Inductive Inference: An Axiomatic Approach
提出一种公理化方法，研究预测者基于过去案例对事件进行排序的规则，证明在一致性要求下排序可由矩阵数值表示，并解释为理论排序与似然函数一致。
A predictor is asked to rank eventualities according to their plausibility, based on past cases. We assume that she can form a ranking given any memory that consists of repetitions of past cases. Mild consistency requirements on these rankings imply that they have a numerical representation via a matrix assigning numbers to eventualitycase pairs, as follows. A memory is identified with a vector, counting the number of repetitions of each case. Multiplication of the matrix by a memory vector yields a numerical representation of the ordinal plausibility ranking given that memory. Interpreting this result for the ranking of theories or hypotheses, rather than of specific eventualities, it is shown that one may ascribe to the predictor subjective conditional probabilities of cases given theories, such that her rankings of theories agree with their likelihood functions. 1 Introduction It is well known that inductive inference is not logically valid. As David Hume (1748) put it, "... The co...