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  1. Acting on belief functions.Nicholas J. J. Smith - 2023 - Theory and Decision 95 (4):575-621.
    The degrees of belief of rational agents should be guided by the evidence available to them. This paper takes as a starting point the view—argued elsewhere—that the formal model best able to capture this idea is one that represents degrees of belief using Dempster–Shafer belief functions. However degrees of belief should not only respect evidence: they also guide decision and action. Whatever formal model of degrees of belief we adopt, we need a decision theory that works with it: that takes (...)
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  2. Implementing Dempster-Shafer Theory for property similarity in Conceptual Spaces modeling.Jeremy R. Chapman, John L. Crassidis, James Llinas, Barry Smith & David Kasmier - 2022 - Sensor Systems and Information Systems IV, American Institute of Aeronautics and Astronautics (AIAA) SCITECH Forum 2022.
    Previous work has shown that the Complex Conceptual Spaces − Single Observation Mathematical framework is a useful tool for event characterization. This mathematical framework is developed on the basis of Conceptual Spaces and uses integer linear programming to find the needed similarity values. The work of this paper is focused primarily on space event characterization. In particular, the focus is on the ranking of threats for malicious space events such as a kinetic kill. To make the Conceptual Spaces framework work, (...)
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  3. Respecting Evidence: Belief Functions not Imprecise Probabilities.Nicholas J. J. Smith - 2022 - Synthese 200 (475):1-30.
    The received model of degrees of belief represents them as probabilities. Over the last half century, many philosophers have been convinced that this model fails because it cannot make room for the idea that an agent’s degrees of belief should respect the available evidence. In its place they have advocated a model that represents degrees of belief using imprecise probabilities (sets of probability functions). This paper presents a model of degrees of belief based on Dempster–Shafer belief functions and then presents (...)
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  4. Conditioning and Interpretation Shifts.Jan-Willem Romeijn - 2012 - 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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  5. Luminosity and vagueness.Elia Zardini - 2012 - Dialectica 66 (3):375-410.
    The paper discusses some ways in which vagueness and its phenomena may be thought to impose certain limits on our knowledge and, more specifically, may be thought to bear on the traditional philosophical idea that certain domains of facts are luminous, i.e., roughly, fully open to our view. The discussion focuses on a very influential argument to the effect that almost no such interesting domains exist. Many commentators have felt that the vagueness unavoidably inherent in the description of the facts (...)
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  6. A betting interpretation for probabilities and Dempster-Shafer degrees of belief.Glenn Shafer - 2010 - International Journal of Approximate Reasoning.
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  7. Dempster-Shafer Theory.Jonathan Weisberg - 2010
    An introduction to Dempster-Shafter Theory, from a lecture at the Northern Institute of Philosophy in 2010.
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  8. Comparing approximate reasoning and probabilistic reasoning using the Dempster-Shafer framework.Ronald R. Yager - 2009 - International Journal of Approximate Reasoning 50 (5):812--821.
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  9. The Dempster-Shafer calculus for statisticians.Arthur Dempster - 2008 - International Journal of Approximate Reasoning 48 (2):365--377.
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  10. Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence.Thierry Denoeux - 2008 - Artificial Intelligence 172 (2--3):234--264.
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  11. Formal Representations of Belief.Franz Huber - 2008 - 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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  12. The metaphysical character of the criticisms raised against the use of probability for dealing with uncertainty in artificial intelligence.Carlotta Piscopo & Mauro Birattari - 2008 - Minds and Machines 18 (2):273-288.
    In artificial intelligence (AI), a number of criticisms were raised against the use of probability for dealing with uncertainty. All these criticisms, except what in this article we call the non-adequacy claim, have been eventually confuted. The non-adequacy claim is an exception because, unlike the other criticisms, it is exquisitely philosophical and, possibly for this reason, it was not discussed in the technical literature. A lack of clarity and understanding of this claim had a major impact on AI. Indeed, mostly (...)
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  13. Characterizing and reasoning about probabilistic and non-probabilistic expectation.Joseph Y. Halpern & Riccardo Pucella - 2007 - J. Acm 54 (3):15.
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  14. Modeling Partially Reliable Information Sources: A General Approach Based on Dempster-Shafer Theory.Stephan Hartmann & Rolf Haenni - 2006 - Information Fusion 7:361-379.
    Combining testimonial reports from independent and partially reliable information sources is an important epistemological 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 on the basis of a comprehensive model taxonomy. This 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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  15. Analyzing the degree of conflict among belief functions.Weiru Liu - 2006 - Artificial Intelligence 170 (11):909--924.
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  16. Reasoning About Uncertainty.Joseph Y. Halpern - 2003 - MIT Press.
    Using formal systems to represent and reason about uncertainty.
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  17. Belief function independence: II. The conditional case.Boutheina Ben Yaghlane, Phillippe Smets & Khaled Mellouli - 2002 - International Journal of Approximate Reasoning 31 (1--2):31--75.
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  18. Belief function independence: I. The marginal case.Boutheina Ben Yaghlane, Phillippe Smets & Khaled Mellouli - 2002 - International Journal of Approximate Reasoning 29 (1):47--70.
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  19. Connecting dempster–shafer belief functions with likelihood-based inference.Mikel Aickin - 2000 - Synthese 123 (3):347-364.
    The Dempster–Shafer approach to expressing beliefabout a parameter in a statistical model is notconsistent with the likelihood principle. Thisinconsistency has been recognized for some time, andmanifests itself as a non-commutativity, in which theorder of operations (combining belief, combininglikelihood) makes a difference. It is proposed herethat requiring the expression of belief to be committed to the model (and to certain of itssubmodels) makes likelihood inference very nearly aspecial case of the Dempster–Shafer theory.
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  20. Belief functions and default reasoning.Salem Benferhat, Alessandro Saffiotti & Philippe Smets - 2000 - Artificial Intelligence 122 (1--2):1--69.
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  21. Knowledge-driven versus data-driven logics.Didier Dubois, Petr Hájek & Henri Prade - 2000 - 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 (...)
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  22. Evidence theory in multivalued models of modal logic.Elena Tsiporkova, Bernard De Baets & Veselka Boeva - 2000 - Journal of Applied Non-Classical Logics 10 (1):55-81.
    ABSTRACT A modal logic interpretation of Dempster-Shafer theory is developed in the framework of multivalued models of modal logic, i.e. models in which in any possible world an arbitrary number (possibly zero) of atomic propositions can be true. Several approaches to conditioning in multivalued models of modal logic are presented.
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  23. Dempster-Shafer theory framed in modal logic.Elena Tsiporkova, Vesilka Boeva & Bernard De Baets - 1999 - International Journal of Approximate Reasoning 21 (2):157--175.
  24. Towards a rough mereology-based logic for approximate solution synthesis. Part.Jan Komorowski, Lech T. Polkowski & Andrzej Skowron - 1997 - 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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  25. The normative representation of quantified beliefs by belief functions.Philippe Smets - 1997 - Artificial Intelligence 92 (1--2):229--242.
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  26. Modal logic interpretation of Dempster-Shafer theory: An infinite case.David Harmanec, George Klir & Zhenyuan Wang - 1996 - International Journal of Approximate Reasoning 14 (2--3):81--93.
  27. Set-based bayesianism.H. Kyburg & M. Pittarelli - 1996 - Ieee Transactions on Systems, Man and Cybernetics A 26 (3):324--339.
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  28. Decision Making with Belief Functions.J. Y. Jaffray - 1994 - In R. Yager, M. Fedrizzi & J. Kacprzyk (eds.), Advances in the Dempster- Shafer Theory of Evidence. John Wiley. pp. 331-352.
  29. Advances in the Dempster- Shafer Theory of Evidence.R. Yager, M. Fedrizzi & J. Kacprzyk (eds.) - 1994 - John Wiley.
    Builds on classical probability theory and offers an extremely workable solution to the many problems of artificial intelligence, concentrating on the rapidly growing areas of fuzzy reasoning and neural computing. Contains a collection of previously unpublished articles by leading researchers in the field.
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  30. Belief functions: The disjunctive rule of combination and the generalized bayesian theorem.Phillippe Smets - 1993 - International Journal of Approximate Reasoning 9 (1):1--35.
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  31. Getting fancy with probability.Henry E. Kyburg - 1992 - 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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  32. Rejoinder to comments on ``reasoning with belief functions: An analysis of compatibility.Judea Pearl - 1992 - International Journal of Approximate Reasoning 6 (3):425--443.
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  33. Resolving misunderstandings about belief functions.Phillippe Smets - 1992 - International Journal of Approximate Reasoning 6 (3):321--344.
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  34. Comments on Shafer's``perspectives on the theory and practice of belief functions''.Larry Wasserman - 1992 - International Journal of Approximate Reasoning 6 (2):367--375.
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  35. 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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  36. Reasoning with belief functions: An analysis of compatibility.Judea Pearl - 1990 - International Journal of Approximate Reasoning 4:363--389.
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  37. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference.Judea Pearl - 1988 - 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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  38. Bayesian and Non-Bayesian Evidential Updating.Henry E. Kyburg - 1987 - Artificial Intelligence 31 (3):271--294.
  39. On the Dempster-Shafer framework and new combination rules.Ronald R. Yager - 1987 - Information Sciences 41 (2):93--137.
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  40. Belief structures, possibility theory and decomposable confidence measures on finite sets.Didier Dubois - 1986 - Computers and Artificial Intelligence (5):403--416.
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  41. A Mathematical Theory of Evidence.Glenn Shafer - 1976 - Princeton University Press.
    Degrees of belief; Dempster's rule of combination; Simple and separable support functions; The weights of evidence; Compatible frames of discernment; Support functions; The discernment of evidence; Quasi support functions; Consonance; Statistical evidence; The dual nature of probable reasoning.
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  42. Dempster-Shafer functions as metalinguistic probability functions.Branden Fitelson - manuscript
    Let Ln be a sentential language with n atomic sentences {A1, . . . , An}. Let Sn = {s1, . . . , s2n} be the set of 2n state descriptions of Ln, in the following, canonical lexicographical truth-table order: State Description A1 A2 · · · An−1 An T T T T T s1 = A1 & A2 & · · · &An−1 & An T T T T F s1 = A1 & A2 & · · · (...)
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