SIMILARITY-BASED RELATIONS IN DATALOG PROGRAMS

We consider similarity-based relational databases that allow to retrieve approximate data, find data within a given range of distance or similarity, and support imprecise queries. We focus on the recently introduced relational algebra with similarities on [Formula: see text]-relations, which are annotated with multi-dimensional similarity values with each dimension referring to a single attribute. The codomains of the annotated relations are De Morgan frames, and the annotations express the relevance of the tuples as answers to a similarity-based query. In this paper, we study Datalog programs on [Formula: see text]-relations, with and without negation. We describe the least-fixpoint algorithm for safe and rectified Datalog programs on [Formula: see text]-relations with finite support but without negative literals in the body. We further describe the perfect-minimal-fixpoint algorithm of a Datalog program on [Formula: see text]-relations with finite support and negative literals in the body when rules are safe, rectified and stratified. We introduce the idea of controlling the calculation of the annotations such that the tuples that enter an IDB relation last will be announced less desirable than those that enter first. For this we define a damping function that augments/diminishes the individual annotations that contribute to the final annotations of tuples. With a damping function, for instance, long chains of inferences may be made significantly less desirable or even totally undesirable.