Evidential Probability

We characterize and illustrate evidential probability--an interval-valued measure of uncertainty that applies to sentences. Evidential probability is also taken to be relative to a body of knowledge or a database representing the data on which judgments of uncertainty are to be made. Every statement is equivalent to some statement to which statistics in the database are relevant. The problem is to find the correct statement; this is the problem of finding the correct reference class for a statement. A set of rules for determining the correct reference class is offered.

[1]  H. Jeffreys A Treatise on Probability , 1922, Nature.

[2]  J. Keynes A Treatise on Probability. , 1923 .

[3]  B. D. Finetti La prévision : ses lois logiques, ses sources subjectives , 1937 .

[4]  R. Jeffrey Valuation and Acceptance of Scientific Hypotheses , 1956, Philosophy of Science.

[5]  Howard Raiffa,et al.  Applied Statistical Decision Theory. , 1961 .

[6]  I. N. Moraes,et al.  Introduction to scientific research , 1966 .

[7]  I. Lakatos,et al.  The problem of inductive logic , 1970 .

[8]  Henry E. Kyburg,et al.  Probability and the logic of rational belief , 1970 .

[9]  B. Sauphanor The logical foundations of statistical inference , 1974 .

[10]  L. Dubins Finitely Additive Conditional Probabilities, Conglomerability and Disintegrations , 1975 .

[11]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[12]  Edwin T. Jaynes,et al.  Inference, Method, and Decision: Towards a Bayesian Philosophy of Science. , 1979 .

[13]  Isaac Levi,et al.  The Enterprise Of Knowledge , 1980 .

[14]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[15]  John McCarthy,et al.  SOME PHILOSOPHICAL PROBLEMS FROM THE STANDPOINT OF ARTI CIAL INTELLIGENCE , 1987 .

[16]  William Harper,et al.  Kyburg on Direct Inference , 1981 .

[17]  Henry E. Kyburg,,et al.  The Reference Class , 1983, Philosophy of Science.

[18]  Ronald Prescott Loui Computing reference classes , 1986, UAI.

[19]  D. G. Rees,et al.  Foundations of Statistics , 1989 .

[20]  J. Wiseman A History of the British Pig , 1987 .

[21]  Peter C. Cheeseman,et al.  An inquiry into computer understanding , 1988, Comput. Intell..

[22]  H. Kyburg Uncertainty and the Conditioning of Beliefs , 1990 .

[23]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

[24]  P. Walley Statistical Reasoning with Imprecise Probabilities , 1990 .

[25]  Z. Pawlak Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[26]  Henry E. Kyburg Science and Reason , 1990 .