Relational Model of Data over Domains with Similarities: An Extension for Similarity Queries and Knowledge Extraction

We present an extension of Codd's relational model of data. Our extension is motivated by similarity-based querying. It consists in equipping each domain of attribute values with a similarity relation and in modifying the classical relational model in order to account for issues generated by adding similarities. As a counterpart to data tables over a set of domains of Codd's model, we introduce ranked data tables over domains with similarities. We present a relational algebra, and tuple and domain calculi for our model and prove their equivalence. An interesting point is that our relational algebra contains operations like topk (k best results matching a query). Then, we study functional dependencies extended by similarities, argue that they form a new type of data dependency not captured by the classical model, prove a completeness result w.r.t. Armstrong-like rules, describe non-redundant bases and provide an algorithm for computing the bases. In addition to that, we compare our model with other approaches and outline future research