Characterization and Armstrong Relations for Degenerate Multivalued Dependencies Using Formal Concept Analysis

Functional dependencies, a notion originated in Relational Database Theory, are known to admit interesting characterizations in terms of Formal Concept Analysis. In database terms, two successive, natural extensions of the notion of functional dependency are the so-called degenerate multivalued dependencies, and multivalued dependencies proper. We propose here a new Galois connection, based on any given relation, which gives rise to a formal concept lattice corresponding precisely to the degenerate multivalued dependencies that hold in the relation given. The general form of the construction departs significantly from the most usual way of handling functional dependencies. Then, we extend our approach so as to extract Armstrong relations for the degenerate multivalued dependencies from the concept lattice obtained; the proof of the correctness of this construction is nontrivial.

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