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Logic Journal of IGPL 2007 15(5-6):401-420; doi:10.1093/jigpal/jzm032
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

The Rules of Logic Composition for the Bayesian Epistemic e-Values

Wagner Borges

CCH, Mackenzie Presbiterian University. E-mail: wborges{at}mackenzie.com.br

Julio Michael Stern

IME, University of São Paulo, Brazil. E-mail: jstern{at}ime.usp.br


  Abstract

In this paper, the relationship between the e-value of a complex hypothesis, H, and those of its constituent elementary hypotheses, Hj, j = 1... k, is analyzed, in the independent setup. The e-value of a hypothesis H, ev(H), is a Bayesian epistemic, credibility or truth value defined under the Full Bayesian Significance Testing (FBST) mathematical apparatus. The questions addressed concern the important issue of how the truth value of H, and the truth function of the corresponding FBST structure M, relate to the truth values of its elementary constituents, Hj, and to the truth functions of their corresponding FBST structures Mj, respectively.

Key Words: Bayesian models • Belief Calculi • Complex hypotheses • Compositionality • Convolution • Epistemic values • Possibilistic and Probabilistic reasoning • Significance tests • Truth functions.

Received for publication 21 June 2006.
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