On Nonmonotonic Conditionals that Correspond to Conditional Probabilities Above Thresholds

SPEAKER

James Hawthorne

ABSTRACT

I’ll describe a range of systems (or types) of nonmonotonic conditionals, where each system is associated with conditional probabilities above a specific threshold. That is, for each threshold level t, 0 < t < 1, associate with each conditional probability function P a conditional (P,t)|~ such that (by definition) ‘C (P,t)|~ B’ holds just in case P[B | C] > t (or else P[C] = 0). Call these the t-level-conditionals. For each threshold level t, I'll present probabilistically sound rules for the t-level-conditionals, rules that hold for every conditional probability function at specific threshold t. I'll compare these rules to various well-known rules for nonmonotonic conditionals -- e.g. rules for the preferential consequence relations, P, and for the rational consequence relations, R. The issue of what sets of rules for the various systems of t-level-conditionals are probabilistically complete is still unresolved.