Relational Similarity-Based Model Of Data Part 1: Foundations And Query Systems

We present a general rank-aware model of data which supports handling of similarity in relational databases. The model is based on the assumption that in many cases it is desirable to replace equalities on values in data tables by similarity relations expressing degrees to which the values are similar. In this context, we study various phenomena which emerge in the model, including similarity-based queries and similarity-based data dependencies. Central notion in our model is that of a ranked data table over domains with similarities which is our counterpart to the notion of relation on relation scheme from the classical relational model. Compared to other approaches which cover related problems, we do not propose a similarity-based or ranking module on top of the classical relational model. Instead, we generalize the very core of the model by replacing the classical, two-valued logic upon which the classical model is built by a more general logic involving a scale of truth degrees that, in addition to the classical truth degrees 0 and 1, contains intermediate truth degrees. While the classical truth degrees 0 and 1 represent nonequality and equality of values, and subsequently mismatch and match of queries, the intermediate truth degrees in the new model represent similarity of values and partial match of queries. Moreover, the truth functions of many-valued logical connectives in the new model serve to aggregate degrees of similarity. The presented approach is conceptually clean, logically sound, and retains most properties of the classical model while enabling us to employ new types of queries and data dependencies. Most importantly, similarity is not handled in an ad hoc way or by putting a "similarity module" atop the classical model in our approach. Rather, it is consistently viewed as a notion that generalizes and replaces equality in the very core of the relational model. We present fundamentals of the formal model and two equivalent query systems which are analogues of the classical relational algebra and domain relational calculus with range declarations. In the sequel to this paper, we deal with similarity-based dependencies.