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Reasoning about Knowledge and Probability
 Journal of the ACM
, 1994
"... : We provide a model for reasoning about knowledge and probability together. We allow explicit mention of probabilities in formulas, so that our language has formulas that essentially say "according to agent i, formula ' holds with probability at least b." The language is powerful en ..."
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Cited by 195 (20 self)
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: We provide a model for reasoning about knowledge and probability together. We allow explicit mention of probabilities in formulas, so that our language has formulas that essentially say "according to agent i, formula ' holds with probability at least b." The language is powerful enough to allow reasoning about higherorder probabilities, as well as allowing explicit comparisons of the probabilities an agent places on distinct events. We present a general framework for interpreting such formulas, and consider various properties that might hold of the interrelationship between agents' probability assignments at different states. We provide a complete axiomatization for reasoning about knowledge and probability, prove a small model property, and obtain decision procedures. We then consider the effects of adding common knowledge and a probabilistic variant of common knowledge to the language. A preliminary version of this paper appeared in the Proceedings of the Second Conference on T...
Perspectives on the Theory and Practice of Belief Functions
 International Journal of Approximate Reasoning
, 1990
"... The theory of belief functions provides one way to use mathematical probability in subjective judgment. It is a generalization of the Bayesian theory of subjective probability. When we use the Bayesian theory to quantify judgments about a question, we must assign probabilities to the possible answer ..."
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Cited by 99 (7 self)
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The theory of belief functions provides one way to use mathematical probability in subjective judgment. It is a generalization of the Bayesian theory of subjective probability. When we use the Bayesian theory to quantify judgments about a question, we must assign probabilities to the possible answers to that question. The theory of belief functions is more flexible; it allows us to derive degrees of belief for a question from probabilities for a related question. These degrees of belief may or may not have the mathematical properties of probabilities; how much they differ from probabilities will depend on how closely the two questions are related. Examples of what we would now call belieffunction reasoning can be found in the late seventeenth and early eighteenth centuries, well before Bayesian ideas were developed. In 1689, George Hooper gave rules for combining testimony that can be recognized as special cases of Dempster's rule for combining belief functions (Shafer 1986a). Similar rules were formulated by Jakob Bernoulli in his Ars Conjectandi, published posthumously in 1713, and by JohannHeinrich Lambert in his Neues Organon, published in 1764 (Shafer 1978). Examples of belieffunction reasoning can also be found in more recent work, by authors
Soft Computing: the Convergence of Emerging Reasoning Technologies
 Soft Computing
, 1997
"... The term Soft Computing (SC) represents the combination of emerging problemsolving technologies such as Fuzzy Logic (FL), Probabilistic Reasoning (PR), Neural Networks (NNs), and Genetic Algorithms (GAs). Each of these technologies provide us with complementary reasoning and searching methods to so ..."
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Cited by 68 (11 self)
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The term Soft Computing (SC) represents the combination of emerging problemsolving technologies such as Fuzzy Logic (FL), Probabilistic Reasoning (PR), Neural Networks (NNs), and Genetic Algorithms (GAs). Each of these technologies provide us with complementary reasoning and searching methods to solve complex, realworld problems. After a brief description of each of these technologies, we will analyze some of their most useful combinations, such as the use of FL to control GAs and NNs parameters; the application of GAs to evolve NNs (topologies or weights) or to tune FL controllers; and the implementation of FL controllers as NNs tuned by backpropagationtype algorithms.
DempsterShafer Theory for Sensor Fusion in Autonomous Mobile Robots
 IEEE Transactions on Robotics and Automation
"... This article presents the uncertainty management system used for the execution activity of the Sensor Fusion Effects (SFX) architecture. The SFX architecture is a generic sensor fusion system for autonomous mobile robots, suitable for a wide variety of sensors and environments. The execution acti ..."
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Cited by 60 (5 self)
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This article presents the uncertainty management system used for the execution activity of the Sensor Fusion Effects (SFX) architecture. The SFX architecture is a generic sensor fusion system for autonomous mobile robots, suitable for a wide variety of sensors and environments. The execution activity uses the belief generated for a percept to either proceed with a task safely (e.g., navigate to a specific location), terminate the task (e.g., can't recognize the location), or investigate the situation further in the hopes of obtaining sufficient belief (e.g., what has changed?). DempsterShafer (DS) theory serves as the foundation for uncertainty management. The SFX implementation of DS theory incorporates evidence from sensor observations and domain knowledge into three levels of perceptual abstraction. It also makes use of the DS weight of conflict metric to prevent the robot from acting on faulty observations. Experiments with four types of sensor data collected by a mobil...
Data Fusion in the Transferable Belief Model.
, 2000
"... When Shafer introduced his theory of evidence based on the use of belief functions, he proposed a rule to combine belief functions induced by distinct pieces of evidence. Since then, theoretical justifications of this socalled Dempster's rule of combination have been produced and the meaning of ..."
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Cited by 52 (0 self)
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When Shafer introduced his theory of evidence based on the use of belief functions, he proposed a rule to combine belief functions induced by distinct pieces of evidence. Since then, theoretical justifications of this socalled Dempster's rule of combination have been produced and the meaning of distinctness has been assessed. We will present practical applications where the fusion of uncertain data is well achieved by Dempster's rule of combination. It is essential that the meaning of the belief functions used to represent uncertainty be well fixed, as the adequacy of the rule depends strongly on a correct understanding of the context in which they are applied. Missing to distinguish between the upper and lower probabilities theory and the transferable belief model can lead to serious confusion, as Dempster's rule of combination is central in the transferable belief model whereas it hardly fits with the upper and lower probabilities theory. Keywords: belief function, transferable beli...
A logical approach to multilevel security of probabilistic systems
, 1998
"... We set out a modal logic for reasoning about multilevel security of probabilistic systems. This logic contains expressions for time, probability, and knowledge. Making use of the HalpernTuttle framework for reasoning about knowledge and probability, we give a semantics for our logic and prove it i ..."
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Cited by 39 (2 self)
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We set out a modal logic for reasoning about multilevel security of probabilistic systems. This logic contains expressions for time, probability, and knowledge. Making use of the HalpernTuttle framework for reasoning about knowledge and probability, we give a semantics for our logic and prove it is sound. We give two syntactic definitions of perfect multilevel security and show that their semantic interpretations are equivalent to earlier, independently motivated characterizations. We also discuss the relation between these characterizations of security and between their usefulness in security analysis.
Decision Making in a Context where Uncertainty is Represented by Belief Functions.
, 2000
"... A quantified model to represent uncertainty is incomplete if its use in a decision environment is not explained. When belief functions were first introduced to represent quantified uncertainty, no associated decision model was proposed. Since then, it became clear that the belief functions meani ..."
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Cited by 29 (4 self)
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A quantified model to represent uncertainty is incomplete if its use in a decision environment is not explained. When belief functions were first introduced to represent quantified uncertainty, no associated decision model was proposed. Since then, it became clear that the belief functions meaning is multiple. The models based on belief functions could be understood as an upper and lower probabilities model, as the hint model, as the transferable belief model and as a probability model extended to modal propositions. These models are mathematically identical at the static level, their behaviors diverge at their dynamic level (under conditioning and/or revision). For decision making, some authors defend that decisions must be based on expected utilities, in which case a probability function must be determined. When uncertainty is represented by belief functions, the choice of the appropriate probability function must be explained and justified. This probability function doe...
Characterizing Belief with Minimum Commitment
, 1991
"... We describe a new approach for reasoning with belief functions in this paper. This approach is fundamentally unrelated to probabilities and is consistent with Shafer and Tversky's canonical examples. ..."
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Cited by 16 (0 self)
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We describe a new approach for reasoning with belief functions in this paper. This approach is fundamentally unrelated to probabilities and is consistent with Shafer and Tversky's canonical examples.
Reasoning about knowledge and probability: preliminary report
 Proc. Second Conference on Theoretical Aspects of Reasoning about Knowledge
, 1988
"... Abstract: We provide a model for reasoning about knowledge anti probability together. We a.llow explicit mention of probabilities in formulas, so that our language has formulas tha.t essentia.lly say "a.ccording to agent i, formula. (p holds with probability a.t least o~. " The la ..."
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Cited by 13 (7 self)
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Abstract: We provide a model for reasoning about knowledge anti probability together. We a.llow explicit mention of probabilities in formulas, so that our language has formulas tha.t essentia.lly say &quot;a.ccording to agent i, formula. (p holds with probability a.t least o~. &quot; The language is powerfid enough to allow reasoning a~bout higherorder probabilities, as well as allowing explicit comparisons of the probabilities an agent places on distinct events. We present a general framework for interpreting such formulas, a.nd consider various properties that might hold of the interrelationship between agents ' subjective probability spaces at different states. We provide a. complete a.xiomatiza.tion for rea.soning about knowledge a.nd probability, prove a. small model property, and obtain decision procedures. We then consider the effects of adding common knowledge and a. probabilistic va.ria.nt of common knowledge to the language.
Markov Chain MonteCarlo Algorithms for the Calculation of DempsterShafer Belief
, 1994
"... A simple MonteCarlo algorithm can be used to calculate DempsterShafer belief very efficiently unless the conflict between the evidences is very high. This paper introduces and explores Markov Chain MonteCarlo algorithms for calculating DempsterShafer belief that can also work well when the confl ..."
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Cited by 10 (6 self)
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A simple MonteCarlo algorithm can be used to calculate DempsterShafer belief very efficiently unless the conflict between the evidences is very high. This paper introduces and explores Markov Chain MonteCarlo algorithms for calculating DempsterShafer belief that can also work well when the conflict is high.