A Model Counting Characterization of Diagnoses

Given the description of a physical system in one of several forms (a set of constraints, Bayesian network etc.) and a set of observations made, the task of model-based diagnosis is to find a suitable assignment to the modes of behavior of individual components (this notion can also be extended to handle transitions and dynamic systems [Kurien and Nayak, 2000]. Many formalisms have been proposed in the past to characterize diagnoses and systems. These include consistency-based diagnosis, fault models, abduction, combinatorial optimization, Bayesian model selection etc. Different approaches are apparently well suited for different applications and representational forms in which the system description is available. In this paper, we provide a unifying theme behind all these approaches based on the notion of model counting. By doing this, we are able to provide a universal characterization of diagnoses that is independent of the representational form of the system description. We also show how the shortcomings of previous approaches (mostly associated with their inability to reason about different elements of knowledge like probabilities and constraints) are removed in our framework. Finally, we report on the computational tractability of diagnosis-algorithms based on model counting.