Bayesian Reasoning, Conditional Asymmetries and Mental Mechanisms
|Mike Oaksford and Nick Chater
|Department of Psychology, Birkbeck and Department of Psychology, UCL , UK
In this talk we look at two aspects of treating conditional reasoning as Bayesian inference. First, we propose a resolution of the notorious asymmetry between endorsements of the logically valid conditional inferences, modus ponens (MP: if p then q, p, therefore q) and modus tollens (MT: if p then q, ¬q, therefore ¬p). The probabilistic approach treats conditional inference as Bayesian conditionalisation, which assumes rigidity, i.e., the prior and posterior conditional probabilities are the same, i.e., P 0(q|p) = P 1(q|p). Recent work in the normative literature (Sobel, 2005; Wagner, 2004), suggests that MT frequently violates the rigidity condition. We show how such violations may explain the MPMT asymmetry. Second, we look at some of the implications for conditional inference by a taking a Bayesian network approach. This approach suggests that people build a mental mechanism from conditional premises. We suggest that providing people directly with the mechanism should make inferences particularly easy even where the inference is normally complex.