The Logic and Metaphysics Workshop will meet on November 17th from 2:00-4:00 in-person at the Graduate Center (Room 8203) for a talk by Giuliano Rosella (Turin).

Title: The probability and logical representation of suppositional conditionals

Abstract: We present new results concerning the probability and logical representation of suppositional conditionals—conditionals whose truth depends on the consequent holding in appropriately selected worlds where the antecedent is true (e.g., Stalnaker conditionals and Lewis counterfactuals). We show that the probability of such conditionals can be precisely captured by an updated Belief function within the framework of Dempster–Shafer Theory of Evidence (DST). A key consequence of this result is that the probability of suppositional conditionals is bounded by standard imaging-updated probabilities. This finding generalizes Lewis’s earlier characterization of Stalnaker conditionals in terms of Imaging and addresses an open problem concerning the characterization of the probability of counterfactuals. Our approach formally bridges DST with conditional logic and employs a logical reconstruction of Lewis’s counterfactuals as a form of necessitated Stalnaker conditionals, leveraging a notable correspondence between modal operators and Belief functions.

Note: This is joint work with Tommaso Flaminio (IIIA-CSIC, Barcelona), Lluis Godo (IIIA-CSIC, Barcelona), and Jan Sprenger (Turin).