Dynamic inference and everyday conditional reasoning in the new paradigm

Abstract

One of the principal motivations for the new paradigm in reasoning was a reaction to the old (binary truth functional) paradigm's inability to deal with everyday non-monotonic inference. Within the new paradigm the problem of non-monotonicity is recast as the problem of belief revision or dynamic inference; that is, what happens when the probability distribution over which inferences are made changes from Pr0 to Pr1. Non-monotonicity arises when the new distribution, conditional on new information, I, changes the relevant probabilities, so that Pr0(x) ≠ Pr1(x), i.e., Pr0(x) ≠ Pr0(x|I). In this paper we first introduce the general problem of dynamic inference. We then consider the specific problems for dynamic conditional inference, in particular for modus tollens (MT). We then turn to possible reactions to these problems, looking at Oaksford and Chater's (2007) learning approach and causal Bayes nets. We conclude that most of the recent research on the non-monotonic effects observed in casual conditional inference and the suppression effect require a dynamic approach. However, the rational constraints on the transition from Pr0 to Pr1, when Pr0(x) ≠ Pr0(x|I), remain unclear.