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  1. Conditional Probability From an Ontological Point of View.Rani Lill Anjum, Johan Arnt Myrstad & Stephen Mumford - manuscript
    This paper argues that the technical notion of conditional probability, as given by the ratio analysis, is unsuitable for dealing with our pretheoretical and intuitive understanding of both conditionality and probability. This is an ontological account of conditionals that include an irreducible dispositional connection between the antecedent and consequent conditions and where the conditional has to be treated as an indivisible whole rather than compositional. The relevant type of conditionality is found in some well-defined group of conditional statements. As an (...)
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  2. Conditional Probability and Defeasible Inference.Horacio Arlo-Costa & Rohit Parikh - manuscript
    Journal of Philosophical Logic 34, 97-119, 2005.
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  3. In Defence of a Naïve Conditional Epistemology.Andrew Bacon - manuscript
    Numerous triviality results have been directed at a collection of views that tie the probability of a conditional sentence to the conditional probability of the consequent on its antecedent. -/- In this paper I argue that this identification makes little sense if conditional sentences are context sensitive. The best alternative, I argue, is a version of the thesis which states that if your total evidence is E then the evidential probability of a conditional evaluated in a context where E is (...)
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  4. Stalnaker’s Thesis in Context.Andrew Bacon - 2015 - Review of Symbolic Logic 8 (1):131-163.
    In this paper I present a precise version of Stalnaker's thesis and show that it is both consistent and predicts our intuitive judgments about the probabilities of conditionals. The thesis states that someone whose total evidence is E should have the same credence in the proposition expressed by 'if A then B' in a context where E is salient as they have conditional credence in the proposition B expresses given the proposition A expresses in that context. The thesis is formalised (...)
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  5. 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 and safe belief (...)
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  6. Entailment with Near Surety of Scaled Assertions of High Conditional Probability.Donald Bamber - 2000 - Journal of Philosophical Logic 29 (1):1-74.
    An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal (...)
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  7. Betting on Conditionals.Jean Baratgin, David E. Over & Guy Politzer - 2010 - Thinking and Reasoning 16 (3):172-197.
    A study is reported testing two hypotheses about a close parallel relation between indicative conditionals, if A then B , and conditional bets, I bet you that if A then B . The first is that both the indicative conditional and the conditional bet are related to the conditional probability, P(B|A). The second is that de Finetti's three-valued truth table has psychological reality for both types of conditional— true , false , or void for indicative conditionals and win , lose (...)
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  8. The Shooting-Room Paradox and Conditionalizing on Measurably Challenged Sets.Paul Bartha & Christopher Hitchcock - 1999 - Synthese 118 (3):403-437.
    We provide a solution to the well-known “Shooting-Room” paradox, developed by John Leslie in connection with his Doomsday Argument. In the “Shooting-Room” paradox, the death of an individual is contingent upon an event that has a 1/36 chance of occurring, yet the relative frequency of death in the relevant population is 0.9. There are two intuitively plausible arguments, one concluding that the appropriate subjective probability of death is 1/36, the other that this probability is 0.9. How are these two values (...)
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  9. Weisberg on Design: What Fine-Tuning's Got to Do with It.Darren Bradley - 2012 - Erkenntnis 77 (3):435-438.
    Jonathan Weisberg (2010 ) argues that, given that life exists, the fact that the universe is fine-tuned for life does not confirm the design hypothesis. And if the fact that life exists confirms the design hypothesis, fine-tuning is irrelevant. So either way, fine-tuning has nothing to do with it. I will defend a design argument that survives Weisberg’s critique — the fact that life exists supports the design hypothesis, but it only does so given fine-tuning.
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  10. Multidimensional Possible-World Semantics for Conditionals.R. Bradley - 2012 - Philosophical Review 121 (4):539-571.
    Adams’s Thesis, the claim that the probabilities of indicative conditionals equal the conditional probabilities of their consequents given their antecedents, has proven impossible to accommodate within orthodox possible-world semantics. This essay proposes a modification to the orthodoxy that removes this impossibility. The starting point is a proposal by Jeffrey and Stalnaker that conditionals take semantic values in the unit interval, interpreting these (à la McGee) as their expected truth-values at a world. Their theories imply a false principle, namely, that the (...)
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  11. Quantum Logic, Conditional Probability, and Interference.Jeffrey Bub - 1982 - Philosophy of Science 49 (3):402-421.
    Friedman and Putnam have argued (Friedman and Putnam 1978) that the quantum logical interpretation of quantum mechanics gives us an explanation of interference that the Copenhagen interpretation cannot supply without invoking an additional ad hoc principle, the projection postulate. I show that it is possible to define a notion of equivalence of experimental arrangements relative to a pure state φ , or (correspondingly) equivalence of Boolean subalgebras in the partial Boolean algebra of projection operators of a system, which plays a (...)
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  12. Conditional Intention.J. P. W. Cartwright - 1990 - Philosophical Studies 60 (3):233 - 255.
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  13. The Spacing of Sequentially Dependent Trials in Probability Learning.Jean P. Chapman - 1961 - Journal of Experimental Psychology 62 (6):545.
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  14. Comparative Probability for Conditional Events: A New Look Through Coherence.Giulianella Coletti, Angelo Gilio & Romano Scozzafava - 1993 - Theory and Decision 35 (3):237-258.
  15. Representability of Ordinal Relations on a Set of Conditional Events.Giulianella Coletti & Barbara Vantaggi - 2006 - Theory and Decision 60 (2-3):137-174.
  16. A Result in Renyi's Conditional Probability Theory with Application to Subjective Probability.Roger M. Cooke - 1983 - Journal of Philosophical Logic 12 (1):19 - 32.
  17. A Characterization of Imaging in Terms of Popper Functions.Charles B. Cross - 2000 - Philosophy of Science 67 (2):316-338.
    Despite the results of David Lewis, Peter Gärdenfors, and others, showing that imaging and classical conditionalization coincide only in the most trivial probabilistic models of belief revision, it turns out that imaging on a proposition A can always be described via Popper function conditionalization on a proposition that entails A. This result generalizes to any method of belief revision meeting certain minimal requirements. The proof is illustrated by an application of imaging in the context of the Monty Hall Problem.
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  18. On a Problem in Conditional Probability.A. I. Dale - 1974 - Philosophy of Science 41 (2):204-206.
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  19. A Theory of Bayesian Groups.Franz Dietrich - manuscript
    A group is often construed as a single agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated contribution “Groupthink”, Russell et al. (2015) apply the Bayesian paradigm to groups by requiring group credences to undergo a Bayesian revision whenever new information is learnt, i.e., whenever the individual credences undergo a Bayesian revision based on this information. Bayesians should often strengthen this requirement by extending it to non-public (...)
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  20. A Unified Characterization of Belief-Revision Rules.Franz Dietrich, Christian List & Richard Bradley - manuscript
    This paper characterizes several belief-revision rules in a unified framework: Bayesian revision upon learning some event, Jeffrey revision upon learning new probabilities of some events, Adams revision upon learning some new conditional probabilities, and 'dual-Jeffrey' revision upon learning a new conditional probability function. Despite their differences, these revision rules can be characterized in terms of the same two axioms: responsiveness, which requires that revised beliefs incorporate what has been learnt, and conservativeness, which requires that beliefs on which the learnt input (...)
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  21. Conditional Probability and Dutch Books.Frank Doring - 2000 - Philosophy of Science 67 (3):391 - 409.
    There is no set Δ of probability axioms that meets the following three desiderata: (1) Δ is vindicated by a Dutch book theorem; (2) Δ does not imply regularity (and thus allows, among other things, updating by conditionalization); (3) Δ constrains the conditional probability q(·,z) even when the unconditional probability p(z) (=q(z,T)) equals 0. This has significant consequences for Bayesian epistemology, some of which are discussed.
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  22. Rationality and the Wason Selection Task: A Logical Account.Simone Duca - 2009 - Psyche 15 (1):109-131.
    The main goal of the paper is to investigate the relation between indicative conditionals and rationality. We wil l do this by consider- ing several interpretations of a very wel l-known example of reasoning involving conditionals, that is the Wason selection task, and showing how those interpretations have different bearings on the notion of ra- tionality. In particular, in the first part of the paper, after having briefly presented the selection task, we wil l take a look at two prag- (...)
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  23. Regularity and Hyperreal Credences.Kenny Easwaran - 2014 - Philosophical Review 123 (1):1-41.
    Many philosophers have become worried about the use of standard real numbers for the probability function that represents an agent's credences. They point out that real numbers can't capture the distinction between certain extremely unlikely events and genuinely impossible ones—they are both represented by credence 0, which violates a principle known as “regularity.” Following Skyrms 1980 and Lewis 1980, they recommend that we should instead use a much richer set of numbers, called the “hyperreals.” This essay argues that this popular (...)
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  24. Varieties of Conditional Probability.Kenny Easwaran - 2011 - In Prasanta Bandyopadhyay & Malcolm Forster (eds.), Handbook for Philosophy of Statistics. North Holland.
    I consider the notions of logical probability, degree of belief, and objective chance, and argue that a different formalism for conditional probability is appropriate for each.
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  25. Lowe on Conditional Probability.Dorothy Edgington - 1996 - Mind 105 (420):617-630.
  26. Probability and Conditionals: Belief Revision and Rational Decision.Ellery Eells & Brian Skyrms (eds.) - 1994 - Cambridge University Press.
    This collection of essays is on the relation between probabilities, especially conditional probabilities, and conditionals. It provides negative results which sharply limit the ways conditionals can be related to conditional probabilities. There are also positive ideas and results which will open up areas of research. The collection is intended to honour Ernest W. Adams, whose seminal work is largely responsible for creating this area of inquiry. As well as describing, evaluating, and applying Adams's work the contributions extend his ideas in (...)
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  27. Conditional Response Distributions in a Multiple-Choice Probability-Learning Situtation.James R. Erickson & Karen K. Block - 1970 - Journal of Experimental Psychology 86 (2):328.
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  28. Probability Logic with Conditional Expectation.Sergio Fajardo - 1983 - Annals of Pure and Applied Logic 28 (2):137-161.
  29. Choice and the Conditional Probability of Alternation: Some New Data.J. Gregor Fetterman & Stanley S. Pliskoff - 1981 - Bulletin of the Psychonomic Society 18 (2):95-98.
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  30. NP-Containment for the Coherence Test of Assessments of Conditional Probability: A Fuzzy Logical Approach. [REVIEW]Tommaso Flaminio - 2007 - Archive for Mathematical Logic 46 (3-4):301-319.
    In this paper we investigate the problem of testing the coherence of an assessment of conditional probability following a purely logical setting. In particular we will prove that the coherence of an assessment of conditional probability χ can be characterized by means of the logical consistency of a suitable theory T χ defined on the modal-fuzzy logic FP k (RŁΔ) built up over the many-valued logic RŁΔ. Such modal-fuzzy logic was previously introduced in Flaminio (Lecture Notes in Computer Science, vol. (...)
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  31. A Logical and Algebraic Treatment of Conditional Probability.Tommaso Flaminio & Franco Montagna - 2004 - Archive for Mathematical Logic 44 (2):245-262.
  32. Shafer on Conditional Probability.Bas C. Fraassen - 1983 - Journal of Philosophical Logic 12 (4):467 - 470.
  33. Probabilistic Theories of Reasoning Need Pragmatics Too: Modulating Relevance in Uncertain Conditionals.A. J. B. Fugard, Niki Pfeifer & B. Mayerhofer - 2011 - Journal of Pragmatics 43:2034–2042.
    According to probabilistic theories of reasoning in psychology, people's degree of belief in an indicative conditional `if A, then B' is given by the conditional probability, P(B|A). The role of language pragmatics is relatively unexplored in the new probabilistic paradigm. We investigated how consequent relevance a ects participants' degrees of belief in conditionals about a randomly chosen card. The set of events referred to by the consequent was either a strict superset or a strict subset of the set of events (...)
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  34. L'exigence de l'Explication En Biologie au Regard d'Une Philosophie de la Morphogenèse.Philippe Gagnon - 2010 - Eikasia. Revista de Filosofía 35 (November):123-180.
    In a first part I present the results of the philosophy of scientific explanation with an attempt to apply them to the case of the theory of evolution. Then I observe that the requirements of modelization of phenomena with the help of inductive logic do not capture efficiently the pertinent factors and fail just as much to exclude those which end up being neutral as explanatory premises. I then query in the direction of confirmation theory, and show that probabilistic reasoning (...)
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  35. Reasonable Doubt : Uncertainty in Education, Science and Law.Tony Gardner-Medwin - 2011 - In Philip Dawid, William Twining & Mimi Vasilaki (eds.), Evidence, Inference and Enquiry. Oup/British Academy. pp. 465-483.
    The use of evidence to resolve uncertainties is key to many endeavours, most conspicuously science and law. Despite this, the logic of uncertainty is seldom taught explicitly, and often seems misunderstood. Traditional educational practice even fails to encourage students to identify uncertainty when they express knowledge, though mark schemes that reward the identification of reliable and uncertain responses have long been shown to encourage more insightful understanding. In our information-rich society the ability to identify uncertainty is often more important than (...)
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  36. Probabilistic Logic Under Coherence, Conditional Interpretations, and Default Reasoning.Angelo Gilio - 2005 - Synthese 146 (1-2):139-152.
    We study a probabilistic logic based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence). We examine probabilistic conditional knowledge bases associated with imprecise probability assessments defined on arbitrary families of conditional events. We introduce a notion of conditional interpretation defined directly in terms of precise probability assessments. We also examine a property of strong satisfiability which is related to the notion of toleration well known in default reasoning. In our framework we give more (...)
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  37. Transitivity in Coherence-Based Probability Logic.Angelo Gilio, Niki Pfeifer & Giuseppe Sanfilippo - 2016 - Journal of Applied Logic 14:46-64.
    We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study selected probabilistic (...)
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  38. Transitive Reasoning with Imprecise Probabilities.Angelo Gilio, Niki Pfeifer & Giuseppe Sanfilippo - 2015 - In S. Destercke & T. Denoeux (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2015). Springer LNAI 9161. pp. 95-105.
    We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Finally, we present the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases.
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  39. Conjunction, Disjunction and Iterated Conditioning of Conditional Events.Angelo Gilio & Giuseppe Sanfilippo - 2013 - In R. Kruse (ed.), Advances in Intelligent Systems and Computing. Springer.
    Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the (...)
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  40. Copi's Conditional Probability Problem.Samuel Goldberg - 1976 - Philosophy of Science 43 (2):286-289.
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  41. Probability and Random Processes.Geoffrey Grimmett & David Stirzaker - 2001 - Oxford University Press.
    A Markov chain is a random process with the property that, conditional on its present value, the future is independent of the past. The Chapman- Kolmogorov equations are derived, and used to explore the persistence and transience of states.
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  42. On Quantum Conditional Probability.Isabel Guerra Bobo - 2013 - Theoria: An International Journal for Theory, History and Foundations of Science 28 (1):115-137.
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  43. What Conditional Probability Could Not Be.Alan Hájek - 2003 - Synthese 137 (3):273--323.
    Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.
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  44. Conditional Probability Is the Very Guide of Life.Alan Hájek - 2003 - In Kyburg Jr, E. Henry & Mariam Thalos (eds.), Probability is the Very Guide of Life: The Philosophical Uses of Chance. Open Court. pp. 183--203.
    in Probability is the Very Guide of Life: The Philosophical Uses of Chance, eds. Henry Kyburg, Jr. and Mariam Thalos, Open Court. Abridged version in Proceedings of the International Society for Bayesian Analysis 2002.
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  45. The Conditional Construal of Conditional Probability.Alan Roy Hajek - 1993 - Dissertation, Princeton University
    Very roughly, the conditional construal of conditional probability is the hypothesis that the conditional probability P equals the probability of the conditional 'if A, then B'. My main purposes are to hone this rough statement down to various precise versions of the Hypothesis, as I call it, and to argue that virtually none of them is tenable. ;In S 1, I distinguish four versions of the Hypothesis. The subsequent four sections are largely an opinionated historical survey, tracing the motivations for (...)
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  46. The Hypothesis of the Conditional Construal of Conditional Probability.Alan Hájek & N. Hall - 1994 - In Ellery Eells, Brian Skyrms & Ernest W. Adams (eds.), Probability and Conditionals: Belief Revision and Rational Decision. Cambridge University Press. pp. 75.
  47. Nonmonotonic Conditionals That Behave Like Conditional Probabilities Above a Threshold.James Hawthorne - 2007 - Journal of Applied Logic 5 (4):625-637.
    I’ll describe a range of systems for nonmonotonic conditionals that behave like conditional probabilities above a threshold. The rules that govern each system are probabilistically sound in that each rule holds when the conditionals are interpreted as conditional probabilities above a threshold level specific to that system. The well-known preferential and rational consequence relations turn out to be special cases in which the threshold level is 1. I’ll describe systems that employ weaker rules appropriate to thresholds lower than 1, and (...)
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  48. On the Logic of Nonmonotonic Conditionals and Conditional Probabilities: Predicate Logic. [REVIEW]James Hawthorne - 1998 - Journal of Philosophical Logic 27 (1):1-34.
    In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional interpretation (...)
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  49. On the Logic of Nonmonotonic Conditionals and Conditional Probabilities.James Hawthorne - 1996 - Journal of Philosophical Logic 25 (2):185-218.
    I will describe the logics of a range of conditionals that behave like conditional probabilities at various levels of probabilistic support. Families of these conditionals will be characterized in terms of the rules that their members obey. I will show that for each conditional, →, in a given family, there is a probabilistic support level r and a conditional probability function P such that, for all sentences C and B, 'C → B' holds just in case P[B | C] ≥ (...)
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  50. The Quantitative/Qualitative Watershed for Rules of Uncertain Inference.James Hawthorne & David Makinson - 2007 - Studia Logica 86 (2):247-297.
    We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; and threshold-sensitive conditions such as `preface' and `lottery' rules.
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