Analogical Proportions in a Lattice of Sets of Alignments Built on the Common Subwords in a Finite Language

Laurent Miclet 1 Nelly Barbot 2 Baptiste Jeudy 3
1 Dyliss - Dynamics, Logics and Inference for biological Systems and Sequences
Inria Rennes – Bretagne Atlantique , IRISA-D7 - GESTION DES DONNÉES ET DE LA CONNAISSANCE
2 EXPRESSION - Expressiveness in Human Centered Data/Media
UBS - Université de Bretagne Sud, IRISA-D6 - MEDIA ET INTERACTIONS
Abstract : We define the locally maximal subwords and locally minimal superwords common to a finite set of words. We also define the corresponding sets of alignments. We give a partial order relation between such sets of alignments, as well as two operations between them. We show that the constructed family of sets of alignments has the lattice structure. The study of analogical proportion in lattices gives hints to use this structure as a machine learning basis, aiming at inducing a generalization of the set of words.
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https://hal.inria.fr/hal-00974656
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Submitted on : Monday, April 7, 2014 - 12:06:37 PM
Last modification on : Friday, November 16, 2018 - 1:38:57 AM

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Laurent Miclet, Nelly Barbot, Baptiste Jeudy. Analogical Proportions in a Lattice of Sets of Alignments Built on the Common Subwords in a Finite Language. Prade, Henri and Richard, Gilles. Computational Approaches to Analogical Reasoning: Current Trends, Studies in Computational Intelligence, Springer-Verlag Berlin Heidelberg, pp.245-260, 2014, 978-3-642-54515-3. ⟨10.1007/978-3-642-54516-0_10⟩. ⟨hal-00974656⟩

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