Functional Dependencies of Data Tables Over Domains with Similarity Relations

We study attribute dependencies in a setting of fuzzy logic. Our dependencies are described by formulas A ⇒ B where A and B are fuzzy sets of attributes. The meaning of A ⇒ B is that any two objects that have similar values on attributes from A have also similar values on attributes from B. Our approach generalizes classical functional dependencies from databases and also several approaches to functional dependencies in fuzzy databases. We show a connection to other interpretation of formulas A ⇒ B which we studied before. Although the two interpretations are different, they have the same concept of semantic entailment. This connection enables us to find a complete axiomatization of reasoning with our attribute dependencies. We prove completeness theorem in the usual as well as in a so-called graded style. The connection also enables us to compute a complete non-redundant basis of all functional dependencies which are true in a data table. We present examples and and outline future research.