phenomenon because they are ‘rigid’. Here I generalize and bolster that argument. I first show that the update rules of Dempster–Shafer theory and ranking theory are rigid too, hence also at odds with the defeasibility of appearances. I then rebut three Bayesian attempts to solve the problem. I conclude that defeasible appearances pose a more difficult (...)
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  9. Making Ranking Theory Useful for Psychology of Reasoning.Niels Skovgaard Olsen - 2014 - Dissertation, University of Konstanz
    An organizing theme of the dissertation is the issue of how to make philosophical theories useful for scientific purposes. An argument for the contention is presented that it doesn’t suffice merely to theoretically motivate one’s theories, and make them compatible with existing data, but that philosophers having this aim should ideally contribute to identifying unique and hard to vary predictions of their theories. This methodological recommendation is applied to the ranking-theoretic approach to conditionals, which emphasizes the epistemic relevance and the (...)
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  10. Unvergleichbarkeit und unabhängige Bedeutung.Hans Rott - 2014 - Zeitschrift für Philosophische Forschung 68 (2):237–241.
    This is a short discussion review of Wolfgang Spohn, The Laws of Belief, Oxford UP 2012. I argue, first, that it is important to account for incomparabilities in the plausibilities of possible worlds or propositions, and second, that the meaning of input parameters specifying the degree to which a proposition is to be accepted should be independent of the agent's belief state.
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  11. Acceptance, Aggregation and Scoring Rules.Jake Chandler - 2013 - Erkenntnis 78 (1):201-217.
    As the ongoing literature on the paradoxes of the Lottery and the Preface reminds us, the nature of the relation between probability and rational acceptability remains far from settled. This article provides a novel perspective on the matter by exploiting a recently noted structural parallel with the problem of judgment aggregation. After offering a number of general desiderata on the relation between finite probability models and sets of accepted sentences in a Boolean sentential language, it is noted that a number (...)
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  12. Three Approaches to Iterated Belief Contraction.Raghav Ramachandran, Abhaya C. Nayak & Mehmet A. Orgun - 2012 - Journal of Philosophical Logic 41 (1):115-142.
    In this paper we investigate three approaches to iterated contraction, namely: the Moderate (or Priority) contraction, the Natural (or Conservative) contraction, and the Lexicographic contraction. We characterise these three contraction functions using certain, arguably plausible, properties of an iterated contraction function. While we provide the characterisation of the first two contraction operations using rationality postulates of the standard variety for iterated contraction, we found doing the same for the Lexicographic contraction more challenging. We provide its characterisation using a variation of (...)
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  13. The Laws of Belief: Ranking Theory and its Philosophical Applications.Wolfgang Spohn - 2012 - Oxford: Oxford University Press.
    Wolfgang Spohn presents the first full account of the dynamic laws of belief, by means of ranking theory. This book is his long-awaited presentation of ranking theory and its ramifications.
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  14. Conditional Ranking Revision: Iterated Revision with Sets of Conditionals.Emil Weydert - 2012 - Journal of Philosophical Logic 41 (1):237-271.
    In the context of a general framework for belief dynamics which interprets revision as doxastic constraint satisfaction, we discuss a proposal for revising quasi-probabilistic belief measures with finite sets of graded conditionals. The belief states are ranking measures with divisible values (generalizing Spohn’s epistemology), and the conditionals are interpreted as ranking constraints. The approach is inspired by the minimal information paradigm and based on the principle-guided canonical construction of a ranking model of the input conditionals. This is achieved by extending (...)
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  15. Belief and Degrees of Belief.Franz Huber - 2009 - In F. Huber & C. Schmidt-Petri (eds.), Degrees of Belief. Springer.
    Degrees of belief are familiar to all of us. Our confidence in the truth of some propositions is higher than our confidence in the truth of other propositions. We are pretty confident that our computers will boot when we push their power button, but we are much more confident that the sun will rise tomorrow. Degrees of belief formally represent the strength with which we believe the truth of various propositions. The higher an agent’s degree of belief for a particular (...)
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  16. Ranking Functions.Franz Huber - 2009 - In A. Pazos Sierra, J. R. Rabunal Dopico & J. Dorado de la Calle (eds.), Encyclopedia of Artificial Intelligence. Hershey.
    Ranking functions have been introduced under the name of ordinal conditional functions in Spohn (1988; 1990). They are representations of epistemic states and their dynamics. The most comprehensive and up to date presentation is Spohn (manuscript).
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  17. Degrees all the way down: Beliefs, non-beliefs and disbeliefs.Hans Rott - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Springer. pp. 301--339.
    This paper combines various structures representing degrees of belief, degrees of disbelief, and degrees of non-belief (degrees of expectations) into a unified whole. The representation uses relations of comparative necessity and possibility, as well as non-probabilistic functions assigning numerical values of necessity and possibility. We define all-encompassing necessity structures which have weak expectations (mere hypotheses, guesses, conjectures, etc.) occupying the lowest ranks and very strong, ineradicable ('a priori') beliefs occupying the highest ranks. Structurally, there are no differences from the top (...)
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  18. A Survey of Ranking Theory.Wolfgang Spohn - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Springer.
    "A Survey of Ranking Theory": The paper gives an up-to-date survey of ranking theory. It carefully explains the basics. It elaborates on the ranking theoretic explication of reasons and their balance. It explains the dynamics of belief statable in ranking terms and indicates how the ranks can thereby be measured. It suggests how the theory of Bayesian nets can be carried over to ranking theory. It indicates what it might mean to objectify ranks. It discusses the formal and the philosophical (...)
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  19. Information Structures in Belief Revision.Hans Rott - 2008 - In Johan Van Benthem & Pieter Adriaans (eds.), Philosophy of Information, Vol. 8 of the Handbook of the Philosophy of Science. Amsterdam: Elsevier. pp. 457–482.
    This is a survey paper. Contents: 1 Introduction ― 2 Preliminary remarks on information, truth and mind - 2.1 Remarks on information and truth - 2.2 Some clues from the philosophy of mind - 2.3 Functionalism as applied to belief revision - 2.4 Filling in the parameters ― 3 Belief change = revision + reflection - 3.1 Foundationalism - 3.2 Coherentism ― 4 Inference operations for simple change operations: three examples - 4.1 Example 1: flat data bases - 4.2 Example (...)
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  20. The Measurement of Ranks and the Laws of Iterated Contraction.Wolfgang Spohn & Matthias Hild - 2008 - Artificial Intelligence 172 (10):1195-1218.
    Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper shows how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multiplicative constant and thus how to measure ranks on a ratio scale. Thereby, it also shows how to completely axiomatize that behavior. The complete set of laws of iterated contraction it specifies amend the laws hitherto discussed in the literature.
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  21. The Consistency Argument for Ranking Functions.Franz Huber - 2007 - Studia Logica 86 (2):299-329.
    The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem. The latter says that an agent’s belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update rules.
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  22. The Logic of Theory Assessment.Franz Huber - 2007 - Journal of Philosophical Logic 36 (5):511-538.
    This paper starts by indicating the analysis of Hempel's conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper (...)
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  23. Ranking Functions and Rankings on Languages.Franz Huber - 2006 - Artificial Intelligence 170 (4-5):462-471.
    The Spohnian paradigm of ranking functions is in many respects like an order-of-magnitude reverse of subjective probability theory. Unlike probabilities, however, ranking functions are only indirectly—via a pointwise ranking function on the underlying set of possibilities W —defined on a field of propositions A over W. This research note shows under which conditions ranking functions on a field of propositions A over W and rankings on a language L are induced by pointwise ranking functions on W and the set of (...)
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  24. Isaac Levi’s potentially surprising epistemologicalpicture.Wolfgang Spohn - 2006 - In Erik J. Olsson (ed.), Knowledge and Inquiry: Essays on the Pragmatism of Isaac Levi. Cambridge University Press.
    This paper compares the epistemological conception of Isaac Levi with mine. We are joined in both giving a constructive answer to the relation of belief and probability, without reducing one to the other. However, our constructions differ in at least nine more or less important ways, all discussed in the paper. In particular, the paper explains the similarities and differences of Shackle's functions of potential surprise, as used by Levi, and my ranking functions in formal as well as in philosophical (...)
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  25. Causation: An alternative.Wolfgang Spohn - 2006 - British Journal for the Philosophy of Science 57 (1):93-119.
    The paper builds on the basically Humean idea that A is a cause of B iff A and B both occur, A precedes B, and A raises the metaphysical or epistemic status of B given the obtaining circumstances. It argues that in pursuit of a theory of deterministic causation this ‘status raising’ is best explicated not in regularity or counterfactual terms, but in terms of ranking functions. On this basis, it constructs a rigorous theory of deterministic causation that successfully deals (...)
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  26. Enumerative Induction and Lawlikeness.Wolfgang Spohn - 2005 - Philosophy of Science 72 (1):164-187.
    The paper is based on ranking theory, a theory of degrees of disbelief (and hence belief). On this basis, it explains enumerative induction, the confirmation of a law by its positive instances, which may indeed take various schemes. It gives a ranking theoretic explication of a possible law or a nomological hypothesis. It proves, then, that such schemes of enumerative induction uniquely correspond to mixtures of such nomological hypotheses. Thus, it shows that de Finetti's probabilistic representation theorems may be transformed (...)
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  27. Laws Are Persistent Inductives Schemes.Wolfgang Spohn - 2004 - In F. Stadler (ed.), Vienna Circle Institute Yearbook. Kluwer Academic Publishers. pp. 11--135.
    The characteristic difference between laws and accidental generalizations lies in our epistemic or inductive attitude towards them. This idea has taken various forms and dominated the discussion about lawlikeness in the last decades. Hence, ranking theory with its resources of formalizing defeasible reasoning or inductive schemes seems ideally suited to explicate the idea in a formal way. This is what the paper attempts to do. Thus it will turn out that a law is simply the deterministic analogue of a sequence (...)
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  28. A brief comparison of Pollock's defeasible reasoning and ranking functions.Wolfgang Spohn - 2002 - Synthese 131 (1):39-56.
    In this paper two theories of defeasible reasoning, Pollock's account and my theory of ranking functions, are compared, on a strategic level, since a strictly formal comparison would have been unfeasible. A brief summary of the accounts shows their basic difference: Pollock's is a strictly computational one, whereas ranking functions provide a regulative theory. Consequently, I argue that Pollock's theory is normatively defective, unable to provide a theoretical justification for its basic inference rules and thus an independent notion of admissible (...)
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  29. Laws, ceteris paribus conditions, and the dynamics of belief.Wolfgang Spohn - 2002 - Erkenntnis 57 (3):373-394.
    The characteristic difference between laws and accidental generalizations lies in our epistemic or inductive attitude towards them. This idea has taken various forms and dominated the discussion about lawlikeness in the last decades. Likewise, the issue about ceteris paribus conditions is essentially about how we epistemically deal with exceptions. Hence, ranking theory with its resources of defeasible reasoning seems ideally suited to explicate these points in a formal way. This is what the paper attempts to do. Thus it will turn (...)
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  30. Lehrer Meets Ranking Theory.Wolfgang Spohn - 2002 - In Erik J. Olsson (ed.), The Epistemology of Keith Lehrer. Kluwer Academic Publishers.
    Meets what? Ranking theory is, as far as I know, the only existing theory suited for underpinning Keith Lehrer’s account of knowledge and justification. If this is true, it’s high time to bring both together. This is what I shall do in this paper. However, the result of defining Lehrer’s primitive notions in terms of ranking theory will be disappointing: justified acceptance will, depending on the interpretation, either have an unintelligible structure or reduce to mere acceptance, and in the latter (...)
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  31. A Qualitative Linear Utility Theory for Spohn's Theory of Epistemic Beliefs.Phan H. Giang & Prakash P. Shenoy - 2000 - In C. Boutilier & M. Goldszmidt (eds.), Uncertainty in Artificial Intelligence 16. Morgan Kaufmann.
    In this paper, we formulate a qualitative “linear” utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision problem in which the uncertainty is expressed qualitatively should behave so as to maximize “qualitative expected utility.” Our axiomatization of the qualitative utility is similar to the axiomatization developed by von Neumann and Morgenstern for probabilistic lotteries. We compare our results with other recent results in qualitative (...)
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  32. On Transformations between Probability and Spohnian Disbelief Functions.Phan H. Giang & Prakash P. Shenoy - 1999 - In K. B. Laskey & H. Prade (eds.), Uncertainty in Artificial Intelligence 15. Morgan Kaufmann.
    In this paper, we analyze the relationship between probability and Spohn's theory for representation of uncertain beliefs. Using the intuitive idea that the more probable a proposition is, the more believable it is, we study transformations from probability to Spohnian disbelief and vice-versa. The transformations described in this paper are different from those described in the literature. In particular, the former satisfies the principle of ordinal congurence while the latter does not. Such transformations between probability and Spohn's calculi can contribute (...)
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  33. 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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  34. 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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  35. 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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  36. Qualitative probabilities for default reasoning, belief revision, and causal modeling.Moisés Goldszmidt & Judea Pearl - 1996 - Artificial Intelligence 84 (1-2):57-112.
    This paper presents a formalism that combines useful properties of both logic and probabilities. Like logic, the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and, like probability, it permits us to express if-then rules with different levels of firmness and to retract beliefs in response to changing observations. Rules are interpreted as order-of-magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds. Inferences are supported by a unique priority ordering on rules (...)
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  37. 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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  38. On the Properties of Conditional Independence.Wolfgang Spohn - 1994 - In Paul Humphreys (ed.), Patrick Suppes, Scientific Philosopher Vol. 1: Probability and Probabilistic Causality. Kluwer Academic Publishers.
    As the paper explains, it is crucial to epistemology in general and to the theory of causation in particular to investigate the properties of conditional independence as completely as possible. The paper summarizes the most important results concerning conditional independence with respect to two important representations of epistemic states, namely (strictly positive) probability measures and natural conditional (or disbelief or ranking) functions. It finally adds some new observations.
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  39. On Spohn’s rule for revision of beliefs.Prakash P. Shenoy - 1991 - International Journal of Approximate Reasoning 5 (2):149-181.
    The main ingredients of Spohn's theory of epistemic beliefs are (1) a functional representation of an epistemic state called a disbelief function and (2) a rule for revising this function in light of new information. The main contribution of this paper is as follows. First, we provide a new axiomatic definition of an epistemic state and study some of its properties. Second, we study some properties of an alternative functional representation of an epistemic state called a Spohnian belief function. Third, (...)
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  40. On Spohn's theory of epistemic beliefs.Prakash P. Shenoy - 1991 - In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. pp. 1--13.
    This paper is about Spohn's theory of epistemic beliefs. The main ingredients of Spohn's theory are (i) a functional representation of an epistemic state called a disbelief function, and (ii) a rule for revising this function in light of new information. The main contribution of this paper is as follows. First, we provide a new axiomatic definition of an epistemic state and study some of its properties. Second, we state a rule for combining disbelief functions that is mathematically equivalent to (...)
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  41. A General Non-Probabilistic Theory of Inductive Reasoning.Wolfgang Spohn - 1990 - In R. D. Shachter, T. S. Levitt, J. Lemmer & L. N. Kanal (eds.), Uncertainty in Artificial Intelligence 4. Elsevier.
    Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through information or experience; induction and belief change are one and same topic, after all. The most basic of these rules is simply to conditionalize with respect to the information received; and there are similar and more general rules. 1 Hence, a fundamental reason for the epistemological success of (...)
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  42. Unfolding and consensus ranking: A prestige ladder for technical occupations.G. De Soete, H. Feger & K. C. Klauer - 1989 - In Geert de Soete, Hubert Feger & Karl C. Klauer (eds.), New Developments in Psychological Choice Modeling. Distributors for the United States and Canada, Elsevier Science.
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  43. 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 only for one step (...)
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  44. Preference, Rational Choice, and Arrow's Theorem.Tal Scriven - 1981 - Journal of Philosophy 78 (12):778-785.
  45. Belief Revision in Dynamic Epistemic Logic and Ranking Theory.Peter Fritz - manuscript
    I want to look at recent developments of representing AGM-style belief revision in dynamic epistemic logics and the options for doing something similar for ranking theory. Formally, my aim will be modest: I will define a version of basic dynamic doxastic logic using ranking functions as the semantics. I will show why formalizing ranking theory this way is useful for the ranking theorist first by showing how it enables one to compare ranking theory more easily with other approaches to belief (...)
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