An overview of ordinal and numerical approaches to causal diagnostic problem solving

International audienceDiagnostic problem solving aims at finding out disorders which may have caused observed symptoms of ill-behaviour. It is often called “abductive reasoning”. The pattern which, from the two premises “if disorder is present then symptom is observed” and “symptom is observed”, infers the conclusion “disorder is plausible”, can be viewed as the simplest pattern of abductive reasoning [Peirce, 1940]. This pattern can be contrasted with deductive inference which, from “if disorder is present then symptom is observed” and “disorder is present” infers that “symptom is observed”. Clearly, a key problem in abduction is to provide some status to the abductive conclusion “disorder is plausible” and maybe to assign some degree of plausibility to this disorder, or at least to be able to rank possible causes of an observed state of facts according to their relative plausibilities. The abductive pattern, although considered by many authors (e.g., [Pólya, 19681), has not been given any logical or numerical formalization until recently, if we except the Bayesian model (which requires more information and where we compute the a posteriori probability of disorders on the basis of observations), and some heuristic, numerically quantified attempts (e.g., [Friedman, 1981; Bandler and Kohout, 1984; Hall, 1987])