Abstract
Analogical proportions are statements of the form ”A is to B as C is to D” which play a key role in analogical reasoning. We propose a logical encoding of analogical proportions in a propositional setting, which is then extended to different fuzzy logics. Being in an analogical proportion is viewed as a quaternary connective relating four propositional variables. Interestingly enough, the fuzzy formalizations that are thus obtained parallel numerical models of analogical proportions. Potential applications to case-based reasoning and learning are outlined.
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References
Aamodt, A., Plaza, E.: Case-based reasoning: Foundational issues, methodological variations, and system approaches. Artificial Intelligence Com., 39–59 (1994)
Bayoudh, S., Miclet, L., Delhay, A.: Learning by analogy: a classification rule for binary and nominal data. In: Veloso, M. (ed.) Proc. IJCAI 2007, pp. 678–683. AAAI Press, Menlo Park (2007)
Bouchon-Meunier, B., Valverde, L.: A fuzzy approach to analogical reasoning. Soft Computing 3, 141–147 (1999)
Dubois, D., Esteva, F., Garcia, P., Godo, L., Lopez de Mantaras, R., Prade, H.: Fuzzy modelling of cased-based reasoning and decision. In: Leake, D.B., Plaza, E. (eds.) ICCBR 1997. LNCS, vol. 1266, pp. 599–610. Springer, Heidelberg (1997)
Dubois, D., Hüllermeier, E., Prade, H.: Fuzzy set-based methods in instance-based reasoning. IEEE Trans. on Fuzzy Systems 10, 322–332 (2002)
Evans, T.: A heuristic program to solve geometry analogy problem. In: Minsky, M. (ed.) Semantic Information Processing. MIT Press, Cambridge (1968)
Gentner, D., Kurtz, K.J.: Relations, objects, and the composition of analogies. Cognitive Science 30, 609–642 (2006)
Hirowatari, E., Arikawa, S.: Incorporating explanation-based generalization with analogical reasoning. Bulletin of Informatics and Cybernetics 26, 13–33 (1994)
Hüllermeier, E., Dubois, D., Prade, H.: Model adaptation in possibilistic instance-based reasoning. IEEE Trans. on Fuzzy Systems 10, 333–339 (2002)
Klein, S.: Culture, mysticism and social structure and the calculation of behavior. In: Proc. Europ. Conf. on Artificial Intelligence (ECAI 1982), pp. 141–146 (1982)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Acad. Publ., Dordrecht (2000)
Kling, R.E.: A paradigm for reasoning by analogy. Artif. Intellig. 2, 147–178 (1971)
Lepage, Y.: De l’analogie rendant compte de la commutation en linguistique. Habilitation (2003), http://www.slt.atr.jp/~lepage/pdf/dhdryl.pdf
Lieber, J.: Application of the revision theory to adaptation in case-based reasoning: The conservative adaptation. In: Weber, R.O., Richter, M.M. (eds.) ICCBR 2007. LNCS, vol. 4626, pp. 239–253. Springer, Heidelberg (2007)
Miclet, L., Delhay, A.: Analogical dissimilarity: definition, algorithms and first experiments in machine learning. Technical Report 5694, INRIA (September 2005)
Mitchell, T.: Machine Learning. McGraw-Hill, New York (1997)
Polya, G.: Mathematics and Plausible Reasoning. Patterns of Plausible Inference, vol. II. Princeton University Press, Princeton (1954)
Sowa, J.F., Majumdar, A.K.: Analogical reasoning. In: Ganter, B., de Moor, A., Lex, W. (eds.) ICCS 2003. LNCS (LNAI), vol. 2746, pp. 16–36. Springer, Heidelberg (2003)
Stroppa, N., Yvon, F.: Analogical learning and formal proportions: Definitions and methodological issues. Technical Report ENST-2005-D004 (June 2005), http://www.tsi.enst.fr/publications/enst/techreport-2007-6830.pdf
Stroppa, N., Yvon, F.: Formal models of analogical proportions. Technical report 2006D008, Ecole Nat. Sup. des Telecommunications, Paris (2006)
Tausend, B., Bell, S.: Analogical reasoning for logic programming. In: Kodratoff, Y. (ed.) EWSL 1991. LNCS, vol. 482, pp. 391–397. Springer, Heidelberg (1991)
Winston, P.H.: Learning and reasoning by analogy. Com. of ACM, pp. 689–703 (1980)
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Miclet, L., Prade, H. (2009). Handling Analogical Proportions in Classical Logic and Fuzzy Logics Settings. In: Sossai, C., Chemello, G. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2009. Lecture Notes in Computer Science(), vol 5590. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02906-6_55
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DOI: https://doi.org/10.1007/978-3-642-02906-6_55
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