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 depen- dencies from databases and also several approaches to functional depen- dencies in fuzzy databases. We show a connection to other interpretation of formulas A ) B which we studied before. Although the two interpre- tations are dierent, they have the same concept of semantic entailment. This connection enables us to find a complete axiomatization of reason- ing with our attribute dependencies. We prove completeness theorem in the usual as well as in a so-called graded style. The connection also en- ables 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.

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