On Independence and Compound and Iterated Conditionals

Understanding the logic of uncertain conditionals is a key problem in the new paradigm psychology of reasoning and related fields. We investigate conjunctions of conditionals, iterated conditionals, and independence within the theory of logical operations on conditionals, where compound conditionals are suitably defined as conditional random quantities. We show how conjunctions of conditionals and conditionals which feature conditionals in the antecedent and the consequent can be rationally interpreted. In particular, we study the behavior of such objects under different logical constraints, by also considering a kind of "independence" property. Unlike alternative approaches, in our framework we avoid counterintuitive consequences, which is necessary for understanding, or improving, human and artificial rationality in general.