Explanatory diagnoses and their characterization by circumscription

Abstract

Making a diagnosis amounts to determining what is the state of each component in a given system on the basis of a set of observations from the behaviour of that system. In the “model-based” approach to diagnosis, a diagnosis relies on a (possibly incomplete) description of the expected behaviour of the system. A diagnosis thus consists of the state of the components of the system and has to be consistent with the description (i.e. the model) of the system and the observations that are made. Yet, it is not enough, and additional criteria are needed to select some diagnoses that are more likely to coincide with the true state of the system. The criteria which are most often quoted in the literature are minimality, parsimony, exoneration, explainability. Non-monotonic logics are well suited to express such preferences formally. Indeed, Reiter shows how the minimality criterion can be formalized in default logic; Console, Dupré and Torasso employ predicate completion to model an abductive approach to diagnosis; Raiman resorts to circumscription as a means to exonerate the components exhibiting a normal behaviour. In this paper, we focus on an abduction-based explainability approach to diagnosis, through a formalization in terms of circumscription. The approach that we develop here deals with deductive-abductive diagnoses which explain the observations “as far as possible”. For this reason we call themexplanatory diagnoses. After an introductory section, we first define explanatory diagnoses precisely. Next, we show how circumscription can be used to give a formal characterization of explanatory diagnoses and illustrate it with an example. We stress that, with this approach, no completeness condition is imposed on the description of the system which can consist of fault models and/or models of correct behaviour.