The lattices of closure systems, closure operators, and implicational systems on a finite set: A survey
type: Item
instance of: scholarly article
title: The lattices of closure systems, closure operators, and implicational systems on a finite set: A survey
zbMATH Open document ID: 1026.06008
DOI: 10.1016/S0166-218X(02)00209-3
author: Nathalie Caspard
author: Bernard Monjardet
published in: Discrete Applied Mathematics
publication date: 2003-05-25T00:00:00Z
Mathematics Subject Classification ID: 06A15
Mathematics Subject Classification ID: 68P15
zbMATH DE Number: 1915697
zbMATH Keywords: canonical basis
zbMATH Keywords: closure operator
zbMATH Keywords: closure system
zbMATH Keywords: dependence relation
zbMATH Keywords: functional dependency
zbMATH Keywords: implicational system
zbMATH Keywords: lower bounded lattice
zbMATH Keywords: meet-distributive lattice
zbMATH Keywords: relational databases
zbMATH Keywords: survey
MaRDI profile type: Publication
cites work: Semidistributive and coalgebraic lattices of subsemilattices
cites work: Two embedding theorems for lower bounded lattices
cites work: Q5202665
cites work: Q4050122
cites work: Q5685119
cites work: Q5331549
cites work: The lattice of strict completions of a finite poset.
cites work: Q4692772
cites work: Organization by rules in finite sequences
cites work: The poset of closures as a model of changing databases
cites work: On the number of databases and closure operations
cites work: Q4284610
cites work: A characterization theorem for the canonical basis of a closure operator
cites work: Q4692885
cites work: Characterizations of Finite Lattices that are Bounded-Homomqrphic Images or Sublattices of Free Lattices
cites work: THE LATTICE THEORY OF FUNCTIONAL DEPENDENCIES AND NORMAL DECOMPOSITIONS
cites work: Q4326636
cites work: Functional dependencies in relational databases: A lattice point of view
cites work: Q4859897
cites work: Knowledge Spaces
cites work: How to build a knowledge space by querying an expert
cites work: A note on the correspondence among entail relations, rough set dependencies, and logical consequence
cites work: The core of finite lattices
cites work: Latticial structures in data analysis.
cites work: Q4834373
cites work: Attribute exploration with background knowledge
cites work: Q4230685
cites work: Q4165427
cites work: Q5058462
cites work: The lattice of closure relations on a poset
cites work: Lattices of closure operators
cites work: Q5805057
cites work: Q3912586
cites work: Partition numbers for trees and ordered sets
cites work: Choice functions and abstract convex geometries
cites work: Direct decompositions of atomistic algebraic lattices
cites work: Q3831065
cites work: Q3831064
cites work: Q3668890
cites work: Path independence in serial-parallel data processing
cites work: Q4395495
cites work: Q4055674
cites work: Q4895873
cites work: Arrowian characterizations of latticial federation consensus functions
cites work: On a dependence relation in finite lattices
cites work: The duality between the anti-exchange closure operators and the path independent choice operators on a finite set
cites work: Q5837206
cites work: Q3294258
cites work: Q5508998
cites work: The lattice of completions of an ordered set
cites work: Q3714092
cites work: Combinations of closure relations
cites work: On finite lattices which are embeddable in subsemigroup lattices
cites work: Q4395026
cites work: Q5185609
cites work: Supersolvable lattices
cites work: Q4256200

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The lattices of closure systems, closure operators, and implicational systems on a finite set: A survey (full work available at URL)
full work available at URL: s0166-218x(02)00209-3

The lattices of closure systems, closure operators, and implicational systems on a finite set: A survey (OpenAlex ID)
OpenAlex ID: W2158470853

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