Analogy

• Didier Dubois
• Henri Prade
• Gilles Richard

Similarity and Analogy

The idea of similarity can be encountered in different types of reasoning (case-based reasoning, approximate reasoning, enlargement of sets of models of propositions for restoring consistency between them) which have been studied in the research group.

The recent works have mainly focused on analogical reasoning:

• Reasoning on the basis of analogical proportions (statements of the form “a is to b as c is to d”) may be also used for interpolation and extrapolation. A thorough study of so-called logical proportions that state comparisons in terms of similarity and dissimilarity between 4 Boolean variables has led to identify other noticeable proportions, apart from the analogical proportion. It has been established that Boolean affine functions are the only ones for which analogical extrapolation can never make any error when predicting missing values. It has been shown that the use of analogical proportions is instrumental for solving different IQ tests in a systematic manner. Analogical proportions have been extended from Boolean to numerical values.
• Case-based reasoning takes advantage of the proximity of the cases listed in the memory with the new considered case. An extension using analogical extrapolation has been recently proposed.

References

• Henri Prade, Gilles Richard. Analogical proportions: From equality to inequality. Dans / In : International Journal of Approximate Reasoning (IJAR), Elsevier, Vol. 101: 234-254, 2018.
• Jean Lieber, Emmanuel Nauer, Henri Prade, Gilles Richard. Making the Best of Cases by Approximation, Interpolation and Extrapolation. Dans / In : International Conference on Case Based Reasoning (ICCBR 2018), Cox, Funk, Begum (Eds.), Springer, LNCS, Vol. 11156: p. 580-596, 2018.
• Henri Prade, Gilles Richard. Analogical proportions and analogical reasoning – An introduction. Dans / In : International Conference on Case Based Reasoning (ICCBR 2017), Aha, Lieber (Eds.), Springer, LNCS, Vol. 10339, p. 16-32, 2017.
• Miguel Couceiro, Nicolas Hug, Henri Prade, Gilles Richard. Analogy-preserving functions: A way to extend Boolean samples. Dans / In : International Joint Conference on Artificial Intelligence (IJCAI),p. 1575-1581,2017.
• Didier Dubois, Henri Prade, Gilles Richard. Multiple-valued extensions of analogical proportions. Fuzzy Sets and Systems, Vol. 292: 193-202, 2016.
• William Correa Beltran, Henri Prade, Gilles Richard.
  Constructive Solving of Raven’s IQ Tests with Analogical Proportions. Dans / In : International Journal of Intelligent Systems, Wiley, Vol. 31 N. 11, p. 1072-1103, 2016.
• Henri Prade, Gilles Richard. Homogenous and heterogeneous logical proportions. Dans / In : Handbook of Philosophical logic, Gabbay, Guenthner, (Eds.), Vol. 18: p. 51-103, 2018.