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Similarity in relational databases and in information systems theory

Pomykała J. A.

Demonstratio Mathematica

2002

Vol. 35, nr 4

927-953

The motivation of the paper comes form two sources-theory of relational databases (RDB) and the information systems theory (1ST). On the one hand functional and multivalued dependencies in RDB capture a large portion of the semantics of real world relations, but it has proved useful to consider also other classes of dependencies eg. join or template dependencies. It is known that there is an equivalence between functional dependencies in a relational database and a certain fragment of prepositional logic. This was extended by many authors to include both functional and multivalued dependencies, and complete axiomatizations were given. Also for fully join and for template dependencies complete axioms are known. Dependencies of attributes in information systems theory (1ST) can be expressed in terms of indiscernibility relations derived from the system, in particular data constraints are modeled by them. A generalization of this theory to dependencies in other information frames is an open problem. We propose here an attempt to solve it for frames based on similarity relations. We define dependencies for weak and strong similarity relations with parameters and develop logical formalism for reasoning about them. In RDB theory we propose the notion of "similarity of records", giving the motivations from medicine (eg. similar symptoms should imply similar diagnosis or treatment) and from economy (similar market informations should be followed by similar economic movement or decisions). In consequence we introduced the notions of similarity dependency between sets of attributes in RDB. Examples are shown that the notion introduced is different from functional, multivalued, join and template dependencies in RDB. We analyse Armstrong axioms and Fagin axioms in this context, finding sound (but as yet not necessarily complete) axiomatization of similarity dependency in RDB.