Abstract
One of reasons for arising the statistical ambiguity is using in the course of reasoning laws which have probabilistic, but not logical justification. Carl Hempel supposed that one can avoid the statistical ambiguity if we will use in the probabilistic reasoning maximal specific probabilistic laws. In the present work we deal with laws of the form \(\varphi \Rightarrow \psi \), where \(\varphi \) and \(\psi \) are arbitrary propositional formulas. Given a probability on the set of formulas we define the notion of a maximal specific probabilistic law. Further, we define a prediction operator as an inference with the help of maximal specific laws and prove that applying the prediction operator to some consistent set of formulas we obtain a consistent set of consequences.
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Notes
- 1.
In [10], rules are of the form \(\alpha _1\wedge \ldots \wedge \alpha _n\Rightarrow \beta \), where \(\alpha _1\), ...,\(\alpha _n\), \(\beta \) are literals, i.e., atoms or negations of atoms.
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Acknowledgements
The first of the authors (Sects. 1 and 2, also a coauthor of Theorem 1) was supported by the Russian Science Foundation (project # 17-11-01176). Both authors are grateful to the anonymous referees for their helpful reports and to participants of ESCIM’17 for the interesting discussion.
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Vityaev, E., Odintsov, S. (2019). How to Predict Consistently?. In: Cornejo, M., Kóczy, L., Medina, J., De Barros Ruano, A. (eds) Trends in Mathematics and Computational Intelligence. Studies in Computational Intelligence, vol 796. Springer, Cham. https://doi.org/10.1007/978-3-030-00485-9_4
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DOI: https://doi.org/10.1007/978-3-030-00485-9_4
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