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Dynamic Update with Probabilities
, 2008
"... Current dynamicepistemic logics model different types of information change in multiagent scenarios. We propose a way to generalize these logics to a probabilistic setting, obtaining a calculus for multiagent update with different slots for probability, and a matching dynamic logic of information ..."
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Cited by 15 (2 self)
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Current dynamicepistemic logics model different types of information change in multiagent scenarios. We propose a way to generalize these logics to a probabilistic setting, obtaining a calculus for multiagent update with different slots for probability, and a matching dynamic logic of information change that has a probabilistic character itself. We present a general completeness result that not only holds for the particular logical system set out in this paper, but for a larger class of dynamic probabilistic logics as well. Finally, we discuss how our basic update rule can be parameterized for different ‘update policies’.
A New Understanding of Subjective Probability and Its Generalization to Lower and Upper Prevision
, 2002
"... This article introduces a new wa of understanding subjective probabilit and its generalization to lower and upper prevision. ..."
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Cited by 14 (6 self)
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This article introduces a new wa of understanding subjective probabilit and its generalization to lower and upper prevision.
Revision Rules for Convex Sets of Probabilities
, 1995
"... INTRODUCTION The best understood and most highly developed theory of uncertainty is Bayesian probability. There is a large literature on its foundations and there are many different justifications of the theory; however, all of these assume that for any proposition a, the beliefs in a and :a are st ..."
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Cited by 11 (2 self)
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INTRODUCTION The best understood and most highly developed theory of uncertainty is Bayesian probability. There is a large literature on its foundations and there are many different justifications of the theory; however, all of these assume that for any proposition a, the beliefs in a and :a are strongly tied together. Without compelling justification, this assumption greatly restricts the type of information that can be satisfactorily represented, e.g., it makes it impossible to represent adequately partial information about an unknown chance distribution P such as 0:6 P(a) 0:8. The strict Bayesian requirement that an epistemic state be a single probability function seems unreasonable. A natural extension of the Bayesian theory is thus to allow sets of probability functions and to consider constraints and bounds on these, and to calculate s
Interpretations of belief functions in the theory of rough sets
 Information Sciences
, 1998
"... This paper reviews and examines interpretations of belief functions in the theory of rough sets with finite universe. The concept of standard rough set algebras is generalized in two directions. One is based on the use of nonequivalence relations. The other is based on relations over two universes, ..."
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Cited by 11 (3 self)
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This paper reviews and examines interpretations of belief functions in the theory of rough sets with finite universe. The concept of standard rough set algebras is generalized in two directions. One is based on the use of nonequivalence relations. The other is based on relations over two universes, which leads to the notion of interval algebras. Pawlak rough set algebras may be used to interpret belief functions whose focal elements form a partition of the universe. Generalized rough set algebras using nonequivalence relations may be used to interpret belief functions which have less than U  focal elements, where U  is the cardinality of the universe U on which belief functions are defined. Interval algebras may be used to interpret any belief functions. 1.
Hybrid Probabilistic Logic Programs
 Journal of Logic Programming
, 2000
"... Abstract There are many applications where the precise time at which an event will occur (or has occurred) is uncertain. Temporal probabilistic logic programs (TPLPs) allow a programmer to express knowledge about such events. In this paper, we develop a model theory, fixpoint theory, and proof theor ..."
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Cited by 10 (2 self)
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Abstract There are many applications where the precise time at which an event will occur (or has occurred) is uncertain. Temporal probabilistic logic programs (TPLPs) allow a programmer to express knowledge about such events. In this paper, we develop a model theory, fixpoint theory, and proof theory for TPLPs, and show that the fixpoint theory may be used to enumerate consequences of a TPLP in a sound and complete manner. Likewise the proof theory provides a sound and complete inference system. Last, but not least, we provide complexity results for TPLPs, showing in particular, that reasonable classes of TPLPs have polynomial data complexity. 1 Introduction There are a vast number of applications where uncertainty and time are indelibly intertwined. For example, the US Postal Service (USPS) as well as most commercial shippers have detailed statistics on how long shipments take to reach their destinations. Likewise, we are working on a Viennese historical land deed application where the precise time at which certain properties passed from one owner to another is also highly uncertain. Historical radio carbon dating methods are yet another source of uncertainty, providing approximate information about when a piece was created. Logical reasoning in situations involving temporal uncertainty is definitely important. For example, an individual querying the USPS express mail tracking system may want to know when he can expect his package to be delivered today he may then choose to stay home during the period when the probability of delivery seems very high, and leave a note authorizing the delivery official to leave the package by the door at other times.
THE SHAPE OF INCOMPLETE PREFERENCES
, 2006
"... Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape o ..."
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Cited by 10 (2 self)
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Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption from the axiom system of Anscombe and Aumann yields preferences represented by a convex set of statedependent expected utilities, of which at least one must be a probability/utility pair. A strengthening of the stateindependence axiom is needed to obtain a representation purely in terms of a set of probability/utility pairs.
Conservative inference rule for uncertain reasoning under incompleteness
 Journal of Artificial Intelligence Research
"... In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process ’ behaviour to be partly unknown. Then we use Walley’s theory ..."
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Cited by 10 (7 self)
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In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process ’ behaviour to be partly unknown. Then we use Walley’s theory of coherent lower previsions, a generalisation of the Bayesian theory to imprecision, to derive the rule to update beliefs under incompleteness that logically follows from our assumptions, and that we call conservative inference rule. This rule has some remarkable properties: it is an abstract rule to update beliefs that can be applied in any situation or domain; it gives us the opportunity to be neither too optimistic nor too pessimistic about the incompleteness process, which is a necessary condition to draw reliable while strong enough conclusions; and it is a coherent rule, in the sense that it cannot lead to inconsistencies. We give examples to show how the new rule can be applied in expert systems, in parametric statistical inference, and in pattern classification, and discuss more generally the view of incompleteness processes defended here as well as some of its consequences. 1.
Sleeping Beauty Reconsidered: Conditioning and Reflection
 in Asynchronous Systems”, Proceedings of the Twentieth Conference on Uncertainty in AI, AUAI
, 2004
"... A careful analysis of conditioning in the Sleeping Beauty problem is done, using the formal model for reasoning about knowledge and probability developed by Halpern and Tuttle. While the Sleeping Beauty problem has been viewed as revealing problems with conditioning in the presence of imperfect reca ..."
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Cited by 5 (2 self)
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A careful analysis of conditioning in the Sleeping Beauty problem is done, using the formal model for reasoning about knowledge and probability developed by Halpern and Tuttle. While the Sleeping Beauty problem has been viewed as revealing problems with conditioning in the presence of imperfect recall, the analysis done here reveals that the problems are not so much due to imperfect recall as to asynchrony. The implications of this analysis for van Fraassen’s Reflection Principle and Savage’s SureThing Principle are considered. 1
Intertemporal Discount Factors as a Measure of Trustworthiness in Electronic Commerce
"... Abstract—In multiagent interactions, such as ecommerce and file sharing, being able to accurately assess the trustworthiness of others is important for agents to protect themselves from losing utility. Focusing on rational agents in ecommerce, we prove that an agent’s discount factor (time prefere ..."
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Cited by 5 (3 self)
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Abstract—In multiagent interactions, such as ecommerce and file sharing, being able to accurately assess the trustworthiness of others is important for agents to protect themselves from losing utility. Focusing on rational agents in ecommerce, we prove that an agent’s discount factor (time preference of utility) is a direct measure of the agent’s trustworthiness for a set of reasonably general assumptions and definitions. We propose a general list of desiderata for trust systems and discuss how discount factors as trustworthiness meet these desiderata. We discuss how discount factors are a robust measure when entering commitments that exhibit moral hazards. Using an online market as a motivating example, we derive some analytical methods both for measuring discount factors and for aggregating the measurements. 1
Updating With Incomplete Observations
 Uncertainty in Artificial Intelligence: Proceedings of the Nineteenth Conference (UAI2003
, 2003
"... 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, and of particular interest for Bayesian networks. Recently, Gr unwald and Halpern have shown that commonly u ..."
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Cited by 4 (2 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, and of particular interest for Bayesian networks. Recently, Gr unwald and Halpern have shown that commonly used updating strategies fail here, except under very special assumptions. We propose a new rule for updating probabilities with incomplete observations. Our approach is deliberately conservative: we make no or weak assumptions about the socalled incompleteness mechanism that produces incomplete observations. We model our ignorance about this mechanism by a vacuous lower prevision, a tool from the theory of imprecise probabilities, and we derive a new updating rule using coherence arguments. In general, our rule produces lower posterior probabilities, as well as partially determinate decisions.