On the Problem of Prediction

Weconsiderpredictionsprovidedby Inductive-Statistical (I-S) inference. It was noted by Hempel that I-S inference is statistically ambiguous. To avoid this problem Hempel introduced the Requirement of Maximal Specificity (RMS). We define the formal notion of RMS in terms of probabilistic logic, and maximally specific rules (MS-rules), i. e. rules satisfying RMS. Then we prove that any set of MS-rules draws no contradictions in I-S inference, therefore predictions based on MS-rules avoid statistical ambiguity. I-S inference may be used for predictions in knowledge bases or expert systems. In the last we need to calculate the probabilistic estimations for predictions. Though one may use existing probabilistic logics or “quantitative deductions” to obtain these estimations, instead we define a semantic probabilistic inference and prove that it approximates logical inference in some sense. We also developed a program system ‘Discovery’ which realizes this inference and was successfully applied to the solution of many practical tasks.