Case-based reasoning, analogical reasoning, and interpolation B´ eatrice Fuchs, Jean Lieber, Laurent Miclet, Alain Mille, Amedeo Napoli, Henri Prade, and Gilles Richard Abstract This chapter presents several types of reasoning based on analogy and similarity. Case-based reasoning, presented in Section 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 Section 4 in the formal setting of fuzzy set representations, is another form of similarity-based reasoning. B´ eatrice Fuchs Univ Lyon, IAE-Universit´ e Lyon 3, CNRS, LIRIS, F-69372 Lyon Cedex 08, e-mail: beatrice.fuchs@liris.cnrs.fr Jean Lieber Universit´ e de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France, e-mail: jean.lieber@ loria.fr Laurent Miclet IRISA, 22300 Lannion, e-mail: laurent.miclet@gmail.com Alain Mille Univ Lyon1, CNRS, LIRIS UMR 5205, F-69622 Villeurbanne, e-mail: alain.mille@liris.cnrs.fr Amedeo Napoli Universit´ e de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France, e-mail: amedeo. napoli@loria.fr Henri Prade IRIT, CNRS & Universit´ e, 31062 Toulouse cedex 9, France,e-mail: prade@irit.fr Gilles Richard IRIT, CNRS & Universit´ e, 31062 Toulouse cedex 9, France,e-mail: richard@irit.fr 1