This long-awaited work by prominent Harvard psychologist Stephen Kosslyn integrates a twenty-year research program on the nature of high-level vision and mental ...

"This is an important new Cummins work.

We advance a theoretical framework which combines recent insights of research in logic, psychology, and formal semantics, on the nature of diagrammatic representation and reasoning. In particular, we wish to explain the varied efficacy of reasoning and representing with diagrams. In general we consider diagrammatic representations to be restricted in expressive power, and we wish to explain efficacy of reasoning with diagrams via the semantical and computational properties of such restricted `languages'. Connecting these foundational insights (from semantics and complexity theory) (...) to the psychology of reasoning with diagrams requires us to develop the notion of the {\it availability} (to an agent) of {\it constraints} operating within representation systems, as a consequence of their direct semantic interpretation. Thus we offer a number of fundamental definitions as well as a research programme which aligns current efforts in the logical and psychological analysis of diagrammatic representation systems. (shrink)

In Volume 33:1 of the Notre Dame Journal of Formal Logic, a system for diagramming syllogistic inferences using straight line segments is presented by Englebretsen. In light of recent research on the representational power of diagrammatic representation systems by the authors, we point out some problems with the proposal, and indeed, with any proposal for representing logically possible situations diagrammatically. We shall first outline the proposed linear diagrammatic system of Englebretsen, and then show by means of counterexamples that it is (...) inadequate as a representation scheme for general logical inferences (the task for which the system is intended). We also show that modifications to the system fail to remedy the problems. The considerations we present are not limited to the particular proposal of Englebretsen; we thus draw a more general moral about the use of spatial relations in representation systems. (shrink)

We define a "representation" as an external object with which we denote another object and present information about it to ourselves or others. All the following objects count as representations in our sense: a set of Japanese declarative sentences describing Mount Fuji, a time table of the Boston subway system, a geometry diagram used to demonstrate the Pythagorean theorem, a state map of the United States, a relief map of a Rocky terrain, a ball-and-stick model of a molecular, and a (...) scale model of the Rockefeller center. ;The dissertation studies how different modes of presenting information exhibit different degrees and kinds of efficacy as an aid for human reasoning. The main hypothesis, which we dub the "Constraint Hypothesis," is that the variance in inferential potentials of different modes of representation is largely attributable to particular ways in which structural constraints on representations match and mismatch with constraints on their targets. The hypothesis is intended to provide a definite perspective for the general study of information representation, which is gradually taking the shape of an independent branch of science. ;As the basis for our analysis, we adopt the mathematical framework of the "qualitative information theory" being developed by Dretske, Barwise, Perry, and Seligman. We analyze several key properties that account for the efficacy of particular modes of representation, including the capacity of providing "free rides" in inference, the property of being over-specific in representing information, and the property of being self-consistent in information content. We also propose an analysis of the conceptual boundary between the "linguistic" modes and the "graphical" modes of representation, and explain some of the important differences in their cognitive potentials. All of these analyses crucially refer to structural constraints on representations and their match and mismatch with constraints on the targets, and hence lend piecemeal yet sturdy supports to our main hypothesis. (shrink)