Logical Foundations for Similarity-Based Databases

Extensions of relational databases which aim at utilizing various aspects of similarity and imprecision in data processing are widespread in the literature. A need for development of solid foundations for such extensions, sometimes called similarity-based relational databases, has repeatedly been emphasized by leading database experts. This paper argues that, contrary to what may be perceived from the literature, solid foundations for similarity-based databases can be developed in a conceptually simple way. In this paper, we outline such foundations and develop in detail a part of the the facet related to similarity-based queries and relational algebra. The foundations are close in principle to Codd's foundations for relational databases, yet they account for the main aspects of similarity-based data manipulation. A major implication of the paper is that similarity-based data manipulation can be made an integral part of an extended, similarity-based, relational model of data, rather than glued atop the classic relational model in an ad hoc manner.