Abstract
Among the diverse processes at work in human cognition, the ability to establish analogies plays a crucial role and is often evaluated via IQ tests where an incomplete sequence has to be completed with a suitable item. This has motivated the AI community for developing various computational models of analogy-making. A Boolean logic view of analogical proportions (a basic form of analogical statements of the form “a is to b as c is to d”) has been recently proposed and extended to another logical proportion, namely paralogical proportion (stating that “what a and b have in common, c and d have it also”). When used in combination, these 2 proportions provide an enhanced power to complete IQ tests. This Boolean modeling essentially relies on the assessment of the differences and similarities between the items involved, and in the case of analogy, satisfies the expected properties of an analogical proportion. An extension to multiple-valued features has also been defined, reinforcing their scope of applications. It is then possible to complete, in a deterministic manner, some incomplete proportions where the last item d is missing. In this paper, we show how this can be the basis of a simple inference paradigm that provides a rigorous way to solve representative analogy-based IQ tests by computing the missing items rather than by choosing in a list of options. The result of the analogical/paralogical inference depends on the way the items are represented. The paper discusses how this approach can be used in analogy-making for both determining missing items in proportions and laying bare the relation linking the components of such proportions. The novelty of the approach is stressed w.r.t. other proposals existing in the literature.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aamodt, A., Plaza, E.: Case-based reasoning; foundational issues, methodological variations, and system approaches. AICom 7(1), 39–59 (1994)
Carter, P., Russell, K.: IQ Firepower. Robinson (1995)
Cornuéjols, A.: Analogie, principe d’économie et complexité algorithmique. In: Actes des 11èmes Journées Francaises de l’Apprentissage, Sète, France (1996)
Evans, T.G.: A heuristic program to solve geometry-analogy problems. In: Proc. A.F.I.P. Spring Joint Computer Conference, vol. 25, pp. 5–16 (1964)
French, R.M.: The computational modeling of analogy-making. Trends in Cognitive Sciences 6(5), 200–205 (2002)
Gentner, D.: The Mechanisms of Analogical Learning. In: Similarity and Analogical Reasoning, pp. 197–241. Cambridge University Press, Cambridge (1989)
Hofstadter, D., Mitchell, M.: Copycat project: a model of mental fluidity and analogy-making, pp. 205–267. Basic Books, Inc., New York (1995)
Holyoak, J., Thagard, P.: Analogical mapping by constraint satisfaction. Cognitive Science 13, 295–355 (1989)
Hummel, J.E., Holyoak, K.J.: Distributed representations of structure: a theory of analogical access and mapping. Psychological Review 104(3), 427–466 (1997)
Klein, S.: Culture, mysticism & social structure and the calculation of behavior. In: Proc. 5th Europ. Conf. in Artif. Intellig. (ECAI 1982), Orsay, pp. 141–146 (1982)
Kling, R.: A paradigm for reasoning by analogy. In: Proc. IJCAI, pp. 568–585 (1971)
Lepage, Y.: Analogy and formal languages. In: Proc. FG/MOL 2001, pp. 373–378 (2001), http://www.slt.atr.co.jp/~lepage/pdf/dhdryl.pdf.gz
Lieber, J.: Reformulations and adaptation decomposition. In: Proc. ICCBR Workshops, pp. 27–34 (1999)
Miclet, L., Bayoudh, S., Delhay, A.: Analogical dissimilarity: definition, algorithms and two experiments in machine learning. JAIR 32, 793–824 (2008)
Miclet, L., Prade, H.: Handling analogical proportions in classical logic and fuzzy logics settings. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS, vol. 5590, pp. 638–650. Springer, Heidelberg (2009)
O’Donoghue, D.P., Bohan, A.J., Keane, M.T.: Seeing things: Inventive reasoning with geometric analogies and topographic maps. New Generation Comput. 24, 267–288 (2006)
Prade, H., Richard, G.: Multiple-valued logic interpretations of analogical, reverse analogical, and paralogical proportions. In: Proc. 40th IEEE Int. Symp. on Multiple-Valued Logic (ISMVL 2010), Barcelona, pp. 258–263 (2010)
Prade, H., Richard, G.: Reasoning with logical proportions. In: Proc. Int. Conf. on Principles of Knowledge Repres. and Reas (KR 2010), Toronto, pp. 546–555 (2010)
Prade, H., Richard, G., Yao, B.: Classification by means of fuzzy analogy-related proportions: A preliminary report. In: Proc. 2nd IEEE Int. Conf. on Soft Computing and Pattern Recognition (SocPar 2010), Evry, pp. 297–302 (2010)
Stroppa, N., Yvon, F.: Analogical learning and formal proportions: Definitions and methodological issues. ENST Paris report (2005)
Weller, S., Schmid, U.: Solving proportional analogies by generalization. In: Freksa, C., Kohlhase, M., Schill, K. (eds.) KI 2006. LNCS (LNAI), vol. 4314, pp. 64–75. Springer, Heidelberg (2007)
Winston, P.H.: Learning and reasoning by analogy. Com. ACM 23, 689–703 (1980)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Prade, H., Richard, G. (2011). Analogy-Making for Solving IQ Tests: A Logical View. In: Ram, A., Wiratunga, N. (eds) Case-Based Reasoning Research and Development. ICCBR 2011. Lecture Notes in Computer Science(), vol 6880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23291-6_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-23291-6_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23290-9
Online ISBN: 978-3-642-23291-6
eBook Packages: Computer ScienceComputer Science (R0)