This paper presents a simple framework for Horn-clause 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...

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.

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Many different formal techniques, both numerical and symbolic, have been developed over the past two decades for dealing with incomplete and uncertain information. In this paper we review some of the most important of these formalisms, describing how they work, and in what ways they differ from one another. We also consider heterogeneous approaches which incorporate two or more approximate reasoning mechanisms within a single reasoning system. These have been proposed to address limitations in the use of individual formalisms.

The mathematical foundations of model-based diagnostics or diagnosis from first principles have been laid by Reiter [31]. In this paper we extend Reiter’s ideas of model-based diagnostics by introducing probabilities into Reiter’s framework. This is done in a mathematically sound and precise way which allows one to compute the posterior probability that a certain component is not working correctly given some observations of the system. A straightforward computation of these probabilities is not efficient and in this paper we propose a new method to solve this problem. Our method is logic-based and borrows ideas from assumption-based reasoning and ATMS. We show how it is possible to determine arguments in favor of the hypothesis that a certain group of components is not working correctly. These arguments represent the symbolic or qualitative aspect of the diagnosis process. Then they are used to derive a quantitative or numerical aspect represented by the posterior probabilities. Using two new theorems about the relation between Reiter’s notion of conflict and our notion of argument, we prove that our so-called degree of support is nothing but the posterior probability that we are looking for. Furthermore, a model where each component may have more than two different operating modes is discussed and a new algorithm to compute posterior probabilities in this case is presented. Key words: Model-based diagnostics; Assumption-based reasoning; ATMS;

Bayesian Belief Networks (bbns) are a powerful formalism for reasoning under uncertainty but bear some severe limitations: they require a large amount of information before any reasoning process can start, they have limited contradiction handling capabilities, and their ability to provide explanations for their conclusion is still controversial. There exists a class of reasoning systems, called Truth Maintenance Systems (tmss), which are able to deal with partially specified knowledge, to provide well-founded explanation for their conclusions, and to detect and handle contradictions. tmss incorporating measure of uncertainty are called Belief Maintenance Systems (bmss). This paper describes how a bms based on probabilitistic logic can be applied to bbns, thus introducing a new class of bbns, called Ignorant Belief Networks, able to incrementally deal with partially specified conditional dependencies, to provide explanations, and to detect and handle contradictions.

Belief maintenance systems are natural extensions of truth maintenance systems that use probabilities rather than boolean truth-values. This paper introduces a general method for belief maintenance, based on (the propositional fragment of) probabilistic logic, that extends the Boolean Constraint Propagation method used by the logic-based truth maintenance systems. From the concept of probabilistic entailment, we derive a set of constraints on the (probabilistic) truth-values of propositions and we prove their soundness. These constraints are complete with respect to a well-defined set of clauses, and their partial incompleteness is compensated by a gain in computational efficiency. 1 Introduction Truth maintenance systems (tmss) are independent reasoning modules which incrementally maintain the beliefs of a general problem solving system, enabling it to reason with temporary assumptions in the growth of incomplete information. The concept of truth maintenance system is due to Doyle ...

In this paper the classical propositional assumption-based model is extended to incorporate probabilities for the assumptions. Then the whole model is placed into the framework of the Dempster-Shafer theory of evidence. Laskey, Lehner [1] and Provan [2] have already proposed a similar point of view but these papers do not emphasize the mathematical foundations of the probabilistic assumptionbased reasoning paradigm. These foundations are thoroughly exposed in the rst part of this paper. Then we address the computational problems related to the assumption-based model. The idea is to translate evidence theory problems into propositional logic problems and then use the powerful techniques of logic to solve them. In particular, advanced consequence nding algorithms developed by Inoue [3] and Siegel [4] will be used. These logic-based techniques can be considered as alternatives to the classical method of local propagation in Markov trees. Finally, we switch back from logic to the theory of evidence in order to compute degrees of support of hypotheses. We show that some recently proposed methods for computing simple disjunctive normal forms can be used to compute these degrees of support.

This paper presents a simple framework for Hornclause abduction, with probabilities associated with hypotheses. It is shown how this representation can represent any probabilistic knowledge representable in a Bayesian belief network. The main contributions are in finding a relationship between logical and probabilistic notions of evidential reasoning. This can be used as a basis for a new way to implement Bayesian Networks that allows for approximations to the value of the posterior probabilities, and also points to a way that Bayesian networks can be extended beyond a propositional language. 1

Influence Diagrams (ids) are a graphic formalism able to provide a compact representation of decision problems. ids are based on the axioms of probability and decision theory, and they define a normative framework to model decision making. Unfortunately, ids require a large amount of information that is not always available to the decision maker. This paper introduces a new class of ids, called Ignorant Influence Diagrams (iids), able to reason on the basis of incomplete information and to improve the accuracy of their decisions as a monotonically increasing function of the available information. iids represent a net gain with respect to the traditional ids, since they are able to explicitly represent lack of information, without loosing any capability of traditional ids when the required information is available. Furthermore, iids provide a new method to assess the reliability of the decisions by replacing the traditional sensitivity analysis with a single analytical measure.