Results 1 
3 of
3
Spatial Logic and the Complexity of Diagrammatic Reasoning
 MACHINE GRAPHICS AND VISION
, 1997
"... Researchers have sought to explain the observed "efficacy" of diagrammatic reasoning (DR) via the notions of "limited abstraction" and inexpressivity [17, 20]. We argue that application of the concepts of computational complexity to systems of diagrammatic representation is neces ..."
Abstract

Cited by 22 (2 self)
 Add to MetaCart
(Show Context)
Researchers have sought to explain the observed "efficacy" of diagrammatic reasoning (DR) via the notions of "limited abstraction" and inexpressivity [17, 20]. We argue that application of the concepts of computational complexity to systems of diagrammatic representation is necessary for the evaluation of precise claims about their efficacy. We show here how to give such an analysis. Centrally, we claim that recent formal analyses of diagrammatic representations (DRs) (eg: [14]) fail to account for the ways in which they employ spatial relations in their representational work. This focus raises some problems for the expressive power of graphical systems, related to the topological and geometrical constraints of the medium. A further idea is that some diagrammatic reasoning may be analysed as a variety of topological inference [15]. In particular, we show how reasoning in some diagrammatic systems is of polynomial complexity, while reasoning in others is NP hard. A simple case study i...
Studies on the Uses and Usefulness of Diagrams
 UNIVERSITY OF AMSTERDAM
, 2000
"... ..."
(Show Context)
“Drawing Illusions ” – a case study in the incorrectness of diagrammatic reasoning
, 1999
"... In “Something to Reckon With ” [6], a system for diagramming syllogistic inferences using straight line segments is presented (see also Englebretsen [5]). In the light of recent research on the representational power of diagrammatic representation systems (Lemon and Pratt [12, 13]) we point out some ..."
Abstract
 Add to MetaCart
(Show Context)
In “Something to Reckon With ” [6], a system for diagramming syllogistic inferences using straight line segments is presented (see also Englebretsen [5]). In the light of recent research on the representational power of diagrammatic representation systems (Lemon and Pratt [12, 13]) 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 [5], 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 proposals of Englebretsen [5, 6]; we thus draw a more general moral about the use of spatial relations in representation systems. 1 1 Diagrammatic representation systems