TY - CHAP

T1 - How to predict consistently?

AU - Vityaev, Evgeni

AU - Odintsov, Sergei

PY - 2019

Y1 - 2019

N2 - 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 φ⇒ ψ, where φ and ψ 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.

AB - 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 φ⇒ ψ, where φ and ψ 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.

KW - Consistency

KW - Maximal specificity

KW - Prediction

KW - Probabilistic inference

UR - http://www.scopus.com/inward/record.url?scp=85054706604&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-00485-9_4

DO - 10.1007/978-3-030-00485-9_4

M3 - Chapter

AN - SCOPUS:85054706604

T3 - Studies in Computational Intelligence

SP - 35

EP - 41

BT - Studies in Computational Intelligence

PB - Springer-Verlag GmbH and Co. KG

ER -