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Secrecy in multiagent systems
"... We introduce a general framework for reasoning about secrecy requirements in multiagent systems. Because secrecy requirements are closely connected with the knowledge of individual agents of a system, our framework employs the modal logic of knowledge within the context of the wellstudied runs and ..."
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Cited by 41 (5 self)
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We introduce a general framework for reasoning about secrecy requirements in multiagent systems. Because secrecy requirements are closely connected with the knowledge of individual agents of a system, our framework employs the modal logic of knowledge within the context of the wellstudied runs and systems framework. Put simply, “secrets ” are facts about a system that lowlevel agents are never allowed to know. The framework presented here allows us to formalize this intuition precisely, in a way that is much in the spirit of Sutherland’s notion of nondeducibility. Several wellknown attempts to characterize the absence of information flow, including separability, generalized noninterference, and nondeducibility on strategies, turn out to be special cases of our definition of secrecy. However, our approach lets us go well beyond these definitions. It can handle probabilistic secrecy in a clean way, and it suggests generalizations of secrecy that may be useful for dealing with resourcebounded reasoning and with issues such as downgrading of information.
Towards a unified theory of imprecise probability
 Int. J. Approx. Reasoning
, 2000
"... Belief functions, possibility measures and Choquet capacities of order 2, which are special kinds of coherent upper or lower probability, are amongst the most popular mathematical models for uncertainty and partial ignorance. I give examples to show that these models are not sufficiently general to ..."
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Cited by 40 (0 self)
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Belief functions, possibility measures and Choquet capacities of order 2, which are special kinds of coherent upper or lower probability, are amongst the most popular mathematical models for uncertainty and partial ignorance. I give examples to show that these models are not sufficiently general to represent some common types of uncertainty. Coherent lower previsions and sets of probability measures are considerably more general but they may not be sufficiently informative for some purposes. I discuss two other models for uncertainty, involving sets of desirable gambles and partial preference orderings. These are more informative and more general than the previous models, and they may provide a suitable mathematical setting for a unified theory of imprecise probability.
Weak probabilistic anonymity
 INRIA FUTURS AND LIX
, 2005
"... Anonymity means that the identity of the user performing a certain action is maintained secret. The protocols for ensuring anonymity often use random mechanisms which can be described probabilistically. In this paper we propose a notion of weak probabilistic anonymity, where weak refers to the fact ..."
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Cited by 36 (10 self)
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Anonymity means that the identity of the user performing a certain action is maintained secret. The protocols for ensuring anonymity often use random mechanisms which can be described probabilistically. In this paper we propose a notion of weak probabilistic anonymity, where weak refers to the fact that some amount of probabilistic information may be revealed by the protocol. This information can be used by an observer to infer the likeliness that the action has been performed by a certain user. The aim of this work is to study the degree of anonymity that the protocol can still ensure, despite the leakage of information. We illustrate our ideas by using the example of the dining cryptographers with biased coins. We consider both the cases of nondeterministic and probabilistic users. Correspondingly, we propose two notions of weak anonymity and we investigate their respective dependencies on the biased factor of the coins.
Updating Beliefs with Incomplete Observations
"... Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete (or setvalued). This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently, Gr unwald and Halpern have shown that co ..."
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Cited by 32 (12 self)
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Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete (or setvalued). This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently, Gr unwald and Halpern have shown that commonly used updating strategies fail in this case, except under very special assumptions. In this paper we propose a new method for updating probabilities with incomplete observations. Our approach is deliberately conservative: we make no assumptions about the socalled incompleteness mechanism that associates complete with incomplete observations. We model our ignorance about this mechanism by a vacuous lower prevision, a tool from the theory of imprecise probabilities, and we use only coherence arguments to turn prior into posterior (updated) probabilities. In general, this new approach to updating produces lower and upper posterior probabilities and previsions (expectations), as well as partially determinate decisions. This is a logical consequence of the existing ignorance about the incompleteness mechanism. As an example, we use the new updating method to properly address the apparent paradox in the `Monty Hall' puzzle. More importantly, we apply it to the problem of classification of new evidence in probabilistic expert systems, where it leads to a new, socalled conservative updating rule.
Epistemic logics, probability, and the calculus of evidence
 In Proceedings of the 10 th International Joint Conference on Artificial Intelligence
, 1987
"... This paper presents results of the application to epistemic logic structures of the method proposed by Carnap for the development of logical foundations of probability theory. These results, which provide firm conceptual bases ..."
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Cited by 31 (0 self)
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This paper presents results of the application to epistemic logic structures of the method proposed by Carnap for the development of logical foundations of probability theory. These results, which provide firm conceptual bases
Using probability trees to compute marginals with imprecise probabilities
 INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
, 2002
"... This paper presents an approximate algorithm to obtain a posteriori intervals of probability, when available information is also given with intervals. The algorithm uses probability trees as a means of representing and computing with the convex sets of ..."
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Cited by 23 (2 self)
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This paper presents an approximate algorithm to obtain a posteriori intervals of probability, when available information is also given with intervals. The algorithm uses probability trees as a means of representing and computing with the convex sets of
Ignorability for categorical data
 The Annals of Statistics
"... We study the problem of ignorability in likelihoodbased inference from incomplete categorical data. Two versions of the coarsened at random assumption (car) are distinguished, their compatibility with the parameter distinctness assumption is investigated and several conditions for ignorability that ..."
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Cited by 20 (3 self)
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We study the problem of ignorability in likelihoodbased inference from incomplete categorical data. Two versions of the coarsened at random assumption (car) are distinguished, their compatibility with the parameter distinctness assumption is investigated and several conditions for ignorability that do not require an extra parameter distinctness assumption are established. It is shown that car assumptions have quite different implications depending on whether the underlying completedata model is saturated or parametric. In the latter case, car assumptions can become inconsistent with observed data. 1. Introduction. In a sequence of papers Rubin [15], Heitjan and Rubin [11] and Heitjan [9, 10] have investigated the question under what conditions a mechanism that causes observed data to be incomplete or, more generally, coarse, can be ignored in the statistical analysis of the data. The key condition that has been identified is that the data should be missing at
A Logic for Reasoning about Upper Probabilities
, 2002
"... We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show that the satisfiability problem is ..."
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Cited by 17 (4 self)
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We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show that the satisfiability problem is NPcomplete, no harder than satisfiability for propositional logic.
Probabilistic approaches to rough sets
 Expert Systems
, 2003
"... This paper reviews probabilistic approaches to rough sets in granulation, approximation, and rule induction. The Shannon entropy function is used to quantitatively characterize partitions of a universe. Both algebraic and probabilistic rough set approximations are studied. The probabilistic approxim ..."
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Cited by 16 (8 self)
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This paper reviews probabilistic approaches to rough sets in granulation, approximation, and rule induction. The Shannon entropy function is used to quantitatively characterize partitions of a universe. Both algebraic and probabilistic rough set approximations are studied. The probabilistic approximations are defined in a decisiontheoretic framework. The problem of rule induction, a major application of rough set theory, is studied in probabilistic and informationtheoretic terms. Two types of rules are analyzed, the local, low order rules, and the global, high order rules. 1