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An overview of ordinal and numerical approaches to causal diagnostic problem solving. (English) Zbl 0971.68149
Gabbay, Dov M. (ed.) et al., Handbook of defeasible reasoning and uncertainty management systems. Vol. 4: Abductive reasoning and learning. Dordrecht: Kluwer Academic Publishers. 231-280 (2000).
Summary: The paper is organized as follows. In Section 2, the most traditional number-crunching approaches to the diagnosis problem are discussed, namely the statistical Bayesian approach and the pattern-directed rule-based inference school. The former is rigorous but involves very restrictive assumptions, and the latter looks user-friendly but is rather ad hoc. An early diagnosis technique by Smets (1978), that generalizes the early Bayesian scheme to belief functions is also described, as well as a conditional method for possibilistic abduction. These approaches basically come down to a classification procedure. Their limitations are discussed. Section 3 presents the most elementary relational approaches as well as basic issues pertaining to the treatment of uncertainty and intensity of symptoms and disorders in diagnosis problems. First, the parsimonious covering theory developed by J. A. Reggia, D. S. Nau and P. Y. Wang [Inf. Sci. 37, 227-256 (1985; Zbl 0583.68046)], is presented as the underlying framework, and its extension to the handling of incomplete causal knowledge.
A distinction is made between fuzzy relational methods on the one hand, first proposed by E. Sanchez [Fuzzy Sets Syst. 2, 75-86 (1979; Zbl 0399.03040)] and Y. Tsukamoto and T. Terano [Failure diagnosis by using fuzzy logic. In Proc. of the IEEE Conf. on Decision and Control, New Orleans, Louisiana, 1390-1395 (1977)], which are appropriate when the intensity of the disorders and of the symptoms are a matter of degree; and on the other hand methods where the presence of disorders or symptoms is not a matter of intensity but may be pervaded with uncertainty. In this second case, disorders and symptoms are either present or absent, but we are unsure about the presence of a symptom when a disorder is present or about the observation of a symptom. The lack of confidence due to incomplete information can be either graded in terms of certainty and mere possibility, or in terms of probability. Section 4 presents the probabilistic extension of the parsimonious covering approach that can capture prior information and introduces the notion of causation events. The Bayesian network approach is then briefly presented, its merits and its limitations are discussed. Preliminary investigations on a possibility theory-based version of the conditional approach are reported. Section 5 discusses the links between the relational and the logical approaches and briefly reports on the use of possibilistic logic, belief functions and ATMS for abductive reasoning purposes.
Several sections or subsections of this paper are revised and expanded versions of previous works by the authors, Dubois and Prade.
For the entire collection see [Zbl 0953.00020].

68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)