Solving geometric analogy problems through two-stage analogical mapping

Cognitive Science

Volumn 33, Issue 7, 2009, Pages 1192-1231

  Lovett, Andrew ^a   Tomai, Emmett ^a   Forbus, Kenneth ^a   Usher, Jeffrey ^a  

^a NORTHWESTERN UNIVERSITY   (United States)

Author keywords

Analogy; Geometric analogy; Symbolic computational modeling

Indexed keywords

EID: 77953143704     PISSN: 03640213     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1551-6709.2009.01052.x     Document Type: Article

References (44)

1. Biederman, I. (1987). Recognition-by-components: A theory of human image understanding. Psychological Review, 94, 115-147.
2. Biederman, I., & Gerhardstein, P.C. (1993). Recognizing depth-rotated objects: Evidence and conditions for 3D viewpoint invariance. Journal of Experimental Psychology: Human Perception and Performance, 19, 1162-1182.
3. Bohan, A., & O'Donoghue, D. (2000). LUDI: A model for geometric analogies using attribute matching. Proceedings of the eleventh artificial intelligence and cognitive science conference (AICS-2000). Galway, Ireland.
4. Cohn, A. (1996). Calculi for qualitative spatial reasoning. In J. Calmet, J.A. Campbell & J. Pfalzgraph (Eds.), Artificial intelligence and symbolic mathematical computation (pp. 124-143). London: Springer Verlag.
5. Davies, J., & Goel, A. (2001). Visual analogy in problem solving. Proceedings of the 17th international joint conference on artificial intelligence (IJCAI-01). Seattle, WA.
6. Eliasmith, C., & Thagard, P. (2001). Integrating structure and meaning: A distributed model of analogical mapping. Cognitive Science, 25(2), 245-286.
7. Evans, T. (1968). A program for the solution of geometric-analogy intelligence test questions. In M. Minsky (Ed.), Semantic information processing (pp. 271-353). Cambridge, MA: MIT Press.
8. Falkenhainer, B., Forbus, K., & Gentner, D. (1989). The structure-mapping engine: Algorithm and examples. Artificial Intelligence, 41, 1-63.
9. Ferguson, R.W., & Forbus, K. (1999). GeoRep: A flexible tool for spatial representations of line drawings. Proceedings of the thirteenth international workshop on qualitative reasoning (QR'99). Loch Awe, Scotland.
10. Forbus, K., Ferguson, R., & Gentner, D. (1994). Incremental structure-mapping. Proceedings of the sixteenth annual conference of the cognitive science society. Atlanta, GA.
11. Forbus, K., Ferguson, R., & Usher, J. (2001). Towards a computational model of sketching. Proceedings of the 2001 international conference on intelligent user interfaces IUI'01. Santa Fe, NM.
12. Forbus, K., & Oblinger, D. (1990). Making SME greedy and pragmatic. Proceedings of the twelfth annual conference of the cognitive science society. Cambridge, MA.
13. Forbus, K., & Usher, J. (2002). Sketching for knowledge capture: A progress report. Proceedings of 2002 international conference on intelligent user interfaces IUI'02. San Francisco, CA.
14. Forbus, K., Usher, J., Lovett, A., Lockwood, K., & Wetzel, J. (2008). CogSketch: Open-domain sketch understanding for cognitive science research and for education. Proceedings of the fifth eurographics workshop on sketch-based interfaces and modeling. Annecy, France.
15. Forbus, K., Usher, J., & Tomai, E. (2005). Analogical learning of visual/conceptual relationships in sketches. Proceedings of twentieth national conference on artificial intelligence (AAA1-05). Pittsburgh, PA.
16. Forbus, K., Tomai, E., & Usher, J. (2003). Qualitative spatial reasoning for visual grouping in sketches. Proceedings on the 17th international workshop on qualitative reasoning, Brasilia, Brazil.
17. Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7, 155-170.
18. Gentner, D. (1989). Mechanisms of analogical learning. In S. Vosniadou & A. Ortony (Eds.), Similarity and analogical reasoning (pp. 199-241). London: Cambridge University Press.
19. Gentner, D., Brem, S., Ferguson, R.W., Wolff, P., Markman, A.B., & Forbus, K.D. (1997). Analogy and creativity in the works of Johannes Kepler. In T.B. Ward, S.M. Smith, & J. Vaid (Eds.), Creative thought: An investigation of conceptual structures and processes (pp. 403-459). Washington, DC: American Psychological Association.
20. Gentner, D., & Markman, A.B. (1997). Structure mapping in analogy and similarity. Amercian Psychologist, 52, 45-56.
21. Gentner, D., Rattermann, M.J., & Forbus, K. (1993). The roles of similarity in transfer: Separating retrievability from inferential soundness. Cognitive Psychology, 25, 524-575.
22. Holyoak, K.J., & Thagard, P. (1989). Analogical mapping by constraint Satisfaction. Cognitive Science, 13(3), 295-355.
23. Hummel, J.E., & Holyoak, K.J. (1997). Distributed representations of structure: A theory of analogical access and mapping. Psychological Review, 104, 427-466.
24. Jones, R., & Langley, P. (1995). Retrieval and learning in analogical problem solving. Proceedings of the seven-teenth annual conference of the cognitive science society. Pittsburgh, PA.
25. Keane, M.T., & Bradshaw, M. (1988). The incremental analogy machine: A computational model of analogy. In D. Sleeman (Ed.), Third european working session on machine learning (pp. 53-62). London: Pitman; San Mateo, CA: Morgan Kaufmann.
26. Klenk, M., Forbus, K., Tomai, E., Kim, H., & Kyckelhahn, B. (2005). Solving everyday physical reasoning problems by analogy using sketches. Proceedings of the twentieth national conference on artificial intelligence. Pittsburgh, PA.
27. Larkey, L., & Love, B. (2003). CAB: Connectionist analogy builder. Cognitive Science, 27, 781-794.
28. Lovett, A., Lockwood, K., & Forbus, K. (2008). Modeling cross-cultural performance on the visual oddity task. Proceedings of spatial cognition 2008. Freiburg, Germany.
29. Lowe, D.G. (1989). Organization of smooth image curves at multiple scales. International Journal of Computer Vision, 3, 119-130.
30. Markman, A.B., & Gentner, D. (1996). Commonalities and differences in similarity comparisons. Memory & Cognition, 24(2), 235-249.
31. Marr, D. (1982). Vision: A computational investigation into the human representation and processing of visual information. San Francisco: W.H. Freeman.
32. Mitchell, M. (1993). Analogy = making as perception. Cambridge, MA: MIT Press/Bradford.
33. Mokhtarian, F., & Mackworth, A.K. (1986). Scale-based description and recognition of planar curves and two-dimensional shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(1), 34-43.
34. Museros, L., & Escrig, M.T. (2004). A qualitative theory for shape representations and matching. Proceedings of the eighteenth international workshop on qualitative reasoning (QR'04). Evanston, IL.
35. O'Hara, S., & Indurkhya, B. (1995). Adaptation and redescription in the context of geometric proportional analogies. AAAI Fall Symposium on Adaptation of Knowledge for Reuse. Cambridge, MA.
36. Palmer, S. (1999). Vision science: Photons to phenomenology. Cambridge, MA: MIT Press.
37. Parsons, L.M. (1995). Inability to reason about an object's orientation using an axis and angle of rotation. Journal of Experimental Psychology: Human Perception and Performance, 21, 1259-1277.
38. Ragni, M., Schleipen, S., & Steffenhagen, F. (2007). Solving proportional analogies: A computational model. Workshop on analogies: Integrating multiple cognitive abilities, CogSci '07, Nashville, TN.
39. Schwering, A., Krumnack, U., Kühnberger, K., & Gust, H. (2007). Using gestalt principles to compute analogies of geometric figures. Proceedings of the twenty-nineth annual conference of the cognitive science society. Nashville, TN.
40. Shepard, R.N., & Cooper, L.A. (1982). Mental sketches and their transformations. Cambridge: MIT Press.
41. Shepard, R.N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171, 701-703.
42. Tarr, M.J., Bülthoff, H. H., Zabinski, M., & Blanz, V. (1997). To what extent do unique parts influence recognition across viewpoint? Psychological Science, 8(4), 282-289.
43. Veselova, O., & Davis, R. (2004). Perceptually based learning of shape descriptions. Proceedings of the nineteenth national conference on artificial intelligence. San Jose, CA.
44. Witkin, A.P. (1989). Scale-space filtering. Proceedings of the eighth international joint conference on artificial intelligence (IJCAI-89). Detroit, MI.