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Book Sections Year : 2022

Towards Distributivity in FCA for Phylogenetic Data

Alain Gély
Miguel Couceiro
Amedeo Napoli

Abstract

It is known that a distributive lattice is a median graph, and that a distributive ∨-semilattice can be thought of as a median graph iff every triple of elements such that the infimum of each couple of its elements exists, has an infimum. Since a lattice without its bottom element is obviously a ∨-semilattice, using the FCA formalism, we investigate the following problem: Given a semilattice L obtained from a lattice by deletion of the bottom element, is there a minimum distributive ∨-semilattice L d such that L can be order embedded into L d ? We give a negative answer to this question by providing a counterexample .
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Dates and versions

hal-03537989 , version 1 (20-01-2022)

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  • HAL Id : hal-03537989 , version 1

Cite

Alain Gély, Miguel Couceiro, Amedeo Napoli. Towards Distributivity in FCA for Phylogenetic Data. Rokia Missaoui, Leonard Kwuida, Talel Abdessalem. Complex Data Analysis with Formal Concept Analysis, Springer, inPress, Complex Data Analysis with Formal Concept Analysis. ⟨hal-03537989⟩
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