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108
Plausibility Measures and Default Reasoning
 Journal of the ACM
, 1996
"... this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, fflsemantics, possibilistic structures, and rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. W ..."
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Cited by 79 (12 self)
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this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, fflsemantics, possibilistic structures, and rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. While this was viewed as a surprise, we show here that it is almost inevitable. In the framework of plausibility measures, we can give a necessary condition for the KLM axioms to be sound, and an additional condition necessary and sufficient to ensure that the KLM axioms are complete. This additional condition is so weak that it is almost always met whenever the axioms are sound. In particular, it is easily seen to hold for all the proposals made in the literature. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]:
DecisionTheoretic Foundations of Qualitative Possibility Theory
 European Journal of Operational Research
, 2000
"... This paper presents a justification of two qualitative counterparts of the expected utility criterion for decision under uncertainty, which only require bounded, linearly ordered, valuation sets for expressing uncertainty and preferences. This is carried out in the style of Savage, starting with ..."
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Cited by 51 (7 self)
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This paper presents a justification of two qualitative counterparts of the expected utility criterion for decision under uncertainty, which only require bounded, linearly ordered, valuation sets for expressing uncertainty and preferences. This is carried out in the style of Savage, starting with a set of acts equipped with a complete preordering relation. Conditions on acts are given that imply a possibilistic representation of the decisionmaker uncertainty. In this framework, pessimistic (i.e., uncertaintyaverse) as well as optimistic attitudes can be explicitly captured. The approach thus proposes an operationally testable description of possibility theory. 1
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.
Supremum Preserving Upper Probabilities
, 1998
"... We study the relation between possibility measures and the theory of imprecise probabilities, and argue that possibility measures have an important part in this theory. It is shown that a possibility measure is a coherent upper probability if and only if it is normal. A detailed comparison is giv ..."
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Cited by 38 (12 self)
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We study the relation between possibility measures and the theory of imprecise probabilities, and argue that possibility measures have an important part in this theory. It is shown that a possibility measure is a coherent upper probability if and only if it is normal. A detailed comparison is given between the possibilistic and natural extension of an upper probability, both in the general case and for upper probabilities dened on a class of nested sets. We prove in particular that a possibility measure is the restriction to events of the natural extension of a special kind of upper probability, dened on a class of nested sets. We show that possibilistic extension can be interpreted in terms of natural extension. We also prove that when either the upper or the lower cumulative distribution function of a random quantity is specied, possibility measures very naturally emerge as the corresponding natural extensions. Next, we go from upper probabilities to upper previsions...
Modeling Belief in Dynamic Systems. Part II: Revision and Update
 Journal of A.I. Research
, 1999
"... The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper [Friedman and Halpern 1997a], we introduce a new framework to model belief change. This fr ..."
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Cited by 26 (7 self)
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The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper [Friedman and Halpern 1997a], we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update [Katsuno and Mendelzon 1991a] depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revi...
Plausibility Measures: A User's Guide
 In Proc. Eleventh Conference on Uncertainty in Artificial Intelligence (UAI '95
, 1995
"... We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probab ..."
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Cited by 24 (7 self)
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We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility measures. The lack of structure in a plausibility measure makes it easy for us to add structure on an "as needed" basis, letting us examine what is required to ensure that a plausibility measure has certain properties of interest. This gives us insight into the essential features of the properties in question, while allowing us to prove general results that apply to many approaches to reasoning about uncertainty. Plausibility measures have already proved useful in analyzing default reasoning. In this paper, we examine their "algebraic properties", analogues to the use of + and \Theta in probability theory. An understanding of such properties ...
Modeling Belief in Dynamic Systems. Part I: Foundations
 Artificial Intelligence
, 1997
"... Belief change is a fundamental problem in AI: Agents constantly have to update their beliefs to accommodate new observations. In recent years, there has been much work on axiomatic characterizations of belief change. We claim that a better understanding of belief change can be gained from examining ..."
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Cited by 23 (11 self)
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Belief change is a fundamental problem in AI: Agents constantly have to update their beliefs to accommodate new observations. In recent years, there has been much work on axiomatic characterizations of belief change. We claim that a better understanding of belief change can be gained from examining appropriate semantic models. In this paper we propose a general framework in which to model belief change. We begin by defining belief in terms of knowledge and plausibility: an agent believes OE if he knows that OE is more plausible than :OE. We then consider some properties defining the interaction between knowledge and plausibility, and show how these properties affect the properties of belief. In particular, we show that by assuming two of the most natural properties, belief becomes a KD45 operator. Finally, we add time to the picture. This gives us a framework in which we can talk about knowledge, plausibility (and hence belief), and time, which extends the framework of Halpern and Fagi...
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 22 (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
On The Extension Of PConsistent Mappings
 Foundations and Applications of Possibility Theory
, 1995
"... In this paper, the notion of Pconsistency is extended to complete latticevalued mappings. It is proven that a Pconsistent mapping possesses a distribution if and only if it is extendable to a possibility measure defined on an ample field. A necessary and sufficient condition is given for extendab ..."
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Cited by 17 (13 self)
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In this paper, the notion of Pconsistency is extended to complete latticevalued mappings. It is proven that a Pconsistent mapping possesses a distribution if and only if it is extendable to a possibility measure defined on an ample field. A necessary and sufficient condition is given for extendability, and it is shown by counterexamples that this condition is not always satisfied. Finally, sufficient conditions are given under which a Pconsistent mapping is always extendable, and it is shown that every complete lattice can be embedded in another complete lattice in such a way that every Pconsistent mapping is extendable to a possibility measure taking values in the second complete lattice. 1. Introduction Ever since the introduction of possibility theory by Zadeh 8 in 1978, various attempts have been made to generalize Zadeh's original definition of a possibility measure. Essentially, Zadeh defined a possibility measure \Pi as a mapping from the power class (X) of a nonempty s...
A Syllable, ArticulatoryFeature, and StressAccent Model of Speech Recognition
, 2002
"... Currentgeneration automatic speech recognition (ASR) systems assume that words are readily decomposable into constituent phonetic components ("phonemes"). A detailed linguistic dissection of stateoftheart speech recognition systems indicates that the conventional phonemic "beadsonastring" app ..."
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Cited by 16 (5 self)
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Currentgeneration automatic speech recognition (ASR) systems assume that words are readily decomposable into constituent phonetic components ("phonemes"). A detailed linguistic dissection of stateoftheart speech recognition systems indicates that the conventional phonemic "beadsonastring" approach is of limited utility, particularly with respect to informal, conversational material. The study shows that there is a significant gap between the observed data and the pronunciation models of current ASR systems. It also shows that many important factors affecting recognition performance are not modeled explicitly in these systems. Motivated by