Geodesic
Bayesian Propositional Logic
Bulletin of the Section of Logic, Tome 46 (2017) no. 3-4.

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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.
Keywords: logical entailment, statistical inference, Bayesian inference, corroboration, confirmation 
@article{BSL_2017_46_3-4_a2,
     author = {Jarmu\.zek, Tomasz and Klonowski, Mateusz and Malinowski, Jacek},
     title = {Bayesian {Propositional} {Logic}},
     journal = {Bulletin of the Section of Logic},
     publisher = {mathdoc},
     volume = {46},
     number = {3-4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BSL_2017_46_3-4_a2/}
}
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Jarmużek, Tomasz; Klonowski, Mateusz; Malinowski, Jacek. Bayesian Propositional Logic. Bulletin of the Section of Logic, Tome 46 (2017) no. 3-4. http://geodesic.mathdoc.fr/item/BSL_2017_46_3-4_a2/