Logical foundations of causal inference

This talk has two aims. The first is to show that empirical problems of causal inference are fruitfully construed as problems of logic. The second is to show that the study of causality raises a host of new and distinctive issues for logic. Specifically, we consider extended probabilistic languages suitable for dealing with (not just correlational but) causal claims, formalizing the so-called ‘causal hierarchy’. After considering questions of axiomatization and complexity, we explain how matters of expressive power are closely tied to fundamental causal inference problems. In that connection, we introduce a topological perspective on the topic and prove a new type of expressivity result: a more expressive language collapses into a less expressive language (topologically) almost-nowhere. The topological spaces we study in this work are motivated by statistical learning theory, but the character of the result is totally general.