# Didactical note: probabilistic conditionality in a Boolean algebra.

Enric Trillas; Claudi Alsina; Settimo Termini

Mathware and Soft Computing (1996)

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

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topTrillas, 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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