Two-Dimensional Specification of Universal Quantification in a Graphical Database Query Language

We propose a technique for specifying universal quantification and existential quantification (combined with negation) in a two-dimensional (graphical) database query language. Unlike other approaches that provide set operators to simulate universal quantification, this technique allows a direct representation of universal quantification. We present syntactic constructs for specifying universal and existential quantifications, two-dimensional translation of universal quantification to existential quantification (with negation), and translation of existentially quantified two-dimensional queries to relational queries. The resulting relational queries can be processed directly by many existing database systems. Traditionally, universal quantification has been considered a difficult concept for typical database programmers. We claim that this technique renders universal quantification easy to understand. To substantiate this claim, we provide a simple, easy-to-follow guideline for constructing universally quantified queries. We believe that the direct representation of universal quantification in a two-dimensional language is new and that our technique contributes significantly to the understanding of universal quantification in the context of database query languages.