Lattice Characterization of Armstrong and Symmetric Dependencies
PhD thesis, Universitat Politecnica de Catalunya.
Dependencies are restrictions or
constraints that apply to a set of data.
They can be found in different
realms: Database Theory, Data Mining, Artificial Intelligence,
Propositional Logic, etc.
Lattice characterization of dependencies has been studied from two
different points of view: its theoretical foundations and its applications,
mainly in the fields of database theory and knowledge discovery.
In the first part of this thesis,
we present a generic and modular lattice characterization
of a set of Armstrong and symmetric dependencies,
from a semantic and a syntactical point of view,
in terms of Formal Concept Analysis,
a formalism used in knowledge discovery.
In the second part of this thesis,
two applications of those lattice characterizations
are also presented: the definition of Armstrong relations for Armstrong
and symmetric dependencies, and the definition
of a formal context for symmetric dependencies.