In data managment, deciding that two values are equal is a problem more complex and more subtle than it seems. In fact, only domain experts can define the meaning of 'equality' on their data. However, declarative frameworks with which experts can specify their definition of equality at a high level of abstraction are missing. In this talk, we introduce a lattice-based framework to cope with this issue. For each attribute of the relation scheme, we give a comparability function mapping every pair of the attribute's domain to a value in a similarity scale ordered as a (truth) lattice. Using particular {0, 1}-interpretations of each truth lattices, we can model several meaning of equalities. These interpretations are called realities. We discuss functional dependencies in this framework. More precisely, when we compare each pair of tuples of a relation, we obtain an abstract lattice and hence a semantic for abstract functional dependencies. Using realities, the classical meaning of FDs can be recovered. We also apply the notions of possible/certain answers to FDs and realities, and briefly mention some complexity results.
BIO I am currently a Ph.D student under the supervision of Prof. Lhouari Nourine, at the Université Clermont Auvergne. My research mainly focuses on lattices, their representations and related algorithms with possible applications in databases or knowledge space theory
