Bayesian Propositional Logic

Tomasz Jarmużek; Mateusz Klonowski; Jacek Malinowski

doi:10.18778/0138-0680.46.3.4.01

Authors

Tomasz Jarmużek Department of Logic, Nicolaus Copernicus University in Toruń
Mateusz Klonowski
Jacek Malinowski Institute of Philosophy and Sociology, Polish Academy of Sciences

DOI:

https://doi.org/10.18778/0138-0680.46.3.4.01

Keywords:

logical entailment, statistical inference, Bayesian inference, corroboration, confirmation

Abstract

We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈_w where w is a probability function on a Boolean language. A |≈_w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the intersection of |≈_w , for all w, and give some formal properties of it.

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