Results 1  10
of
45
A theory of defeasible reasoning
, 1991
"... Reasoning can lead not only to the adoption of beliefs, but also to the retraction of beliefs. In philosophy, this is described by saying that reasoning is defeasible. My ultimate objective is the construction of a general theory of reasoning and its implementation in an automated reasoner capable o ..."
Abstract

Cited by 283 (7 self)
 Add to MetaCart
Reasoning can lead not only to the adoption of beliefs, but also to the retraction of beliefs. In philosophy, this is described by saying that reasoning is defeasible. My ultimate objective is the construction of a general theory of reasoning and its implementation in an automated reasoner capable of both deductive and defeasible reasoning. The resulting system is named “OSCAR. ” This article addresses some of the theoretical underpinnings of OSCAR. This article extends my earlier theory in two directions. First, it addresses the question of what the criteria of adequacy should be for a defeasible reasoner. Second, it extends the theory to accommodate reasons of varying strengths.
Managing Uncertainty and Vagueness in Description Logics for the Semantic Web
, 2007
"... Ontologies play a crucial role in the development of the Semantic Web as a means for defining shared terms in web resources. They are formulated in web ontology languages, which are based on expressive description logics. Significant research efforts in the semantic web community are recently direct ..."
Abstract

Cited by 132 (10 self)
 Add to MetaCart
Ontologies play a crucial role in the development of the Semantic Web as a means for defining shared terms in web resources. They are formulated in web ontology languages, which are based on expressive description logics. Significant research efforts in the semantic web community are recently directed towards representing and reasoning with uncertainty and vagueness in ontologies for the Semantic Web. In this paper, we give an overview of approaches in this context to managing probabilistic uncertainty, possibilistic uncertainty, and vagueness in expressive description logics for the Semantic Web.
Random Worlds and Maximum Entropy
 In Proc. 7th IEEE Symp. on Logic in Computer Science
, 1994
"... Given a knowledge base KB containing firstorder and statistical facts, we consider a principled method, called the randomworlds method, for computing a degree of belief that some formula ' holds given KB . If we are reasoning about a world or system consisting of N individuals, then we can co ..."
Abstract

Cited by 56 (13 self)
 Add to MetaCart
(Show Context)
Given a knowledge base KB containing firstorder and statistical facts, we consider a principled method, called the randomworlds method, for computing a degree of belief that some formula ' holds given KB . If we are reasoning about a world or system consisting of N individuals, then we can consider all possible worlds, or firstorder models, with domain f1; : : : ; Ng that satisfy KB , and compute the fraction of them in which ' is true. We define the degree of belief to be the asymptotic value of this fraction as N grows large. We show that when the vocabulary underlying ' and KB uses constants and unary predicates only, we can naturally associate an entropy with each world. As N grows larger, there are many more worlds with higher entropy. Therefore, we can use a maximumentropy computation to compute the degree of belief. This result is in a similar spirit to previous work in physics and artificial intelligence, but is far more general. Of equal interest to the result itself are...
From Statistics to Beliefs
, 1992
"... An intelligent agent uses known facts, including statistical knowledge, to assign degrees of belief to assertions it is uncertain about. We investigate three principled techniques for doing this. All three are applications of the principle of indifference, because they assign equal degree of belief ..."
Abstract

Cited by 48 (12 self)
 Add to MetaCart
An intelligent agent uses known facts, including statistical knowledge, to assign degrees of belief to assertions it is uncertain about. We investigate three principled techniques for doing this. All three are applications of the principle of indifference, because they assign equal degree of belief to all basic "situations " consistent with the knowledge base. They differ because there are competing intuitions about what the basic situations are. Various natural patterns of reasoning, such as the preference for the most specific statistical data available, turn out to follow from some or all of the techniques. This is an improvement over earlier theories, such as work on direct inference and reference classes, which arbitrarily postulate these patterns without offering any deeper explanations or guarantees of consistency. The three methods we investigate have surprising characterizations: there are connections to the principle of maximum entropy, a principle of maximal independence, an...
Probabilistic Default Reasoning with Conditional Constraints
 ANN. MATH. ARTIF. INTELL
, 2000
"... We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of , lexicographic, ..."
Abstract

Cited by 38 (18 self)
 Add to MetaCart
(Show Context)
We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of , lexicographic, and conditional entailment for conditional constraints, which are probabilistic generalizations of Pearl's entailment in system , Lehmann's lexicographic entailment, and Geffner's conditional entailment, respectively. We show that the new formalisms have nice properties. In particular, they show a similar behavior as referenceclass reasoning in a number of uncontroversial examples. The new formalisms, however, also avoid many drawbacks of referenceclass reasoning. More precisely, they can handle complex scenarios and even purely probabilistic subjective knowledge as input. Moreover, conclusions are drawn in a global way from all the available knowledge as a whole. We then show that the new formalisms also have nice general nonmonotonic properties. In detail, the new notions of , lexicographic, and conditional entailment have similar properties as their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and they have some general irrelevance and direct inference properties. Moreover, the new notions of  and lexicographic entailment satisfy the property of rational monotonicity. Furthermore, the new notions of , lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints. Finally, we provide algorithms for reasoning under the new formalisms, and we analyze its computational com...
IntervalValued Probabilities
, 1998
"... 0 =h 0 in the diagram. The sawtooth line reflects the fact that even when the principle of indifference can be applied, there may be arguments whose strength can be bounded no more precisely than by an adjacent pair of indifference arguments. Note that a=h in the diagram is bounded numerically on ..."
Abstract

Cited by 27 (1 self)
 Add to MetaCart
(Show Context)
0 =h 0 in the diagram. The sawtooth line reflects the fact that even when the principle of indifference can be applied, there may be arguments whose strength can be bounded no more precisely than by an adjacent pair of indifference arguments. Note that a=h in the diagram is bounded numerically only by 0.0 and the strength of a 00 =h 00 . Keynes' ideas were taken up by B. O. Koopman [14, 15, 16], who provided an axiomatization for Keynes' probability values. The axioms are qualitative, and reflect what Keynes said about probability judgment. (It should be remembered that for Keynes probability judgment was intended to be objective in the sense that logic is objective. Although different people may accept different premises, whether or not a conclusion follows logically from a given set of premises is objective. Though Ramsey [26] attacked this aspect of Keynes' theory, it can be argued
Learning Default Concepts
 In Proceedings of the Tenth Canadian Conference on Artificial Intelligence (CSCSI94
, 1994
"... Classical concepts, based on necessary and sufficient defining conditions, cannot classify logically insufficient object descriptions. Many reasoning systems avoid this limitation by using "default concepts" to classify incompletely described objects. This paper addresses the task of learn ..."
Abstract

Cited by 23 (8 self)
 Add to MetaCart
Classical concepts, based on necessary and sufficient defining conditions, cannot classify logically insufficient object descriptions. Many reasoning systems avoid this limitation by using "default concepts" to classify incompletely described objects. This paper addresses the task of learning such default concepts from observational data. We first model the underlying performance task  classifying incomplete examples  as a probabilistic process that passes random test examples through a "blocker" that can hide object attributes from the classifier. We then address the task of learning accurate default concepts from random training examples. After surveying the learning techniques that have been proposed for this task in the machine learning and knowledge representation literatures, and investigating their relative merits, we present a more dataefficient learning technique, developed from wellknown statistical principles. Finally, we extend Valiant's pac learning framework to ...
Weak nonmonotonic probabilistic logics
, 2004
"... Towards probabilistic formalisms for resolving local inconsistencies under modeltheoretic probabilistic entailment, we present probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment. We then analyze the nonmonotonic and semantic properties of the new ..."
Abstract

Cited by 23 (6 self)
 Add to MetaCart
Towards probabilistic formalisms for resolving local inconsistencies under modeltheoretic probabilistic entailment, we present probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment. We then analyze the nonmonotonic and semantic properties of the new notions of entailment. In particular, we show that they satisfy the rationality postulates of System P and the property of Rational Monotonicity. Moreover, we show that modeltheoretic probabilistic entailment is stronger than the new notion of lexicographic entailment, which in turn is stronger than the new notion of entailment in System Z. As an important feature of the new notions of entailment in System Z and lexicographic entailment, we show that they coincide with modeltheoretic probabilistic entailment whenever there are no local inconsistencies. We also show that the new notions of entailment in System Z and lexicographic entailment are proper generalizations of their classical counterparts. Finally, we present algorithms for reasoning under the new formalisms, and we give a precise picture of its computational complexity.
Combining probabilistic logic programming with the power of maximum entropy
 ARTIF. INTELL
, 2004
"... This paper is on the combination of two powerful approaches to uncertain reasoning: logic programming in a probabilistic setting, on the one hand, and the informationtheoretical principle of maximum entropy, on the other hand. More precisely, we present two approaches to probabilistic logic progra ..."
Abstract

Cited by 21 (4 self)
 Add to MetaCart
This paper is on the combination of two powerful approaches to uncertain reasoning: logic programming in a probabilistic setting, on the one hand, and the informationtheoretical principle of maximum entropy, on the other hand. More precisely, we present two approaches to probabilistic logic programming under maximum entropy. The first one is based on the usual notion of entailment under maximum entropy, and is defined for the very general case of probabilistic logic programs over Boolean events. The second one is based on a new notion of entailment under maximum entropy, where the principle of maximum entropy is coupled with the closed world assumption (CWA) from classical logic programming. It is only defined for the more restricted case of probabilistic logic programs over conjunctive events. We then analyze the nonmonotonic behavior of both approaches along benchmark examples and along general properties for default reasoning from conditional knowledge bases. It turns out that both approaches have very nice nonmonotonic features. In particular, they realize some inheritance of probabilistic knowledge along subclass relationships, without suffering from the problem of inheritance blocking and from the drowning problem. They both also satisfy the property of rational monotonicity and several irrelevance properties. We finally present algorithms for both approaches, which are based on generalizations of techniques from probabilistic