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Probability theory versus procedural pessimism
Author(s) -
Morgan Charles G.
Publication year - 1988
Publication title -
computational intelligence
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.353
H-Index - 52
eISSN - 1467-8640
pISSN - 0824-7935
DOI - 10.1111/j.1467-8640.1988.tb00105.x
Subject(s) - pessimism , citation , psychology , computer science , library science , epistemology , philosophy
In response to the procedural pessimism of McDermott (1987) concerning the future course of research in AI, Cheeseman (1988) has made a number of claims concerning the efficacy of Bayesian inference. While I obviously have a sympathy for his reliance on probability theory, there are a number of very serious points on which I would disagree. Like Cheeseman, I believe that probability theory provides a much broader and much more powerful approach to problems in AI than any of the approaches which McDermott criticizes or advocates. However, I believe that Cheeseman’s account is too imprecise to allow a reasonable evaluation of the efficacy of a general probabilistic approach, but at the same time his account is too narrow to do justice to the full range of probabilistic techniques. Further, Cheeseman attempts to use probability theory to dismiss in a rather facile way a number of long-standing philosophical problems; I believe his attempts fail rather badly. Cheeseman is to be commended for reminding AI researchers of the great tool of probability theory. I would not want the very good points of Cheeseman’s advocacy to be lightly dismissed because of a few superficial infelicities in his account. Thus my comments should be read as an attempt to support the general point of view advocated by Cheeseman rather than as an attack upon it. One of the most serious problems with Cheeseman’s discussion is that he fails to make it very clear just what sort of “probability theory” he is advocating. Classical probability theory is usually formulated as a set of restrictions concerning mathematical functions (the probabilify functions) whose domain is a a-field of sets. Alternatively, there are several wellknown ways of formulating probability theory in terms of mathematical functions whose domain is either the set of expressions from a classical propositional language (e.g., Carnap 1950) or the set of ordered pairs of such expressions (e.g., Popper 1965). Only recently has probability theory been formally extended to include languages with quantifiers (Galfmann 1964) and identity (Seager 1983). Cheeseman offhandedly mixes free variables, quantifiers, probability functions, and the conditional of conditional probability theory to construct very formal looking expressions such as the following: