Lattices, closures systems and implication bases: a survey of structural aspects and algorithms

DOI10.1016/j.tcs.2016.11.021zbMath1398.68510OpenAlexW2558796058MaRDI QIDQ1659991

Karell Bertet, Jean-François Viaud, Christophe Demko, Clément Guérin

Publication date: 23 August 2018

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.tcs.2016.11.021

zbMATH Keywords

latticeclosure operatorconcept latticedependence graphclosure systemcanonical basisminimal generatorsGalois latticeimplicational systemclosed set latticecanonical direct basis

Mathematics Subject Classification ID

Knowledge representation (68T30) Complete lattices, completions (06B23) Representation theory of lattices (06B15) Structure theory of lattices (06B05) Galois correspondences, closure operators (in relation to ordered sets) (06A15)

Related Items (13)

Analysis of Complex and Heterogeneous Data Using FCA and Monadic Predicates ⋮ On Dualization over Distributive Lattices ⋮ On the relation between the subadditivity cone and the quantum entropy cone ⋮ Lattice point of view for argumentation framework ⋮ Three views on dependency covers from an FCA perspective ⋮ Hierarchical decompositions of implicational bases for the enumeration of meet-irreducible elements ⋮ \textsc{NextPriorityConcept}: a new and generic algorithm computing concepts from complex and heterogeneous data ⋮ The joy of implications, aka pure Horn formulas: mainly a survey ⋮ Translating between the representations of a ranked convex geometry ⋮ Direct-optimal basis computation by means of the fusion of simplification rules ⋮ Dualization in lattices given by implicational bases ⋮ Quasi-closed elements in fuzzy posets ⋮ Enumerating maximal consistent closed sets in closure systems

Uses Software

• Galicia
• IGLUE
• Concept Explorer

Cites Work

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