A Lattice Representation of Relations, Multivalued Dependencies and Armstrong Relations
Jaume Baixeries and José Balcázar
Complementary Proceedings of the 13th International Conference on Conceptual Structures
We present a lattice-based formalism to relate, in a novel way,
different representation methods for relational data.
Specifically, relations given extensionally by tuples,
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.