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Probabilistic Horn abduction and Bayesian networks
 Artificial Intelligence
, 1993
"... This paper presents a simple framework for Hornclause abduction, with probabilities associated with hypotheses. The framework incorporates assumptions about the rule base and independence assumptions amongst hypotheses. It is shown how any probabilistic knowledge representable in a discrete Bayesia ..."
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Cited by 295 (37 self)
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This paper presents a simple framework for Hornclause abduction, with probabilities associated with hypotheses. The framework incorporates assumptions about the rule base and independence assumptions amongst hypotheses. It is shown how any probabilistic knowledge representable in a discrete Bayesian belief network can be represented in this framework. The main contribution is in finding a relationship between logical and probabilistic notions of evidential reasoning. This provides a useful representation language in its own right, providing a compromise between heuristic and epistemic adequacy. It also shows how Bayesian networks can be extended beyond a propositional language. This paper also shows how a language with only (unconditionally) independent hypotheses can represent any probabilistic knowledge, and argues that it is better to invent new hypotheses to explain dependence rather than having to worry about dependence in the language. Scholar, Canadian Institute for Advanced...
Current Approaches to Handling Imperfect Information in Data and Knowledge Bases
, 1996
"... This paper surveys methods for representing and reasoning with imperfect information. It opens with an attempt to classify the different types of imperfection that may pervade data, and a discussion of the sources of such imperfections. The classification is then used as a framework for considering ..."
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Cited by 54 (1 self)
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This paper surveys methods for representing and reasoning with imperfect information. It opens with an attempt to classify the different types of imperfection that may pervade data, and a discussion of the sources of such imperfections. The classification is then used as a framework for considering work that explicitly concerns the representation of imperfect information, and related work on how imperfect information may be used as a basis for reasoning. The work that is surveyed is drawn from both the field of databases and the field of artificial intelligence. Both of these areas have long been concerned with the problems caused by imperfect information, and this paper stresses the relationships between the approaches developed in each.
Generating Bayesian Networks from Probability Logic Knowledge Bases
 In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence
, 1994
"... We present a method for dynamically generating Bayesian networks from knowledge bases consisting of firstorder probability logic sentences. We present a subset of probability logic sufficient for representing the class of Bayesian networks with discretevalued nodes. We impose constraints on the fo ..."
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Cited by 52 (8 self)
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We present a method for dynamically generating Bayesian networks from knowledge bases consisting of firstorder probability logic sentences. We present a subset of probability logic sufficient for representing the class of Bayesian networks with discretevalued nodes. We impose constraints on the form of the sentences that guarantee that the knowledge base contains all the probabilistic information necessary to generate a network. We define the concept of dseparation for knowledge bases and prove that a knowledge base with independence conditions defined by dseparation is a complete specification of a probability distribution. We present a network generation algorithm that, given an inference problem in the form of a query Q and a set of evidence E, generates a network to compute P (QjE). We prove the algorithm to be correct. 1 Introduction The flexibility of Bayesian networks for representing probabilistic dependencies and the relative efficiency of computational techniques for p...
Logic Programming, Abduction and Probability: a topdown anytime algorithm for estimating prior and posterior probabilities
 New Generation Computing
, 1993
"... Probabilistic Horn abduction is a simple framework to combine probabilistic and logical reasoning into a coherent practical framework. The numbers can be consistently interpreted probabilistically, and all of the rules can be interpreted logically. The relationship between probabilistic Horn abducti ..."
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Cited by 39 (8 self)
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Probabilistic Horn abduction is a simple framework to combine probabilistic and logical reasoning into a coherent practical framework. The numbers can be consistently interpreted probabilistically, and all of the rules can be interpreted logically. The relationship between probabilistic Horn abduction and logic programming is at two levels. At the first level probabilistic Horn abduction is an extension of pure Prolog, that is useful for diagnosis and other evidential reasoning tasks. At another level, current logic programming implementation techniques can be used to efficiently implement probabilistic Horn abduction. This forms the basis of an "anytime" algorithm for estimating arbitrary conditional probabilities. The focus of this paper is on the implementation. Scholar, Canadian Institute for Advanced Research Logic Programming, Abduction and Probability 2 1 Introduction Probabilistic Horn Abduction [22, 21, 23] is a framework for logicbased abduction that incorporates proba...
The Independent Choice Logic and Beyond
"... Abstract. The Independent Choice Logic began in the early 90’s as a way to combine logic programming and probability into a coherent framework. The idea of the Independent Choice Logic is straightforward: there is a set of independent choices with a probability distribution over each choice, and a l ..."
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Cited by 18 (5 self)
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Abstract. The Independent Choice Logic began in the early 90’s as a way to combine logic programming and probability into a coherent framework. The idea of the Independent Choice Logic is straightforward: there is a set of independent choices with a probability distribution over each choice, and a logic program that gives the consequences of the choices. There is a measure over possible worlds that is defined by the probabilities of the independent choices, and what is true in each possible world is given by choices made in that world and the logic program. ICL is interesting because it is a simple, natural and expressive representation of rich probabilistic models. This paper gives an overview of the work done over the last decade and half, and points towards the considerable work ahead, particularly in the areas of lifted inference and the problems of existence and identity. 1
Defining Normative Systems for Qualitative Argumentation
 Practical Reasoning, volume 1085 of Lecture Notes in Computer Science
"... . Inspired by two different approaches to providing a qualitative method for reasoning under uncertaintyqualitative probabilistic networks and systems of argumentationthis paper attempts to combine the advantages of both by defining systems of argumentation that have a probabilistic semantics. ..."
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Cited by 7 (4 self)
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. Inspired by two different approaches to providing a qualitative method for reasoning under uncertaintyqualitative probabilistic networks and systems of argumentationthis paper attempts to combine the advantages of both by defining systems of argumentation that have a probabilistic semantics. 1 Introduction In the last few years there have been a number of attempts to build systems for reasoning under uncertainty that are of a qualitative naturethat is they use qualitative rather than numerical values, dealing with concepts such as increases in belief and the relative magnitude of values. In particular, two types of qualitative system have become well established, namely qualitative probabilistic networks (QPNs) [4, 18], and systems of argumentation [8, 11, 12]. While the former are built as an abstraction of probabilistic networks where the links between nodes are only modelled in terms of the qualitative influence of the parents on the children, and therefore have an under...
NONCOMPUTABLE CONDITIONAL DISTRIBUTIONS
"... Abstract. We study the computability of conditional probability, a fundamental notion in probability theory and Bayesian statistics. In the elementary discrete setting, a ratio of probabilities defines conditional probability. In more general settings, conditional probability is defined axiomaticall ..."
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Cited by 7 (3 self)
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Abstract. We study the computability of conditional probability, a fundamental notion in probability theory and Bayesian statistics. In the elementary discrete setting, a ratio of probabilities defines conditional probability. In more general settings, conditional probability is defined axiomatically, and the search for more constructive definitions is the subject of a rich literature in probability theory and statistics. However, we show that in general one cannot compute conditional probabilities. Specifically, we construct a pair of computable random variables (X, Y) in the unit interval whose conditional distribution P[YX] encodes the halting problem. Nevertheless, probabilistic inference has proven remarkably successful in practice, even in infinitedimensional continuous settings. We prove several results giving general conditions under which conditional distributions are computable. In the discrete or dominated setting, under suitable computability hypotheses, conditional distributions are computable. Likewise, conditioning is a computable operation in the presence of certain additional structure, such as independent absolutely continuous noise.
Principled Construction of Minimal Bayesian Networks from Probability Logic Knowledge Bases
 Journal of AI Research
"... We present a method for dynamically constructing Bayesian networks from knowledge bases consisting of firstorder probability logic sentences. We present a subset of probability logic sufficient for representing the class of Bayesian networks with discretevalued nodes. We impose constraints on the f ..."
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Cited by 2 (1 self)
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We present a method for dynamically constructing Bayesian networks from knowledge bases consisting of firstorder probability logic sentences. We present a subset of probability logic sufficient for representing the class of Bayesian networks with discretevalued nodes. We impose constraints on the form of the sentences that guarantee that the knowledge base contains all the probabilistic information necessary to construct a network. We define the concept of dseparation for knowledge bases and prove that a knowledge base with independence conditions defined by dseparation is a complete specification of a probability distribution. We present a network construction algorithm that, given an inference problem in the form of a query Q and a set of evidence E, constructs the smallest network to compute P (QjE). We prove the algorithm to be correct. Submitted to Journal of AI Research 1 Introduction The flexibility of Bayesian networks for representing probabilistic dependencies and the ...
15 Probabilistic Programming Languages: Independent Choices and Deterministic Systems
"... Pearl [2000, p. 26] attributes to Laplace [1814] the idea of a probabilistic model as a deterministic system with stochastic inputs. Pearl defines causal models in terms of deterministic systems with stochastic inputs. In this paper, I show how deterministic systems with (independent) probabilistic ..."
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Cited by 2 (2 self)
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Pearl [2000, p. 26] attributes to Laplace [1814] the idea of a probabilistic model as a deterministic system with stochastic inputs. Pearl defines causal models in terms of deterministic systems with stochastic inputs. In this paper, I show how deterministic systems with (independent) probabilistic inputs can also be seen as the basis of modern probabilistic programming languages. Probabilistic programs can be seen as consisting of independent choices (over which there are probability distributions) and deterministic programs that give the consequences of these choices. The work on developing such languages has gone in parallel with the development of causal models, and many of the foundations are remarkably similar. Most of the work in probabilistic programming languages has been in the context of specific languages. This paper abstracts the work on probabilistic programming languages from specific languages and explains some design choices in the design of these languages. Probabilistic programming languages have a rich history starting from the use of simulation languages such as Simula [Dahl and Nygaard 1966]. Simula was designed
Comparing Normative Argumentation to Other Probabilistic Systems
 In Proceedings of the International Conference on Information Processing and Management of Uncertainty in KBS
, 1996
"... This paper discusses a system of argumentation with a probabilistic semantics and compares it to two other probabilistic systemsWellman's qualitative probabilistic networks and Neufeld's probabilistic default reasoning. 1 INTRODUCTION In the last few years there have been a number of attempts to ..."
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Cited by 1 (0 self)
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This paper discusses a system of argumentation with a probabilistic semantics and compares it to two other probabilistic systemsWellman's qualitative probabilistic networks and Neufeld's probabilistic default reasoning. 1 INTRODUCTION In the last few years there have been a number of attempts to build systems for reasoning under uncertainty that are of a qualitative naturethat is they use qualitative rather than numerical values, dealing with concepts such as increases in belief and the relative magnitude of values. In particular, two types of qualitative system have become well established qualitative probabilistic networks (QPNs) [2, 12], and systems of argumentation [5, 6]. While the former are built as an abstraction of probabilistic networks where the links between nodes are only modelled in terms of the qualitative influence of the parents on the children, and therefore have an underlying probabilistic semantics, some of the latter lack such a sound foundation. This lac...