Two experiments are reported that investigated the influence of linear spatial organization on transitive inference performance. RewardAio-reward relations between overlapping pairs of elements were presented in a context of linear spatial order or random spatial order. Participants in the linear arrangement condition showed evidence for visual reasoning: They systematically mapped spatial relations to conceptual relation and used the spatial relations to make inferences on a reasoning task in a new spatial context. We suggest that linear ordering may be a "good figure", by constituting a parsinuxiious representation for the integration of premises, as well as for the inferencing process. The late emergence of transitive inference in children may be the result of limited cognitive capacity, which -- unless an extemal spatial array is available -- constrains the construction of an internal spatial array.

Three experiments are reported that examine the impact of people's goals and conceptual understanding on graph interpretation, in order to determine how people use graphical representations to evaluate functional dependencies between continuous variables. Subjects made inferences about the relative rate of two continuous linear variables (altitude and temperature). We varied the assignments of variables to axes, the perceived cause effect relation between the variables, and the causal status of the variable being queried. The most striking finding was that accuracy was greater when the Slope-Mapping Constraint was honored, which requires that the variable being queried - usually the effect or dependent variable, but potentially the cause instead — is assigned to the vertical axis, so that steeper lines map to faster changes in the queried variable. This constraint dominates when it conflicts with others, such as preserving the low-level mapping of altitude onto the vertical axis. Our findings emphasize the basic conclusion that graphs are not pictures, but rather symbolic systems for representing higher-order relations. We propose that graphs provide external instantiations of intermediate mental representations, which enable people to move from pictorial representations to abstractions through the use of natural mappings between perceptual properties and conceptual relations.