Didactical note: probabilistic conditionality in a Boolean algebra.

• Volume: 3, Issue: 1-2, page 149-157
• ISSN: 1134-5632

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Abstract

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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.

How to cite

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Trillas, Enric, Alsina, Claudi, and Termini, Settimo. "Didactical note: probabilistic conditionality in a Boolean algebra.." Mathware and Soft Computing 3.1-2 (1996): 149-157. <http://eudml.org/doc/39068>.

@article{Trillas1996,
abstract = {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.},
author = {Trillas, Enric, Alsina, Claudi, Termini, Settimo},
journal = {Mathware and Soft Computing},
keywords = {Lógica difusa; Probabilidad condicionada; Información condicional; Algebras de Boole; Boolean algebra; probabilities},
language = {eng},
number = {1-2},
pages = {149-157},
title = {Didactical note: probabilistic conditionality in a Boolean algebra.},
url = {http://eudml.org/doc/39068},
volume = {3},
year = {1996},
}

TY - JOUR
AU - Trillas, Enric
AU - Alsina, Claudi
AU - Termini, Settimo
TI - Didactical note: probabilistic conditionality in a Boolean algebra.
JO - Mathware and Soft Computing
PY - 1996
VL - 3
IS - 1-2
SP - 149
EP - 157
AB - 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.
LA - eng
KW - Lógica difusa; Probabilidad condicionada; Información condicional; Algebras de Boole; Boolean algebra; probabilities
UR - http://eudml.org/doc/39068
ER -

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