A Cognitive Theory of Graphical and Linguistic Reasoning: Logic and Implementation

We discuss external and internal graphical and linguistic representational systems. We argue that a cognitive theory of peoples' reasoning performance must account for (a) the logical equivalence of inferences expressed in graphical and linguistic form; and (b) the implementational di erences that a ect facility of inference. Our theory proposes that graphical representations limit abstraction and thereby aid processibility. We discuss the ideas of speci city and abstraction, and their cognitive relevance. Empirical support comes from tasks (i) involving and (ii) not involving the manipulation of external graphics. For (i), we take Euler's Circles, provide a novel computational reconstruction, show how it captures abstractions, and contrast it with earlier construals, and with Mental Models' representations. We demonstrate equivalence of the graphical Euler system, and the nongraphical Mental Models system. For (ii), we discuss text comprehension, and the mental performance of syllogisms. By positing an internal system with the same speci city as Euler's Circles we cover the Mental Models data, and generate new empirical predictions. Finally, we consider how the architecture of working memory explains why such speci c representations are relatively easy to store. Acknowledgements The support of the Economic and Social Research Council for the Human Communication Research Centre is gratefully acknowledged. Our initial thinking on the topics discussed here was greatly in uenced by the work of John Etchemendy and Jon Barwise. Our research progressed through helpful discussions with colleagues in the Inference Working Group of the hcrc, and it has bene tted from the suggestions of audiences at meetings in Kinloch Rannoch, Edinburgh, and Stanford, and from the constructive advice of our reviewers. Continuation of the work has been supported by three grants: `signal', Special Project Grant G9018050, from the Joint Councils Initiative in Cognitive Science and hci; Collaborative Research Grant 910954, from nato; and `grace', Basic Research Action P6296, from the cec esprit Programme.