Lattice-structured domains, imperfect data and inductive queries

Abstract

The relational model, as proposed by Codd, contained the concept of relations as tables composed of tuples of single valued attributes taken from a domain. In most of the early literature this domain was assumed to consist of elementary items such as simple (atomic) values, defined complex data types or arbitrary length binary objects. Subsequent to that the nested relational or non-first normal form model allowing set-valued or relation-valued attributes was proposed. Within this model an attribute could take multiple values or complete relations as values. This paper presents a further extension to the relational model which allows domains to be defined as a hierarchy (specifically a lattice) of concepts, shows how different types of imperfect knowledge can be represented in attributes defined over such domains, and demonstrates how lattices allow the accommodation of some forms of inductive queries. While our model is applied to flat relations, many of the results given are applicable also to nested relations. Necessary extensions to the relational algebra and SQL, a justification for the extension in terms of application areas and future research areas are also discussed.