Robabilistic Semantics ualitative Influences

What’s in an infiuence link? To answer this foundational question, I propose a semantics for qualitative influences: a positively influences b if and only if the posterior distribution for b given o increases with o in the sense of first-order stochastic dominance. By requiring that this condition hold in all contexts, we gain the ability to perform inference across chains of qualitative influences. Under sets of basic desiderata, the proposed definition is necessary as well as sufF~cient for this desirable computational property.