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Book Sections Year : 2023

Analogical Proportions and Binary Trees

Abstract

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.
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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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