Analogical Problem Solving With Visual Models

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

1

Analogical Problem Solving With Visual Models

Jim Davies, Nancy J. Nersessian, Ashok K. Goel {jimmyd, nancyn, goel}@cc.gatech.edu

Program in Cognitive ScienceGeorgia Institute of Technology


2

Outline• Background: where these ideas are

coming from• Our computational account of

visual analogy• Examples: radiation problem and

Maxwell’s case study


3

Motivation

• People use analogy and visual reasoning when problem solving – In Scientific theory creation

• Nersessian’s cognitive-historical analysis of Maxwell

– Psychological studies support this


4

This Work• This work builds a new, cognitively

informed, computational theory of visual analogy for problem solving, one form of which is scientific discovery.

• We hypothesize that representing problems as visual abstractions facilitates the analogical process in problem solving.


5

Visual Analogy

• Visual analogy is analogy with visual elements


6

Bitmap Images

• Neuron432: on• Neuron479: off• Neuron200: off• Neuron136: off• Neuron326: on• Neuron344: on


7

Symbolic ImagesSymbolic Image

contains contains

square

contains

circle triangle

inside right-of


8

Symbols Are Mapped


9

Goel’s Computational Work• Structure-Behavior-Function: Goel et al.

1997• IDEAL: Bhatta & Goel 1997

– Generic Teleological Mechanisms• ToRQUE: Griffith, Nersessian, Goel 2000.

– Generic Structural Transformations


10

Primitive Visualization Language (Privlan)

• Primitive visual transformations (privits)

• Primitive visual elements (privels)• Symbolic images (simages)


11

Privits: Primitive Visual Transformations

• Decompose (object, number)• Move (object, new-location)


12

Privels: Primitive Visual Elements

• Line (thickness, start point, end point)

• Generic-Visual-Element (size, location)


13

System: Galatea


14


15

Maxwell’s Model Development


16

Generic Abstraction


17


18

Primitive Visualization Language (Privlan)

• Primitive visual transformations (privits)– Add-component, decompose, move

• Primitive visual elements (privels)– Circle, line, generic-visual-element

• Symbolic images (simages)


19

Conclusions• Galatea has been applied to two examples,

supporting our computational theory of visual analogy and Privlan.

• This implementation has provided support for visual interpretations of the Duncker case and Nersessian’s interpretation of the Maxwell case.

• We conjecture that visual representations and generic abstractions are useful for a wide variety of problem-solving instances, including scientific discovery.


20

Thank You

• http://www.cc.gatech.edu/~jimmyd/research /visual-analogy/

Analogical Problem Solving With Visual Models

Documents