Search results for "Compound conditional"
showing 2 items of 2 documents
Probabilistic inferences from conjoined to iterated conditionals
2017
Abstract There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, P ( if A then B ) , is the conditional probability of B given A, P ( B | A ) . We identify a conditional which is such that P ( if A then B ) = P ( B | A ) with de Finetti's conditional event, B | A . An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, we illustrate how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds and iterations as cond…
Compound conditionals as random quantities and Boolean algebras
2022
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalised from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued object, with betting-based semantics, and its related approach as random quantity as mainly developed by two of the authors. Compound conditionals have been studied in the literature, but not in full generality. In this paper we provide a natural procedure to explicitly attach conditional random quantities to arbitrary compound conditionals that also allows us to compute their previsions. By studying the properties of these random quantities, we show that, in f…