The Relevance Framework for Category-Based Induction: Evidence From Garden-Path Arguments

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.

An Experimental Investigation into the Pressure Drop for Turbulent 90o Elbow Bends

The prediction of the pressure drop for turbulent single-phase fluid flow around sharp 90° bends is difficult owing to the complexity of the flow arising from frictional and separation effects. Several empirical equations exist, which accurately predict the pressure loss due to frictional effects. More recently, Crawford et al. [1] proposed an equation for the prediction of pressure loss due to separation of the flow. This work proposes a new composite equation for the prediction of pressure drop due to separation of the flow, which incorporates bends with ratio R/r <2. A new composite equation is proposed to predict pressure losses over the Reynolds number range 4 x 103-3 x 105. The predictions from the new equation are within a range of -4 to +6 per cent of existing experimental data.