A Principled Solution to the Disjunction Problem of Diagrammatic Query Representations

TL;DR

This paper presents a comprehensive solution to the longstanding disjunction problem in diagrammatic query representations, enabling unambiguous, concise, and safe visualizations for complex logical formulas with nested disjunctions.

Contribution

It unifies and extends relational diagrams to handle arbitrary disjunctions while maintaining relational patterns and safety, improving succinctness over previous methods.

Findings

Preserves relational patterns and safety for all well-formed TRC queries.

Can be exponentially more succinct than prior relational diagram approaches.

Successfully solves the disjunction problem for diagrammatic query representations.

Abstract

Finding unambiguous diagrammatic representations for first-order logical formulas and relational queries with arbitrarily nested disjunctions has been a surprisingly long-standing unsolved problem. We refer to this problem as the disjunction problem (of diagrammatic query representations). This work solves the disjunction problem. Our solution unifies, generalizes, and overcomes the shortcomings of prior approaches for disjunctions. It extends the recently proposed Relational Diagrams and is identical for disjunction-free queries. However, it can preserve the relational patterns and the safety for all well-formed Tuple Relational Calculus (TRC) queries, even with arbitrary disjunctions. Additionally, its size is proportional to the original TRC query and can thus be exponentially more succinct than Relational Diagrams.