This note deals with two logical topics and concerns Boolean Algebras from an elementary point of view. First we consider the class of operations on a Boolean Algebra that can be used for modelling If-then propositions. These operations, or Conditionals, are characterized under the hypothesis that they only obey to the Modus Ponens-Inequality, and it is shown that only six of them are boolean two-place functions. Is the Conditional Probability the Probability of a Conditional? This problem will be only considered, with the Material Conditional Operation, on a Boolean Algebra endowed with a finite probability and in three different cases: with the Internal-Conditional Probability, with the External-Conditional Probability and with both the External-Conditional and the a priori probabilities. It is shown when and how the problem can have some solution.
@article{urn:eudml:doc:39068,
title = {Didactical note: probabilistic conditionality in a Boolean algebra.},
journal = {Mathware and Soft Computing},
volume = {3},
year = {1996},
pages = {149-157},
zbl = {0862.03038},
mrnumber = {MR1414262},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39068}
}
Trillas, Enric; Alsina, Claudi; Termini, Settimo. Didactical note: probabilistic conditionality in a Boolean algebra.. Mathware and Soft Computing, Tome 3 (1996) pp. 149-157. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39068/