An Information-Theoretic Characterization of Abstraction in Diagnosis and Hypothesis Selection

Abstract

The task of model-based diagnosis is to find a suitable assignment to the behavior modes of components (and/or transition variables) in a system given some observations made on it. A complete diagnosis-candidate is an assignment of behavior modes to all the components in the system and a partial diagnosis-candidate is an assignment of behavior modes to only a subset of them. Corresponding to different characterizations of complete diagnosis-candidates (Bayesian model selection, consistency-based, model counting etc.), partial diagnosis-candidates play different roles. In the Bayesian model selection framework for example, they signify marginal probabilities, while in the consistency-based framework they are used to “represent” complete diagnosis-candidates. In this paper, we provide an information-theoretic characterization of diagnosis-candidates in a more general form — viz. “disjunction of partial assignments”. This approach is motivated by attempting to bridge the gap between previous formalizations and to address the problems associated with them. We argue that the task of diagnosis actually consists of two separate problems, the second of which occurs more generally in hypothesis selection — (1) to characterize the space of complete or partial assignments (like in a posterior probability distribution), and (2) to abstract and approximate the information content of such a space into a representational form that can support tractable answering of diagnosis-queries and decision-making.