I’ll describe a range of systems for nonmonotonic conditionals that behave like conditional probabilities above a threshold. The rules that govern each system are probabilistically sound in that each rule holds when the conditionals are interpreted as conditional probabilities above a threshold level specific to that system. The well-known preferential and rational consequence relations turn out to be special cases in which the threshold level is 1. I’ll describe systems that employ weaker rules appropriate to thresholds lower than 1, and (...) compare them to these two standard systems. (shrink)

Rational consequence relations and Popper functions provide logics for reasoning under uncertainty, the former purely qualitative, the latter probabilistic. But few researchers seem to be aware of the close connection between these two logics. I’ll show that Popper functions are probabilistic versions of rational consequence relations. I’ll not assume that the reader is familiar with either logic. I present them, and explicate the relationship between them, from the ground up. I’ll also present alternative axiomatizations for each logic, showing them to (...) depend on weaker axioms than usually recognized. (shrink)

I extend theories of nonmonotonic reasoning to account for reasons allowing free choice. My approach works with a wide variety of approaches to nonmonotonic reasoning and explains the connection between reasons for kinds of action and reasons for actions or subkinds falling under them. I use an Anderson–Kanger reduction of reason statements, identifying key principles in the logic of reasons.