The Logic of Prediction

We consider the predictions provided by the inductive theories. For these theories predictions are performed by the Inductive Statistical (I-S) inferences. It was noted by Hempel that the I-S inference is statistically ambiguous. To avoid this ambiguity we need to use the rules that satisfy the Requirement of Maximum Specificity (RMS). The formal definition of the RMS wasn’t given by Hempel. We define the notions of law and probabilistic law, and also the sets of all laws L, and probabilistic laws LP. We prove that the set SPL of Strongest Probabilistic Laws (with the maximum values of conditional probability) contains the set L, so we have L ⊂ SPL ⊂ LP. We prove that the maximum specific rules the strongest SPL rules for prediction of atoms satisfy the RMS condition. The maximum specific rules may be used in I-S inference. We prove that the set MSR of all Maximum Specific Rules is consistent and the I-S inferences based on MSR rules avoid the problem of statistical ambiguity. We define Semantic Probabilistic Inferences (SP-inference) that infer the sets L,LP, SPL, MSR. Finally, we mention the program system ‘Discovery’, which realize the SP-inference and discovers the sets L,LP, SPL, MSR. This system was applied for solution of many practical tasks (see website www.math.nsc.ru/AP/ScientificDiscovery).