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Analogical proportions and the factorization of information in distributive lattices

Barbot, Nelly and Miclet, Laurent and Prade, Henri Analogical proportions and the factorization of information in distributive lattices. (2014) In: International Conference on Concept Lattices and Their Applications - CLA 2013, 15 October 2013 - 18 October 2013 (La Rochelle, France).

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Analogical proportions are statements involving four enti- ties, of the form 'A is to B as C is to D'. They play an important role in analogical reasoning. Their formalization has received much attention from different researchers in the last decade, in particular in a proposi- tional logic setting. Analogical proportions have also been algebraically defined in terms of factorization, as a generalization of geometric nu- merical proportions (that equate ratios). In this paper, we define and study analogical proportions in the general setting of lattices, and more particularly of distributive lattices. The decomposition of analogical pro- portions in canonical proportions is discussed in details, as well as the resolution of analogical proportion equations, which plays a crucial role in reasoning. The case of Boolean lattices, which reflects the logical mod- eling, and the case corresponding to entities described in terms of gradual properties, are especially considered for illustration purposes.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to Ceur-ws editor. The definitive version is available at http://ceur-ws.org/Vol-1062/
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > Institut National des Sciences Appliquées de Rennes - INSA (FRANCE)
Other partners > Institut Mines-Télécom (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Ecole Normale Supérieure de Rennes - ENS Rennes (FRANCE)
Other partners > Université de Bretagne Sud - UBS (FRANCE)
Other partners > Université de Rennes 1 (FRANCE)
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Deposited On:09 Apr 2015 07:47

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