A Lattice Representation of Relations, Multivalued Dependencies and Armstrong Relations ## AbstractWe present a lattice-based formalism to relate, in a novel way, different representation methods for relational data. Specifically, relations given extensionally by tuples, multivalued dependencies, and Armstrong relations for multivalued dependencies. The semantics of this formalism is based on a closure operator used to calculate the lattice. We prove that this representation calculates the set of multivalued dependencies that hold in a set of tuples as well as an Armstrong relation. We also discuss a number of issues of this representation with respect to the size of the combinatorial objects obtained, and the logical entailment properties compared to those of multivalued dependencies.
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