This paper presents a simple framework for Horn clause 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.
Abduction is an important inference process underlying much of human intelligent activities, including text understanding, plan recognition, disease diagnosis, and physical device diagnosis. In this paper, we describe some problems encountered using abduction to understand text, and present some solutions to overcome these problems. The solutions we propose center around the use of a different criterion, called explanatory coherence, as the primary measure to evaluate the quality of an explanation. In addition, explanatory coherence plays an important role in the construction of explanations, both in determining the appropriate level of specificity of a preferred explanation, and in guiding the heuristic search to efficiently compute explanations of sufficiently high quality.
Within diagnostic reasoning there have been a number of proposed definitions of a diagnosis, and thus of the most likely diagnosis, including most probable posterior hypothesis, most probable interpretation, most probable covering hypothesis, etc. Most of these approaches assume that the most likely diagnosis must be computed, and that a definition of what should be computed can be made a priori, independent of what the diagnosis is used for. We argue that the diagnostic problem, as currently posed, is incomplete: it does not consider how the diagnosis is to be used, or the utility associated with the treatment of the abnormalities. In this paper we analyze several well-known definitions of diagnosis, showing that the different definitions of the most likely diagnosis have different qualitative meanings, even given the same input data. We argue that the most appropriate definition of (optimal) diagnosis needs to take into account the utility of outcomes and what the diagnosis is used for.