The multiple facets of the canonical direct unit implicational basis

DOI10.1016/j.tcs.2009.12.021zbMath1209.68187OpenAlexW2034262006MaRDI QIDQ974107

Karell Bertet, Bernard Monjardet

Publication date: 27 May 2010

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

Full work available at URL: https://doi.org/10.1016/j.tcs.2009.12.021

zbMATH Keywords

latticeclosure operatorclosure systemcanonical direct unit basisHorn Boolean functionimplicational system

Mathematics Subject Classification ID

Database theory (68P15)

Related Items (28)

Formal Methods in FCA and Big Data ⋮ Lattices, closures systems and implication bases: a survey of structural aspects and algorithms ⋮ Optimum basis of finite convex geometry ⋮ A representation of antimatroids by Horn rules and its application to educational systems ⋮ Construction and learnability of canonical Horn formulas ⋮ Three views on dependency covers from an FCA perspective ⋮ Hierarchical decompositions of implicational bases for the enumeration of meet-irreducible elements ⋮ The joy of implications, aka pure Horn formulas: mainly a survey ⋮ Discovery of the \(D\)-basis in binary tables based on hypergraph dualization ⋮ RQL: a query language for rule discovery in databases ⋮ Algorithms for \(k\)-meet-semidistributive lattices ⋮ On sets of graded attribute implications with witnessed non-redundancy ⋮ Optimizations in computing the Duquenne-Guigues basis of implications ⋮ Fast algorithms for implication bases and attribute exploration using proper premises ⋮ Concept lattices with negative information: a characterization theorem ⋮ Canonical dichotomous direct bases ⋮ Translating between the representations of a ranked convex geometry ⋮ On implication bases in \(n\)-lattices ⋮ Polynomial Time Algorithms for Computing a Minimum Hull Set in Distance-Hereditary and Chordal Graphs ⋮ A depth-first search algorithm for computing pseudo-closed sets ⋮ Algorithms for computing the Shapley value of cooperative games on lattices ⋮ Direct-optimal basis computation by means of the fusion of simplification rules ⋮ A methodology for analysis of concept lattice reduction ⋮ On implicational bases of closure systems with unique critical sets. ⋮ Performance-friendly rule extraction in large water data-sets with AOC posets and relational concept analysis ⋮ Quasi-closed elements in fuzzy posets ⋮ Steps towards causal Formal Concept Analysis ⋮ Measuring the Implications of the D-Basis in Analysis of Data in Biomedical Studies

Uses Software

• JBool

Cites Work

• Horn functions and their DNFs
• Structure identification in relational data
• Functional dependencies in Horn theories
• Attribute exploration with background knowledge
• Latticial structures in data analysis.
• A theory of finite closure spaces based on implications
• The presence of lattice theory in discrete problems of mathematical social sciences. Why.
• Arrowian characterizations of latticial federation consensus functions
• The lattices of closure systems, closure operators, and implicational systems on a finite set: A survey
• Generalized domination in closure systems
• Finite ordered sets. Concepts, results and applications
• Semantic Resolution for Horn Sets
• Functional Dependencies in a Relational Database and Propositional Logic
• Knowledge Spaces
• Computing iceberg concept lattices with Titanic
• A relational model of data for large shared data banks
• Representations of Lattices by Sets
• On sentences which are true of direct unions of algebras
• The decision problem for some classes of sentences without quantifiers
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