Relevance theory (Sperber & Wilson, 1995) suggests that people expend cognitive effort when processing information in proportion to the cognitive effects to be gained from doing so. This theory has been used to explain how people apply their knowledge appropriately when evaluating category-based inductive arguments (Medin, Coley, Storms, & Hayes, 2003). In such arguments, people are told that a property is true of premise categories and are asked to evaluate the likelihood that it is also true of conclusion categories. According to the relevance framework, reasoners generate hypotheses about the relevant relation between the categories in the argument. We reasoned that premises inconsistent with early hypotheses about the relevant relation would have greater effects than consistent premises. We designed three premise garden-path arguments where the same 3rd premise was either consistent or inconsistent with likely hypotheses about the relevant relation. In Experiments 1 and 2, we showed that effort expended processing consistent premises (measured via reading times) was significantly less than effort expended on inconsistent premises. In Experiment 2 and 3, we demonstrated a direct relation between cognitive effect and cognitive effort. For garden-path arguments, belief change given inconsistent 3rd premises was significantly correlated with Premise 3 (Experiment 3) and conclusion (Experiments 2 and 3) reading times. For consistent arguments, the correlation between belief change and reading times did not approach significance. These results support the relevance framework for induction but are difficult to accommodate under other approaches.