An Architecture for Problem Solving with Diagrams

When is a bunch of marks on paper a diagram? Diagrams as homomorphic representations

“…If the computer program can be analyzed as having a module that functionally serves as a model of 2-D space sufficient to answer relevant questions about spatial properties and relations of specific spatial instances, and the logic of the overall reasoning program uses this m odule exactly the same way it would use if the representation were external, then for certain functional purposes, it makes sense to treat is as a diagrammatic representation. We discuss this issue in some detail in Chandrasekaran et al (2004) in the context of the design and implementation of a diagrammatic problem solver.…”

“…Diagrams in practice have as essential non-homomorphic elements, e.g., hashing of sub-regions in Venn diagrams, and alpha-numeric characters as labels. Understanding diagrammatic representations requires viewing the process of diagrammatic reasoning as a multi-step, multi-modal, goal-oriented activity in which some of the steps involve extracting information homomorphically, while other steps either extract information by other means (Chandrasekaran et al 2004). The role of non-homomorphic elements in the overall representation is to support the other non-homomorphic steps, and as attention-drawing and focusing devices.…”

An architectural framework for complex cognition

“…More recently there have been proposals (Chandrasekaran, Kurup, Banerjee, Josephson, & Winkler, 2004;Lathrop & Laird, 2009) that have sought to augment this symbolic representation with visual/diagrammatic representations, and while there has been a long-standing debate (Pylyshyn, 2003) about the exact nature of the differences between these representations, there is significant evidence (Kosslyn, Thompson, & Ganis, 2006) for the role played by the perceptual system in high-level cognition. Moreover, (Chandrasekaran, 2002;Kurup, 2008) have argued that the support for such representations is at the architectural level.…”

“…The specialist's spatial representation is based on the diagrammatic representation system (DRS) first proposed by Chandrasekaran et al (2004). A diagram in DRS consists of three types of objects -points, curves and regions.…”

“…This was because when using a diagrammatic representation, derived properties and consequences of actions are implicit in the model, and do not require separate inference. This ability of diagrammatic representations has been referred to variously as free rides (Barwise & Shimojima, 1995) and emergent properties (Chandrasekaran et al, 2004).…”