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UID:8569@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250320T110000
DTEND;TZID=Europe/Paris:20250320T123000
DTSTAMP:20250313T111740Z
URL:https://www.i2m.univ-amu.fr/evenements/the-e-base-of-finite-semidistri
 butive-closure-lattices-lsc/
SUMMARY:Simon Vilmin (LIS\, Aix-Marseille): The E-base of finite semidistri
 butive closure lattices [LSC]
DESCRIPTION:Simon Vilmin: A (finite) closure space is a pair consisting of 
 a (finite) ground set X\nand a closure operator on X. When ordered by incl
 usion\, the fixpoints of\nthe closure operator---closed sets---are known t
 o form a (closure)\nlattice. Closure spaces and their associated lattices 
 arise in several\nfields of computer science\, usually by means of implici
 t representations\nsuch as implicational bases (IBs). An implicational bas
 e over X is a\ncollection of statements A --&gt\; B\, aka implications\, w
 here A and B are\nsubsets X. While an IB represents a unique closure space
 \, a closure\nspace can be represented via several different IBs. As a con
 sequence\, a\nnumber of particular IBs have been proposed in the literatur
 e. Recently\,\na new specimen coming from the study of free lattices has b
 een\nintroduced in the zoo of IBs: the E-base. Unlike other commonly studi
 ed\nIBs such as the canonical base or the D-base\, though\, the E-base doe
 s\nnot always faithfully represent its associated closure space. This lead
 s\nto an intriguing question: for which classes of (closure) lattices do\n
 closure spaces have a valid E-base? Lower bounded lattices are known to\nf
 orm such a class. Here\, we will show that semidistributive lattices\nalso
  have valid E-base.\n\nThis result comes from a recent collaboration with 
 Kira Adaricheva:\nhttps://arxiv.org/abs/2502.04146.
CATEGORIES:Séminaire,Logique et Interactions
LOCATION:Luminy - LIS\, salle 04.05\, Campus de Luminy\, Marseille\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Campus de Luminy\, Marseill
 e\, France;X-APPLE-RADIUS=100;X-TITLE=Luminy - LIS\, salle 04.05:geo:0,0
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