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Embedding median graphs into minimal distributive ∨-semi-lattices

Alain Gély 1 Miguel Couceiro 1, 2 Amedeo Napoli 2
2 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : It is known that a distributive lattice is a median graph, and that a distributive ∨-semi-lattice can be thought of as a median graph i every triple of elements such that the inmum of each couple of its elements exists, has an inmum. Since a lattice without its bottom element is obviously a ∨-semi-lattice, using the FCA formalism, we investigate the following problem: Given a semi-lattice L obtained from a lattice by deletion of the bottom element, is there a minimum distributive ∨-semi-lattice 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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Alain Gély, Miguel Couceiro, Amedeo Napoli. Embedding median graphs into minimal distributive ∨-semi-lattices. NFMCP 2019 - 8th International Workshop on New Frontiers in Mining Complex Patterns in conjunction with ECML-PKDD 2019, Sep 2019, Wùzburg, Germany. ⟨hal-02912341⟩

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