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  1. Jake Chandler (2013). Acceptance, Aggregation and Scoring Rules. 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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  2. Adnan Darwiche & Judea Pearl (1997). On the Logic of Iterated Belief Revision. Artificial Intelligence 89:1-29.
    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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  3. Peter Fritz, Belief Revision in Dynamic Epistemic Logic and Ranking Theory.
    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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  4. Moisés Goldszmidt & Judea Pearl (1996). Qualitative Probabilities for Default Reasoning, Belief Revision, and Causal Modeling. Artificial Intelligence 84:57-112.
    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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  5. Franz Huber (2009). Belief and Degrees of Belief. 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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  6. Franz Huber (2009). Ranking Functions. 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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  7. Franz Huber (2007). The Logic of Theory Assessment. 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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  8. Franz Huber (2007). The Consistency Argument for Ranking Functions. 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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  9. Franz Huber (2006). Ranking Functions and Rankings on Languages. Artificial Intelligence 170:462-471.
    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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  10. Kevin T. Kelly (1999). Iterated Belief Revision, Reliability, and Inductive Amnesia. 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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  11. Abhaya C. Nayak (1994). Iterated Belief Change Based on Epistemic Entrenchment. 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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  12. Raghav Ramachandran, Abhaya C. Nayak & Mehmet A. Orgun (2012). Three Approaches to Iterated Belief Contraction. 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. Wolfgang Spohn (2012). The Laws of Belief: Ranking Theory and its Philosophical Applications. 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. Wolfgang Spohn (2009). A Survey of Ranking Theory. 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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  15. Wolfgang Spohn (2006). Isaac Levi's Potentially Surprising Epistemological Picture. 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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  16. Wolfgang Spohn (2006). Causation: An Alternative. 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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  17. Wolfgang Spohn (2005). Enumerative Induction and Lawlikeness. 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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  18. Wolfgang Spohn (2004). Laws Are Persistent Inductives Schemes. In F. Stadler (ed.), Induction and Deduction in the Sciences. Kluwer. 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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  19. Wolfgang Spohn (2002). Laws, Ceteris Paribus Conditions, and the Dynamics of Belief. 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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  20. Wolfgang Spohn (2002). A Brief Comparison of Pollock's Defeasible Reasoning and Ranking Functions. 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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  21. Wolfgang Spohn (2002). Lehrer Meets Ranking Theory. In Erik J. Olsson (ed.), The Epistemology of Keith Lehrer. Kluwer.
    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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  22. Wolfgang Spohn, Ranking Functions, AGM Style. 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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  23. Wolfgang Spohn (1994). On the Properties of Conditional Independence. In Paul Humphreys (ed.), Patrick Suppes, Scientific Philosopher Vol. 1: Probability and Probabilistic Causality. Kluwer.
    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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  24. Wolfgang Spohn (1990). A General Non-Probabilistic Theory of Inductive Reasoning. 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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  25. Wolfgang Spohn (1988). Ordinal Conditional Functions. A Dynamic Theory of Epistemic States. In W. L. Harper & B. Skyrms (eds.), Causation in Decision, Belief Change, and Statistics, vol. II. Kluwer.
    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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  26. Wolfgang Spohn & Matthias Hild (2008). The Measurement of Ranks and the Laws of Iterated Contraction. Artificial Intelligence 172:1195-1218.
    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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  27. J. Weisberg (forthcoming). Updating, Undermining, and Independence. British Journal for the Philosophy of Science:axt052.
    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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  28. Emil Weydert (2012). Conditional Ranking Revision. 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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