The aim of this paper is to argue that models in cognitivescience based on probabilistic computation should not be re-stricted to those procedures that almost surely (with probabil-ity 1) terminate. There are several reasons to consider non-terminating procedures as candidate components of cognitivemodels. One theoretical reason is that there is a perfect cor-respondence between the enumerable semi-measures and allprobabilistic programs, as we demonstrate here (generalizinga better-known fact about computable measures and almost-surely halting programs). One practical reason is that the linebetween almost sure termination and non-termination is elu-sive, as well as arbitrary. We argue that this matters not onlyfor theorists, but also potentially for a learner faced with thetask of inducing programs from experience.

We offer an account of the role of normality—both statisti-cal and prescriptive—in judgments of actual causation. Us-ing only standard tools from the literature on causal cognition,we argue that the phenomenon can be explained simply on theassumption that people stochastically sample (counterfactual)scenarios in a way that reflects normality. We show that a for-malization of this idea, giving rise to a novel measure of causalstrength, can account for some of the most puzzling qualitativepatterns uncovered in recent experimental work

We prove that the generalized cancellation axiom for incomplete comparative probability relations introduced by Ríos Insua (Theory Decis 33:83–100, 1992) and Alon and Lehrer (J Econ Theory 151:476–492, 2014) is stronger than the standard cancellation axiom for complete comparative probability relations introduced by Scott (J Math Psychol 1:233–247, 1964), relative to their other axioms for comparative probability in both the finite and infinite cases. This result has been suggested but not proved in the previous literature.