Uncertain reasoning and uncertain argument, as we have been concerned with them here, are reasoning and argument in which the object is to establish the credibility or acceptability of a conclusion on the basis of an argument from premises that do not entail that conclusion. Other terms for the process are inductive reasoning, scientific reasoning, nonmonotonic reasoning, and probabilistic reasoning. What we seek to characterize is that general form of argument that will lead to conclusions that are worth accepting, but that may, on the basis of new evidence, need to be withdrawn.
What is explicitly excluded from uncertain reasoning, in the sense under discussion, is reasoning from one probability statement to another. Genesereth and Nilsson [Nilsson, 1986; Genesereth & Nilsson, 1987], for example, offer as an example of their “probabilistic logic” the way in which constraints on the probability of Q can be established on the basis of probabilities for P and for P → Q. This is a matter of deduction: as we noted in Chapter Five, it is provable that any function prob satisfying the usual axioms for probability will be such that if prob(P) = r and prob(P → Q) = s then prob(Q) must lie between s + r − 1 (or 0) and s. This deductive relation, though often of interest, is not what we are concerned with here. It has been explored by Suppes and Adams [Suppes, 1966; Adams, 1966] as well as Genesereth and Nilson.
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