IDLOG: extending the expressive power of deductive database languages

Abstract

The expressive power of pure deductive database languages, such as DATALOG and stratified DATALOGS, is limited in a sense that some useful queries such as functions involving aggregation are not definable in these languages. Our concern in this paper is to provide a uniform logic framework for deductive databases with greater expressive power. It has been shown that with a linear ordering on the domain of the database, the expressive power of some database languages can be enhanced so that some functions involving aggregation can be defined. Yet, a direct implementation of the linear ordering in deductive database languages may seem unintuitive, and may not be very efficient to use in practice. We propose a logic for deductive databases which employs the notion of “identifying each tuple in a relation”. Through the use of these tuple-identifications, different linear orderings are defined as a result. This intuitively explains the reason why our logic has greater expressive power. The proposed logic language is non-deterministu in nature. However, non-determinism is not the real reason for the enhanced expressive power. A deterministic subset of the programs in this language is computational complete in the sense that it defines all the computable deterministic queries. Although the problem of deciding whether a program is in this subset is in general undecidable, we do provide a rather general sufficient test for identifying such programs. Also discussed in this paper is an extended notion of queries which allows both the input and the output of a query to contain interpreted constants of an infinite domain. We show that extended queries involving aggregation can also be defined in the language.