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Case-Based Reasoning, Analogy, and Interpolation

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Abstract

This chapter presents several types of reasoning based on analogy and similarity. Case-based reasoning, presented in Sect. 2, consists in searching a case (where a case represents a problem-solving episode) similar to the problem to be solved and to adapt it to solve this problem. Section 3 is devoted to analogical reasoning and to recent developments based on analogical proportion. Interpolative reasoning, presented in Sect. 4 in the formal setting of fuzzy set representations, is another form of similarity-based reasoning.

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Notes

  1. 1.

    It is noteworthy that this differs from analogical proportions (presented in Sect. 3) for which these two ways to read the four terms of an analogy are equivalent, according to the “exchange of the means” property.

  2. 2.

    These indicators are also the building blocks of the view of similarity proposed by (Tversky 1977).

  3. 3.

    Or to find all the triples (a, b, c) realizing that and then to make a vote, as in the k-nearest neighbor method. Empirical studies suggest that if we restrict ourselves to triples where c is a k-nearest neighbor (a, b being generally quite far) this does not really harm the results (Bounhas et al. 2017a).

  4. 4.

    Rather then seeing a fuzzy set as a set of elements close to its core value, similarity measures between fuzzy sets themselves can be defined, and then it is possible to give some meaning to the analogical proportion of the form \(A : A'\,{:}{:}\,B : B'\), but \(B'\) obtained this way does not have, in general, a reason to be compatible with the result of the generalized modus ponens as defined above. However, some choice of resemblance relations and of operators allows us to reconcile these two viewpoints; see for example (Bouchon-Meunier and Valverde 1999).

  5. 5.

    Gradual rules have been independently considered under the name of “topoi” in (Raccah 1996), from a cognitive perspective.

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Authors and Affiliations

  1. Université de Lyon, IAE-Université Lyon 3, CNRS, LIRIS, 69372, Lyon Cedex 08, France

    Béatrice Fuchs

  2. Université de Lorraine, CNRS, Inria, LORIA, 54000, Nancy, France

    Jean Lieber & Amedeo Napoli

  3. IRISA, 22300, Lannion, France

    Laurent Miclet

  4. Université Lyon 1, CNRS, LIRIS UMR 5205, 69622, Villeurbanne, France

    Alain Mille

  5. IRIT, CNRS and Université Paul Sabatier, Toulouse, France

    Henri Prade

  6. IRIT, CNRS and Université, 31062, Toulouse Cedex 9, France

    Gilles Richard

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  1. Béatrice Fuchs
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  2. Jean Lieber
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  3. Laurent Miclet
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  4. Alain Mille
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  5. Amedeo Napoli
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  6. Henri Prade
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  7. Gilles Richard
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Correspondence to Béatrice Fuchs .

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Editors and Affiliations

  1. CRIL-CNRS, Université d'Artois and Institut Universitaire de France, Lens, France

    Pierre Marquis

  2. Aix Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France

    Odile Papini

  3. IRIT, CNRS and Université Paul Sabatier, Toulouse, France

    Henri Prade

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Fuchs, B. et al. (2020). Case-Based Reasoning, Analogy, and Interpolation. In: Marquis, P., Papini, O., Prade, H. (eds) A Guided Tour of Artificial Intelligence Research. Springer, Cham. https://doi.org/10.1007/978-3-030-06164-7_10

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