** 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.