The psychology of inferring conditionals from disjunctions: A probabilistic study

There is a new probabilistic paradigm in the psychology of reasoning that is, in part, based on results showing that people judge the probability of the natural language conditional, if $A$then $B$, $P\left(ifAthenB\right)$, to be the conditional probability, $P(B\mid A)$. We apply this new approach to the study of a very common inference form in ordinary reasoning: inferring the conditional if not-$A$then $B$ from the disjunction $A$ or $B$. We show how this inference can be strong, with $P$(if not-$A$then $B$) “close to” $P\left(AorB\right)$, when $A$ or $B$ is non-constructively justified. When $A$ or $B$ is constructively justified, the inference can be very weak. We also define suitable measures of “closeness” and “constructivity”, by providing a probabilistic analysis of these notions.