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Dempster-Shafer Theory
  1. Mikel Aickin (2000). Connecting Dempster–Shafer Belief Functions with Likelihood-Based Inference. 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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  2. Salem Benferhat, Alessandro Saffiotti & Philippe Smets (2000). Belief Functions and Default Reasoning. Artificial Intelligence 122 (1--2):1--69.
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  3. Didier Dubois, Petr Hájek & Henri Prade (2000). Knowledge-Driven Versus Data-Driven Logics. Journal of Logic, Language and Information 9 (1):65--89.
    The starting point of this work is the gap between two distinct traditions in information engineering: knowledge representation and data-driven modelling. The first tradition emphasizes logic as a tool for representing beliefs held by an agent. The second tradition claims that the main source of knowledge is made of observed data, and generally does not use logic as a modelling tool. However, the emergence of fuzzy logic has blurred the boundaries between these two traditions by putting forward fuzzy rules as (...)
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  4. Rolf Haenni & Stephan Hartmann (2006). Modeling Partially Reliable Information Sources: A General Approach Based on Dempster-Shafer Theory. Information Fusion 7:361-379.
    Combining testimonial reports from independent and partially reliable information sources is an important problem of uncertain reasoning. Within the framework of Dempster-Shafer theory, we propose a general model of partially reliable sources which includes several previously known results as special cases. The paper reproduces these results, gives a number of new insights, and thereby contributes to a better understanding of this important application of reasoning with uncertain and incomplete information.
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  5. Joseph Y. Halpern (2003). Reasoning About Uncertainty. Mit Press.
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  6. Joseph Y. Halpern & Riccardo Pucella (2007). Characterizing and Reasoning About Probabilistic and Non-Probabilistic Expectation. J. Acm 54 (3):15.
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  7. Stephan Hartmann & Rolf Haenni, Modeling Partially Reliable Information Sources: A General Approach Based on Dempster-Shafer Theory.
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  8. Franz Huber, Formal Representations of Belief. Stanford Encyclopedia of Philosophy.
    Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...)
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  9. Jan Komorowski, Lech T. Polkowski & Andrzej Skowron (1997). Towards a Rough Mereology-Based Logic for Approximate Solution Synthesis. Part. Studia Logica 58 (1):143-184.
    We are concerned with formal models of reasoning under uncertainty. Many approaches to this problem are known in the literature e.g. Dempster-Shafer theory [29], [42], bayesian-based reasoning [21], [29], belief networks [29], many-valued logics and fuzzy logics [6], non-monotonic logics [29], neural network logics [14]. We propose rough mereology developed by the last two authors [22-25] as a foundation for approximate reasoning about complex objects. Our notion of a complex object includes, among others, proofs understood as schemes constructed in order (...)
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  10. Kyburg Jr, E. Henry & Michael Pittarelli (1996). Set-Based Bayesianism. Ieee Transactions on Systems, Man and Cybernetics A 26 (3):324--339.
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  11. Henry E. Kyburg (1992). Getting Fancy with Probability. Synthese 90 (2):189-203.
    There are a number of reasons for being interested in uncertainty, and there are also a number of uncertainty formalisms. These formalisms are not unrelated. It is argued that they can all be reflected as special cases of the approach of taking probabilities to be determined by sets of probability functions defined on an algebra of statements. Thus, interval probabilities should be construed as maximum and minimum probabilities within a set of distributions, Glenn Shafer's belief functions should be construed as (...)
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  12. E. Kyburg, Henry (1987). Bayesian and Non-Bayesian Evidential Updating. Artificial Intelligence 31:271--294.
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  13. Kyburg, Jr & E. Henry (1987). Bayesian and Non-Bayesian Evidence and Updating. Artificial Intelligence 31:271-293.
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  14. Judea Pearl (1992). Rejoinder to Comments on ``Reasoning with Belief Functions: An Analysis of Compatibility. International Journal of Approximate Reasoning 6 (3):425--443.
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  15. Judea Pearl (1990). Reasoning with Belief Functions: An Analysis of Compatibility. International Journal of Approximate Reasoning 4:363--389.
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  16. Judea Pearl (1988). Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann.
    The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.
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  17. Jan-Willem Romeijn (2012). Conditioning and Interpretation Shifts. Studia Logica 100 (3):583-606.
    This paper develops a probabilistic model of belief change under interpretation shifts, in the context of a problem case from dynamic epistemic logic. Van Benthem [4] has shown that a particular kind of belief change, typical for dynamic epistemic logic, cannot be modelled by standard Bayesian conditioning. I argue that the problems described by van Benthem come about because the belief change alters the semantics in which the change is supposed to be modelled: the new information induces a shift in (...)
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  18. Glenn Shafer (2010). A Betting Interpretation for Probabilities and Dempster-Shafer Degrees of Belief. International Journal of Approximate Reasoning.
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  19. Glenn Shafer (1976). A Mathematical Theory of Evidence. Princeton University Press.
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  20. Larry Wasserman (1992). Comments on Shafer's``Perspectives on the Theory and Practice of Belief Functions''. International Journal of Approximate Reasoning 6 (2):367--375.
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  21. Jonathan Weisberg, Dempster-Shafer Theory.
    An introduction to Dempster-Shafter Theory, from a lecture at the Northern Institute of Philosophy in 2010.
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  22. Elia Zardini (2012). Luminosity and Vagueness. Dialectica 66 (3):375-410.
Plausibility Theory
  1. Nir Friedman, Joseph Halpern, Koller Y. & Daphne (2000). First-Order Conditional Logic for Default Reasoning Revisited. Acm Trans. Comput. Logic 1 (2):175--207.
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  2. Joseph Y. Halpern (2003). Reasoning About Uncertainty. Mit Press.
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  3. Franz Huber, Formal Representations of Belief. Stanford Encyclopedia of Philosophy.
    Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...)
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  4. Zdzislaw Pawlak, Jerzy Grzymala-Busse, Roman Slowinski & Wojciech Ziarko (1995). Rough Sets. Commun. Acm 38 (11):88--95.
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  5. Judea Pearl (1988). Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann.
    The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.
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  6. John R. Welch (forthcoming). Moral Strata. Springer.
    This volume recreates the received notion of reflective equilibrium. It reconfigures reflective equilibrium as both a cognitive ideal and a method for approximating this ideal. The ideal of reflective equilibrium is restructured using the concept of discursive strata, which are formed by sentences and differentiated by function. Sentences that perform the same kind of linguistic function constitute a stratum. The book shows how moral discourse can be analyzed into phenomenal, instrumental, and teleological strata, and the ideal of reflective equilibrium reworked (...)
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  7. John R. Welch (2014). Plausibilistic Coherence. Synthese 191 (10):2239-2253.
    Why should coherence be an epistemic desideratum? One response is that coherence is truth-conducive: mutually coherent propositions are more likely to be true, ceteris paribus, than mutually incoherent ones. But some sets of propositions are more coherent, while others are less so. How could coherence be measured? Probabilistic measures of coherence exist; some are identical to probabilistic measures of confirmation, while others are extensions of such measures. Probabilistic measures of coherence are fine when applicable, but many situations are so information-poor (...)
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  8. John R. Welch (2013). New Tools for Theory Choice and Theory Diagosis. Studies in History and Philosophy of Science 44 (3):318-329.
    Theory choice can be approached in at least four ways. One of these calls for the application of decision theory, and this article endorses this approach. But applying standard forms of decision theory imposes an overly demanding standard of numeric information, supposedly satisfied by point-valued utility and probability functions. To ameliorate this difficulty, a version of decision theory that requires merely comparative utilities and plausibilities is proposed. After a brief summary of this alternative, the article illustrates how comparative decision theory (...)
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  9. John R. Welch (2012). Real-Life Decisions and Decision Theory. In Sabine Roeser, Rafaela Hillerbrand, Per Sandin & Martin Peterson (eds.), Handbook of Risk Theory. Springer.
    Some decisions result in cognitive consequences such as information gained and information lost. The focus of this study, however, is decisions with consequences that are partly or completely noncognitive. These decisions are typically referred to as ‘real-life decisions’. According to a common complaint, the challenges of real-life decision making cannot be met by decision theory. This complaint has at least two principal motives. One is the maximizing objection that to require agents to determine the optimal act under real-world constraints is (...)
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  10. John R. Welch (2011). Decision Theory and Cognitive Choice. European Journal for Philosophy of Science 1 (2):147-172.
    The focus of this study is cognitive choice: the selection of one cognitive option (a hypothesis, a theory, or an axiom, for instance) rather than another. The study proposes that cognitive choice should be based on the plausibilities of states posited by rival cognitive options and the utilities of these options' information outcomes. The proposal introduces a form of decision theory that is novel because comparative; it permits many choices among cognitive options to be based on merely comparative plausibilities and (...)
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Probability and AI
  1. Norman Fenton, Martin Neil & David A. Lagnado (2013). A General Structure for Legal Arguments About Evidence Using Bayesian Networks. Cognitive Science 37 (1):61-102.
    A Bayesian network (BN) is a graphical model of uncertainty that is especially well suited to legal arguments. It enables us to visualize and model dependencies between different hypotheses and pieces of evidence and to calculate the revised probability beliefs about all uncertain factors when any piece of new evidence is presented. Although BNs have been widely discussed and recently used in the context of legal arguments, there is no systematic, repeatable method for modeling legal arguments as BNs. Hence, where (...)
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  2. Jr: Henry E. Kyburg (1990). Probabilistic Inference and Probabilistic Reasoning. Philosophical Topics 18 (2):107-116.
  3. Stephen Leeds (1994). A Note on Pollock's System of Direct Inference. Theory and Decision 36 (3):247-256.
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  4. Thomas Lukasiewicz (2005). Nonmonotonic Probabilistic Reasoning Under Variable-Strength Inheritance with Overriding. Synthese 146 (1-2):153 - 169.
    We present new probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment, called Zλ- and lexλ-entailment, which are parameterized through a value λ ∈ [0,1] that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of λ = 0 and λ = 1, the notions of Zλ- and lexλ-entailment coincide with probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment that have been recently introduced by the author. We show (...)
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  5. Niki Pfeifer (2013). The New Psychology of Reasoning: A Mental Probability Logical Perspective. Thinking and Reasoning 19 (3-4):329-345.
  6. Guy Politzer & Laure Carles (2001). Belief Revision and Uncertain Reasoning. Thinking and Reasoning 7 (3):217 – 234.
    When a new piece of information contradicts a currently held belief, one has to modify the set of beliefs in order to restore its consistency. In the case where it is necessary to give up a belief, some of them are less likely to be abandoned than others. The concept of epistemic entrenchment is used by some AI approaches to explain this fact based on formal properties of the belief set (e.g., transitivity). Two experiments were designed to test the hypothesis (...)
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  7. Raghav Ramachandran, Arthur Ramer & Abhaya C. Nayak (2012). Probabilistic Belief Contraction. Minds and Machines 22 (4):325-351.
    Probabilistic belief contraction has been a much neglected topic in the field of probabilistic reasoning. This is due to the difficulty in establishing a reasonable reversal of the effect of Bayesian conditionalization on a probabilistic distribution. We show that indifferent contraction, a solution proposed by Ramer to this problem through a judicious use of the principle of maximum entropy, is a probabilistic version of a full meet contraction. We then propose variations of indifferent contraction, using both the Shannon entropy measure (...)
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Probabilistic Frameworks, Misc
  1. Lara Buchak (2012). Can It Be Rational to Have Faith? In Jacob Chandler & Victoria Harrison (eds.), Probability in the Philosophy of Religion. Oxford University Press. 225.
    This paper provides an account of what it is to have faith in a proposition p, in both religious and mundane contexts. It is argued that faith in p doesn’t require adopting a degree of belief that isn’t supported by one’s evidence but rather it requires terminating one’s search for further evidence and acting on the supposition that p. It is then shown, by responding to a formal result due to I.J. Good, that doing so can be rational in a (...)
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  2. Eleonora Cresto (2010). Belief and Contextual Acceptance. 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 discuss (...)
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  3. Nikolaus Dalbauer & Andreas Hergovich (2013). Is What is Worse More Likely?—The Probabilistic Explanation of the Epistemic Side-Effect Effect. Review of Philosophy and Psychology 4 (4):639-657.
    One aim of this article is to explore the connection between the Knobe effect and the epistemic side-effect effect (ESEE). Additionally, we report evidence about a further generalization regarding probability judgments. We demonstrate that all effects can be found within German material, using ‘absichtlich’ [intentionally], ‘wissen’ [know] and ‘wahrscheinlich’ [likely]. As the explanations discussed with regard to the Knobe effect do not suffice to explicate the ESEE, we survey whether the characteristic asymmetry in knowledge judgments is caused by a differing (...)
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  4. S. DeVito (1997). A Gruesome Problem for the Curve-Fitting Solution. British Journal for the Philosophy of Science 48 (3):391-396.
    This paper is a response to Forster and Sober's [1994] solution to the curve-fitting problem. If their solution is correct, it will provide us with a solution to the New Riddle of Induction as well as provide a basis for choosing realism over conventionalism. Examining this solution is also important as Forster and Sober incorporate it in much of their other philosophical work (see Forster [1995a, b, 1994] and Sober [1996, 1995, 1993]). I argue that Forster and Sober's solution is (...)
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  5. Scott DeVito (1997). A Gruesome Problem for the Curve-Fitting Solution. British Journal for the Philosophy of Science 48 (3):391-396.
    This paper is a response to Forster and Sober's [1994] solution to the curve-fitting problem. If their solution is correct, it will provide us with a solution to the New Riddle of Induction as well as provide a basis for choosing realism over conventionalism. Examining this solution is also important as Forster and Sober incorporate it in much of their other philosophical work (see Forster [1995a, b, 1994] and Sober [1996, 1995, 1993]). I argue that Forster and Sober's solution is (...)
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  6. Mandeep K. Dhami & David R. Mandel (2012). Forecasted Risk Taking in Youth: Evidence for a Bounded-Rationality Perspective. Synthese 189 (S1):161-171.
    This research examined whether youth's forecasted risk taking is best predicted by a compensatory (namely, subjective expected utility) or non-compensatory (e.g., single-factor) model. Ninety youth assessed the importance of perceived benefits, importance of perceived drawbacks, subjective probability of benefits, and subjective probability of drawbacks for 16 risky behaviors clustered evenly into recreational and health/safety domains. In both domains, there was strong support for a noncompensatory model in which only the perceived importance of the benefits of engaging in a risky behavior (...)
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  7. M. Fattorosi-Barnaba & G. Amati (1987). Modal Operators with Probabilistic Interpretations, I. Studia Logica 46 (4):383 - 393.
    <span class='Hi'></span> We present a class of normal modal calculi PFD,<span class='Hi'></span> whose syntax is endowed with operators M r <span class='Hi'></span>(and their dual ones,<span class='Hi'></span> L r)<span class='Hi'></span>, one for each r <span class='Hi'></span>[0,1]<span class='Hi'></span>: if a is sentence,<span class='Hi'></span> M r is to he read the probability that a is true is strictly greater than r and to he evaluated as true or false in every world of a F-restricted probabilistic kripkean model.<span class='Hi'></span> Every such a model is (...)
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  8. Malcolm Forster & Elliott Sober (1994). How to Tell When Simpler, More Unified, or Less Ad Hoc Theories Will Provide More Accurate Predictions. British Journal for the Philosophy of Science 45 (1):1-35.
    Traditional analyses of the curve fitting problem maintain that the data do not indicate what form the fitted curve should take. Rather, this issue is said to be settled by prior probabilities, by simplicity, or by a background theory. In this paper, we describe a result due to Akaike [1973], which shows how the data can underwrite an inference concerning the curve's form based on an estimate of how predictively accurate it will be. We argue that this approach throws light (...)
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  9. MR Forster (1999). Model Selection in Science: The Problem of Language Variance. British Journal for the Philosophy of Science 50 (1):83-102.
    Recent solutions to the curve-fitting problem, described in Forster and Sober ([1995]), trade off the simplicity and fit of hypotheses by defining simplicity as the paucity of adjustable parameters. Scott De Vito ([1997]) charges that these solutions are 'conventional' because he thinks that the number of adjustable parameters may change when the hypotheses are described differently. This he believes is exactly what is illustrated in Goodman's new riddle of induction, otherwise known as the grue problem. However, the 'number of adjustable (...)
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  10. Joseph S. Fulda (1992). The Mathematical Pull of Temptation. Mind 101 (402):305-307.
    Argues that the mathematical structure of a tempting or, more generally, risk-taking situation may prove far more dispositive of the choice made than either character or the lure/pull of the subject/object of temptation/risk-taking. -/- Briefly discusses some implications of this.
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