Logical Operations Among Conditionals as Conditional Random Quantities

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Giuseppe Sanfilippo Abstract
In the subjectivistic theory, the probability P(E) measure the degree of belief on E being true. The consistency of the probability assessments is guaranteed by a coherence principle. All basic probabilistic properties follow from coherence. A large number of philosophers and psychologists assume valid that the probability of a natural language conditional, P(if H then A), coincides with the conditional subjective probability P(A|H) of the conditional event A|H. Usually, a conditional event is looked at as a three-valued object and compound conditionals have been defined in trivalent logics. We verify that none of these logics satisfies all the basic probabilistic properties valid for unconditional events. Then, we consider an approach to compound conditionals in the setting of conditional random quantities. We verify that all the basic logical and probabilistic properties are preserved and we illustrate applications to the psychology of uncertain reasoning, to connexive logic and to non-monotonic reasoning.

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Giuseppe Sanfilippo

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Students

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