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

  • Laurent Miclet
  • Nelly Barbot
  • Baptiste Jeudy
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 548)

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.

Keywords

Locally maximal subwords Alignments Algebraic structure of sets of alignments on a set of words (lattice) Analogical proportion 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.IRISA-DylissRennesFrance
  2. 2.IRISA-CordialLannionFrance
  3. 3.Laboratoire Hubert CurienUniversité de Saint-ÉtienneSaint-ÉtienneFrance

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