Abstract
We present an approach for solving proportional analogies of the form A : B :: C : D where a plausible outcome for D is computed. The core of the approach is E–Generalization. The generalization method is based on the extraction of the greatest common structure of the terms A, B and C and yields a mapping to compute every possible value for D with respect to some equational theory. This approach to analogical reasoning is formally sound and powerful and at the same time models crucial aspects of human reasoning, that is the guidance of mapping by shared roles and the use of re-representations based on a background theory. The focus of the paper is on the presentation of the approach. It is illustrated by an application for the letter string domain.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Mitchell, M.: Analogy-Making as Perception: A Computer Model. MIT Press, Cambridge (1993)
French, R.M.: The computational modeling of analogy-making. Trends in Cognitive Sciences 6(5), 200–205 (2002)
Evans, T.G.: A Program for the Solution of a Class of Gemetric-Analogy Intelligence-Test Questions. In: Minsky, M. (ed.) Semantic Information Processing, pp. 271–353. MIT Press, Cambridge (1968)
O’Hara, S.: A model of the redescription process in the context of geometric proportional analogy problems. In: Jantke, K.P. (ed.) AII 1992. LNCS, vol. 642, pp. 268–293. Springer, Heidelberg (1992)
Hofstadter, D.: The Fluid Analogies Research Gr.: Fluid Concepts and Creative Analogies. Basic Books, New York (1995)
Heinz, B.: Anti-Unifikation modulo Gleichungstheorie und deren Anwendung zur Lemmagenerierung. Technical report, GMD - Forschungszentrum Informationstechnick GmbH (1996)
Burghardt, J.: E-generalization using grammars. Artificial Intelligence Journal 165(1), 1–35 (2005)
Plotkin, G.D.: A note on inductive generalization. In: Machine Intelligence, vol. 5, pp. 153–163. Edinburgh University Press, Edinburgh (1970)
Reynolds, J.: Transformational Systems and the Algebraic Structure of Atomic Formulas. In: Machine Intelligence, vol. 5, Edinburgh University Press, Edinburgh (1970)
Falkenheimer, B., Forbus, K.D., Gentner, D.: The structure-mapping engine: Algorithm and examples. Artificial Intelligence 41, 1–63 (1989)
Schmid, U., Gust, H.: An algebraic framework for solving proportional and predictive analogies. In: Schmalhofer, F., Young, R., Katz, G. (eds.) Proceedings of the First European Conference on Cognitive Science (EuroCogSci03), pp. 295–300. Lawrence Erlbaum, Mahwah (2003)
Brainerd, W.S.: The minimalization of tree automata. Information and Control 13, 484–491 (1968)
Thatcher, J.W., Wright, J.B.: Generalized finite automata theory with an application to a decision problem of second–order logic. Mathematical Systems Theory 2(1) (1968)
Comon, H., et al.: Tree automata techniques and applications (1997), Available on http://www.grappa.univ-lille3.fr/tata , release October, 1rst 2002
von Thaden, M., Weller, S.: Lösen von Intelligenztestaufgaben mit E-Generalisierung (Solving intelligence tasks by E-Generalization). In: Tagungsband der Informatiktage 2003, pp. 84–87. Gesellschaft für Informatik e.V. (2003)
Emmelmann, H.: Code Selection by Regularly Controlled Term Rewriting. In: Proc. of Int. Workshop on Code Generation (1991)
Weller, S.: Solving Proportional Analogies by Application of Anti-Unification modulo Equational Theory. Bachelor’s Thesis, unpublished (2005), Available on http://www-lehre.inf.uos.de/~stweller/ba/
Yan, J., Gentner, D.: A theory of rerepresentation in analogical matching. In: Proc. of the 25th Annual Conference of the Cognitive Science Society, Lawrence Erlbaum, Mahwah (2003)
Burns, B.D.: Meta-analogical transfer: Transfer between episodes of analogical reasoning. Journal of Experimental Psychology: Learning, Memory, and Cognition 22(4), 1032–1048 (1996)
Cornuejlos, A.: Analogy as minimization of description length. In: Nakhaeizadeh, N., Taylor, C.C. (eds.) Machine Learning and Statistics. The Interface, pp. 321–335. Wiley, New York (1997)
Dastani, M., Indurkhya, B., Scha, R.: An Algebraic Approach to Modeling Analogical Projection in Pattern Perception. In: Proceedings of Mind II (1997)
Leeuwenberg, E.: A perceptual coding language for visual and auditory patterns. American Journal of Psychology 84, 307–349 (1971)
Goldstein, E.B.: Sensation and Perception. Wadsworth Publishing Co., Belmont (1980)
Hasker, R.W.: The Replay of Program Derivations. PhD thesis, Univ. of Illinois at Urbana-Champaign (1995)
Schmid, U., Sinha, U., Wysotzki, F.: Program reuse and abstraction by anti-unification. In: Professionelles Wissensmanagement – Erfahrungen und Visionen, pp. 183–185. Shaker, Aachen (2001), Long Version: http://ki.cs.tu-berlin.de/~schmid/pub-ps/pba-wm01-3a.ps
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Weller, S., Schmid, U. (2007). Solving Proportional Analogies by E–Generalization. In: Freksa, C., Kohlhase, M., Schill, K. (eds) KI 2006: Advances in Artificial Intelligence. KI 2006. Lecture Notes in Computer Science(), vol 4314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69912-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-69912-5_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69911-8
Online ISBN: 978-3-540-69912-5
eBook Packages: Computer ScienceComputer Science (R0)