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34
Generating New Beliefs From Old
, 1994
"... In previous work [BGHK92, BGHK93], we have studied the randomworlds approacha particular (and quite powerful) method for generating degrees of belief (i.e., subjective probabilities) from a knowledge base consisting of objective (firstorder, statistical, and default) information. But allow ..."
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Cited by 13 (1 self)
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In previous work [BGHK92, BGHK93], we have studied the randomworlds approacha particular (and quite powerful) method for generating degrees of belief (i.e., subjective probabilities) from a knowledge base consisting of objective (firstorder, statistical, and default) information. But allowing a knowledge base to contain only objective information is sometimes limiting. We occasionally wish to include information about degrees of belief in the knowledge base as well, because there are contexts in which old beliefs represent important information that should influence new beliefs. In this paper, we describe three quite general techniques for extending a method that generates degrees of belief from objective information to one that can make use of degrees of belief as well. All of our techniques are based on wellknown approaches, such as crossentropy. We discuss general connections between the techniques and in particular show that, although conceptually and techn...
A Logic for Default Reasoning About Probabilities
, 1998
"... A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given are well suited to model the in uence of statistical informa ..."
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Cited by 12 (4 self)
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A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given are well suited to model the in uence of statistical information on the formation of subjective beliefs. Cross entropy minimization is a key element in these semantics, the use of which is justified by showing that the resulting logic exhibits some very reasonable properties.
Asymptotic Conditional Probabilities: The Unary Case
, 1993
"... Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for firstorder sentences. Given firstorder sentences ' and `, we consider the structures with domain f1; : : : ; Ng that satisfy `, and compute the fraction of ..."
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Cited by 11 (3 self)
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Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for firstorder sentences. Given firstorder sentences ' and `, we consider the structures with domain f1; : : : ; Ng that satisfy `, and compute the fraction of them in which ' is true. We then consider what happens to this fraction as N gets large. This extends the work on 01 laws that considers the limiting probability of firstorder sentences, by considering asymptotic conditional probabilities. As shown by Liogon'kii[31] and Grove, Halpern, and Koller [22], in the general case, asymptotic conditional probabilities do not always exist, and most questions relating to this issue are highly undecidable. These results, however, all depend on the assumption that ` can use a nonunary predicate symbol. Liogon'kii [31] shows that if we condition on formulas ` involving unary predicate symbols only (but no equality or constant symbols), then the asymptotic conditional probability does exist and can be effectively computed. This is the case even if we place no corresponding restrictions on '. We extend this result here to the case where ` involves equality and constants. We show that the complexity of computing the limit depends on various factors, such as the depth of quantifier nesting, or whether the vocabulary is finite or infinite. We completely characterize the complexity of the problem in the different cases, and show related results for the associated approximation problem.
Generating Explicit Orderings for Nonmonotonic Logics
 In Proceedings of the Eleventh National Conference on Artificial Intelligence (AAAI'93
, 1993
"... For nonmonotonic reasoning, explicit orderings over formulae offer an important solution to problems such as `multiple extensions'. However, a criticism of such a solution is that it is not clear, in general, from where the orderings should be obtained. Here we show how orderings can be derived fro ..."
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Cited by 10 (9 self)
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For nonmonotonic reasoning, explicit orderings over formulae offer an important solution to problems such as `multiple extensions'. However, a criticism of such a solution is that it is not clear, in general, from where the orderings should be obtained. Here we show how orderings can be derived from statistical information about the domain which the formulae cover. For this we provide an overview of prioritized logicsa general class of logics that incorporate explicit orderings over formulae. This class of logics has been shown elsewhere to capture a wide variety of prooftheoretic approaches to nonmonotonic reasoning, and in particular, to highlight the role of preferencesboth implicit and explicitin such proof theory. We take one particular prioritized logic, called SF logic, and describe an experimental approach for comparing this logic with an important example of a logic that does not use explicit orderings of preferencenamely Horn clause logic with negationasfailu...
Forming Beliefs About a Changing World
, 1994
"... The situation calculus is a popular technique for reasoning about action and change. However, its restriction to a firstorder syntax and pure deductive reasoning makes it unsuitable in many contexts. In particular, we often face uncertainty, due either to lack of knowledge or to some probabilistic a ..."
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Cited by 9 (3 self)
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The situation calculus is a popular technique for reasoning about action and change. However, its restriction to a firstorder syntax and pure deductive reasoning makes it unsuitable in many contexts. In particular, we often face uncertainty, due either to lack of knowledge or to some probabilistic aspects of the world. While attempts have been made to address aspects of this problem, most notably using nonmonotonic reasoning formalisms, the general problem of uncertainty in reasoning about action has not been fully dealt with in a logical framework. In this paper we present a theory of action that extends the situation calculus to deal with uncertainty. Our framework is based on applying the randomworlds approach of [BGHK94] to a situation calculus ontology, enriched to allow the expression of probabilistic action effects. Our approach is able to solve many of the problems imposed by incomplete and probabilistic knowledge within a unified framework. In particular, we obtain a default ...
Asymptotic Conditional Probabilities: The Nonunary Case
 J. SYMBOLIC LOGIC
, 1993
"... Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for firstorder sentences. Given firstorder sentences ' and `, we consider the structures with domain f1; : : : ; Ng that satisfy `, and compute the fraction ..."
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Cited by 9 (2 self)
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Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for firstorder sentences. Given firstorder sentences ' and `, we consider the structures with domain f1; : : : ; Ng that satisfy `, and compute the fraction of them in which ' is true. We then consider what happens to this fraction as N gets large. This extends the work on 01 laws that considers the limiting probability of firstorder sentences, by considering asymptotic conditional probabilities. As shown by Liogon'kii [Lio69], if there is a nonunary predicate symbol in the vocabulary, asymptotic conditional probabilities do not always exist. We extend this result to show that asymptotic conditional probabilities do not always exist for any reasonable notion of limit. Liogon'kii also showed that the problem of deciding whether the limit exists is undecidable. We analyze the complexity of three problems with respect to this limit: deciding whether it is welldefined, whether it exists, and whether it lies in some nontrivial interval. Matching upper and lower bounds are given for all three problems, showing them to be highly undecidable.
time and incomplete information in multiple encounter negotiations among autonomous agents
 Annals of Mathematics and Artificial Intelligence
, 1997
"... In negotiations among autonomous agents over resource allocation, beliefs about opponents, and about opponents ' beliefs, become particularly important when there is incomplete information. This paper considers interactions among selfmotivated, rational, and autonomous agents, each with its own util ..."
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Cited by 8 (1 self)
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In negotiations among autonomous agents over resource allocation, beliefs about opponents, and about opponents ' beliefs, become particularly important when there is incomplete information. This paper considers interactions among selfmotivated, rational, and autonomous agents, each with its own utility function, and each seeking to maximize its expected utility. The paper expands upon previous work and focuses on incomplete information and multiple encounters among the agents. It presents a strategic model that takes into consideration the passage of time during the negotiation and also includes belief systems. The paper provides strategies for a wide range of situations. The framework satis es the following criteria: symmetrical distribution, simplicity, instantaneously, e ciency and stability. 1
Data Publishing against Realistic Adversaries
"... Privacy in data publishing has received much attention recently. The key to defining privacy is to model knowledge of the attacker – if the attacker is assumed to know too little, the published data can be easily attacked, if the attacker is assumed to know too much, the published data has little ut ..."
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Cited by 8 (1 self)
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Privacy in data publishing has received much attention recently. The key to defining privacy is to model knowledge of the attacker – if the attacker is assumed to know too little, the published data can be easily attacked, if the attacker is assumed to know too much, the published data has little utility. Previous work considered either quite ignorant adversaries or nearly omniscient adversaries. In this paper, we introduce a new class of adversaries that we call realistic adversaries who live in the unexplored space in between. Realistic adversaries have knowledge from external sources with an associated stubbornness indicating the strength of their knowledge. We then introduce a novel privacy framework called epsilonprivacy that allows us to guard against realistic adversaries. We also show that prior privacy definitions are instantiations of our framework. In a thorough experimental study with real census data we show that eprivacy allows us to publish data with high utility while defending against strong adversaries. 1.
Discovering Robust Knowledge from Databases that Change
 DATA MINING AND KNOWLEDGE DISCOVERY
, 1998
"... Many applications of knowledge discovery and data mining such as rule discovery for semantic query optimization, database integration and decision support, require the knowledge to be consistent with data. However, databases usually change over time and makemachinediscovered knowledge inconsiste ..."
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Cited by 7 (1 self)
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Many applications of knowledge discovery and data mining such as rule discovery for semantic query optimization, database integration and decision support, require the knowledge to be consistent with data. However, databases usually change over time and makemachinediscovered knowledge inconsistent. Useful knowledge should be robust against database changessothatitisunlikely to become inconsistentafter database changes. This paper defines this notion of robustness in the context of relational databases that contain multiple relations and describes how robustness of firstorder Hornclause rules can be estimated and applied in knowledge discovery.Our experiments show that the estimation approach can accurately predict the robustness of a rule.
Minimum CrossEntropy Reasoning: A Statistical Justification
 Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI95
, 1995
"... Degrees of belief are formed using observed evidence and statistical background information. In this paper we examine the process of how prior degrees of belief derived from the evidence are combined with statistical data to form more specific degrees of belief. A statistical model for this process ..."
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Cited by 4 (4 self)
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Degrees of belief are formed using observed evidence and statistical background information. In this paper we examine the process of how prior degrees of belief derived from the evidence are combined with statistical data to form more specific degrees of belief. A statistical model for this process then is shown to vindicate the crossentropy minimization principle as a rule for probabilistic defaultinference. 1 Introduction A knowledge based system incorporating reasoning with uncertain information gives rise to quantitative statements of two different kinds: statements expressing statistical information and statements of degrees of belief. "10% of applicants seeking employment at company X who are invited to an interview will get a job there" is a statistical statement. "The likelihood that I will be invited for an interview if I apply for a job at company X is about 0.6" expresses a degree of belief. In this paper, both of these kinds of statements are regarded as probabilistic, i...