Boolean algebras of conditionals, probability and logic

Boolean Algebras and Logic

In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone’s representation theorem. Some special classes of Boolean algebras are also concerned with and, in particular, the relations of Boolean algebras to propositional logic and to set theory are studied in more details. We mention here that all what we do for propositional logic can also be extende...

Vagueness, conditionals and probability

This paper explores the interaction of well-motivated (if controversial) principles governing the probability conditionals, with accounts of what it is for a sentence to be indefinite. The conclusion can be played in a variety of ways. It could be regarded as a new reason to be suspicious of the intuitive data about the probability of conditionals; or, holding fixed the data, it could be used t...

The Probability of Conditionals

We report two studies investigating how naïve reasoners evaluate the probability that a conditional assertion is true, and the conditional probability that the consequent of the conditional is true given that the antecedent is true. The mental model theory predicts that individuals should evaluate the probability of a conditional on the basis of the mental models representing the conditional, a...

On possibility and probability measures in finite Boolean algebras

The Logic of Conditionals

The standard use of the propositional calculus ('P.C.') in analyzing the validity of inferences involving conditionals leads to fallacies, and the problem is to determine where P.C. may be 'safely' used. An alternative analysis of criteria of reasonableness of inferences in terms of conditions of justification rather than truth of statements is proposed. It is argued, under certain restrictions...