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 counter-example.
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Gély, A., Couceiro, M., Napoli, A. (2022). Towards Distributivity in FCA for Phylogenetic Data. In: Missaoui, R., Kwuida, L., Abdessalem, T. (eds) Complex Data Analytics with Formal Concept Analysis. Springer, Cham. https://doi.org/10.1007/978-3-030-93278-7_10
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DOI: https://doi.org/10.1007/978-3-030-93278-7_10
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