Anytime Diagnostic Reasoning using Approximate Boolean Constraint Propagation

In contrast with classical reasoning, where a solution is either correct or incorrect, approximate reasoning tries to compute solutions which are close to the ideal solution, without necessarily being perfect. Such approximate reasoning can be used to exchange solution quality for computation time, known as anytime reasoning. In this paper we study approximate versions of diagnostic reasoning. Traditionally, diagnostic reasoning is characterised in terms of the logical entailment relation. In this paper we study the effects of replacing the logical entailment relation with an approximate version of the entailment relation, in particular an approximate version of Boolean Constraint Propagation (BCP). We characterise the cheapest versions of approximate BCP which allows single components and entire systems to be diagnosed correctly. From these upperbounds surprisingly low values follow which are needed to correctly diagnose many of the typical circuit examples from the literature. A particularly interesting property that we discovered is that the point at which approximate diagnosis coincides with classical diagnosis is entirely determined by the nature of the individual components, and not by either the size or the structural complexity of the overall device.