Analogical Proportions and Binary Trees - Inria - Institut national de recherche en sciences et technologies du numérique
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Chapitre D'ouvrage Année : 2023
Analogical Proportions and Binary Trees
Nelly Barbot (1, 2, 3, 4, 5) , Laurent Miclet (1, 3) , Henri Prade (6, 7) , Gilles Richard (6)
1 ENSSAT - École Nationale Supérieure des Sciences Appliquées et de Technologie (6 rue de Kerampont - BP 80518 - 22305 Lannion Cedex - France)
"> ENSSAT - École Nationale Supérieure des Sciences Appliquées et de Technologie
2 EXPRESSION - Expressiveness in Human Centered Data/Media (IRISA/ENSSAT 6 rue de Kerampont - BP 80518 - 22305 Lannion cedex et IRISA/UBS - Campus de Tohannic - rue Yves Mainguy - bâtiment ENSibs - BP 573 - 56000 Vannes cedex - France)
"> EXPRESSION - Expressiveness in Human Centered Data/Media
3 UR - Université de Rennes (Campus de Beaulieu, 263 avenue Général Leclerc, CS 74205, 35042 RENNES CEDEX - France)
"> UR - Université de Rennes
4 IRISA-D6 - SIGNAL, IMAGE ET LANGAGE (France)
"> IRISA-D6 - SIGNAL, IMAGE ET LANGAGE
5 IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires (Avenue du général Leclerc Campus de Beaulieu 35042 RENNES CEDEX - France) "> IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires
6 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (Institut de recherche en informatique de Toulouse - IRIT 118 Route de Narbonne 31062 Toulouse Cedex 9 - France) "> IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
7 CNRS - Centre National de la Recherche Scientifique (France) "> CNRS - Centre National de la Recherche Scientifique

Résumé

Analogical reasoning has been thought for a longtime as something aside, away from logical reasoning. However, it is not exactly so. This chapter in its first part mainly surveys works of the last decade, which have proposed a logical modeling of analogical proportions (i.e., statements of the form “a is to b as c is to d”) among other logically expressible proportions and have shown their use in analogical inference. It also emphasizes the pervasiveness of analogical proportions as soon as we compare situations. The second part of the chapter shows that dichotomous trees built from pairs of mutually exclusive properties have also a reading in terms of Boolean analogical proportions, thus providing another clue of the links existing between analogy and logically expressed taxonomies. This also gives birth to noticeable opposition structures and can be related to formal concept analysis.

Domaines

Intelligence artificielle [cs.AI] Logique en informatique [cs.LO]

Nelly Barbot  : Connectez-vous pour contacter le contributeur

https://inria.hal.science/hal-04147804

Soumis le : samedi 1 juillet 2023-09:27:06

Dernière modification le : lundi 16 septembre 2024-17:52:04

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hal-04147804 , version 1 (01-07-2023)

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Nelly Barbot, Laurent Miclet, Henri Prade, Gilles Richard. Analogical Proportions and Binary Trees. Béziau Jean-Yves; Desclès Jean-Pierre; Moktefi Amirouche; Pascu Anca Christine. Logic in Question: Talks from the Annual Sorbonne Logic Workshop (2011- 2019), Springer International Publishing, pp.435-458, 2023, Studies in Universal Logic book series (SUL), 978-3-030-94451-3. ⟨10.1007/978-3-030-94452-0_22⟩. ⟨hal-04147804⟩

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