How to build a knowledge space by querying an expert
Journal of Mathematical Psychology
On the number of databases and closure operations
Theoretical Computer Science
Discrete Mathematics
Functional dependencies in relational databases: a lattice point of view
Discrete Applied Mathematics - Special issue on combinatorial problems in databases
On a dependence relation in finite lattices
Proceedings of an international symposium on Graphs and combinatorics
Discrete Mathematics
Attribute exploration with background knowledge
Theoretical Computer Science
Latticial structures in data analysis
Theoretical Computer Science
A note on the correspondence among entail relations, rough set dependencies, and logical consequence
Journal of Mathematical Psychology
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Knowledge Spaces
Finite Automata, Their Algebras and Grammars
Finite Automata, Their Algebras and Grammars
Functional Dependencies and the Semilattice of Closed Classes
MFDBS '89 Proceedings of the 2nd Symposium on Mathematical Fundamentals of Database Systems
Computations with Finite Closure Systems and Implications
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
Theory of Relational Databases
Theory of Relational Databases
Generalized domination in closure systems
Discrete Applied Mathematics - Special issue: Discrete mathematics & data mining II (DM & DM II)
Minimum implicational basis for ∧-semidistributive lattices
Information Processing Letters
The structure of the overhanging relations associated with some types of closure systems
Annals of Mathematics and Artificial Intelligence
Non-deterministic ideal operators: An adequate tool for formalization in Data Bases
Discrete Applied Mathematics
Unifying Framework for Rule Semantics: Application to Gene Expression Data
Fundamenta Informaticae - Special issue ISMIS'05
Size of random Galois lattices and number of closed frequent itemsets
Discrete Applied Mathematics
Concept Lattice Orbifolds --- First Steps
ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis
Computing and Visualizing Closure Objects Using Relation Algebra and RelView
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Contact Relations with Applications
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Generalized domination in closure systems
Discrete Applied Mathematics - Special issue: Discrete mathematics & data mining II (DM & DM II)
Fundamental study: The multiple facets of the canonical direct unit implicational basis
Theoretical Computer Science
A formal context for symmetric dependencies
ICFCA'08 Proceedings of the 6th international conference on Formal concept analysis
Galois lattices and bases for MGK-valid association rules
CLA'06 Proceedings of the 4th international conference on Concept lattices and their applications
On approximate horn formula minimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
ICFCA'11 Proceedings of the 9th international conference on Formal concept analysis
Dependence and algebraic structure of formal contexts
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Rough approximation operators in covering approximation spaces
RSCTC'06 Proceedings of the 5th international conference on Rough Sets and Current Trends in Computing
Counting of moore families for n=7
ICFCA'10 Proceedings of the 8th international conference on Formal Concept Analysis
Relationship design using spreadsheet reasoning for sets of functional dependencies
ADBIS'06 Proceedings of the 10th East European conference on Advances in Databases and Information Systems
Matroidal approaches to rough sets via closure operators
International Journal of Approximate Reasoning
Attribute Reduction in Formal Contexts: A Covering Rough Set Approach
Fundamenta Informaticae - Knowledge Technology
Unifying Framework for Rule Semantics: Application to Gene Expression Data
Fundamenta Informaticae - Special issue ISMIS'05
Distributed formal concept analysis algorithms based on an iterative mapreduce framework
ICFCA'12 Proceedings of the 10th international conference on Formal Concept Analysis
Ordered direct implicational basis of a finite closure system
Discrete Applied Mathematics
Recursive decomposition and bounds of the lattice of Moore co-families
Annals of Mathematics and Artificial Intelligence
On implicational bases of closure systems with unique critical sets
Discrete Applied Mathematics
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Closure systems (i.e. families of subsets of a set S containing S and closed by set intersection) or, equivalently, closure operators and full implicational systems appear in many fields in pure or applied mathematics and computer science. We present a survey of properties of the lattice of closure systems on a finite set S with proofs of the more significant results. In particular we show that this lattice is atomistic and lower bounded and that there exists a canonical basis for the representation of any closure system by "implicational" closure systems. Since the lattices of closure operators and of full implicational systems are anti-isomorphic with the lattice of closure systems they have the dual properties.