The design of relational databases
The design of relational databases
Structure identification in relational data
Artificial Intelligence - Special volume on constraint-based reasoning
Information Processing Letters
Logical features of Horn Clauses
Handbook of logic in artificial intelligence and logic programming (vol. 1)
Functional dependencies in Horn theories
Artificial Intelligence
Attribute exploration with background knowledge
Theoretical Computer Science
Latticial structures in data analysis
Theoretical Computer Science
A relational model of data for large shared data banks
Communications of the ACM
Principles of data mining
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Knowledge Spaces
Finite Automata, Their Algebras and Grammars
Finite Automata, Their Algebras and Grammars
Domains for Denotational Semantics
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Discrete Applied Mathematics - Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)
Theory of Relational Databases
Theory of Relational Databases
Boolean Functions
Semantic Resolution for Horn Sets
IEEE Transactions on Computers
Functional dependencies in a relational database and propositional logic
IBM Journal of Research and Development
Generalized domination in closure systems
Discrete Applied Mathematics - Special issue: Discrete mathematics & data mining II (DM & DM II)
Rough Sets and Functional Dependencies in Data: Foundations of Association Reducts
Transactions on Computational Science V
Ordered direct implicational basis of a finite closure system
Discrete Applied Mathematics
On implicational bases of closure systems with unique critical sets
Discrete Applied Mathematics
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The notion of dependencies between ''attributes'' arises in many areas such as relational databases, data analysis, data-mining, formal concept analysis, knowledge structures .... Formalization of dependencies leads to the notion of so-called full implicational systems (or full family of functional dependencies) which is in one-to-one correspondence with the other significant notions of closure operator and of closure system. An efficient generation of a full implicational system (or a closure system) can be performed from equivalent implicational systems and in particular from the bases for such systems, for example, the so-called canonical basis. This paper shows the equality between five other bases originating from different works and satisfying various properties (in particular they are unit implicational systems). The three main properties of this unique basis are the directness, canonical and minimal properties, whence the name canonical direct unit implicational basis given to this unit implicational system. The paper also gives a nice characterization of this canonical basis and makes precise its link with the prime implicants of the Horn function associated to a closure operator. It concludes that it is necessary to compare more closely related works made independently, and with a different terminology, in order to take advantage of the really new results in these works.