Relational Diagrams: a pattern-preserving diagrammatic representation of non-disjunctive Relational Queries

Analyzing relational languages by their logical expressiveness is well understood. Something not well understood or even formalized is the vague concept of relational query patterns. What are query patterns? And how can we reason about query patterns across different relational languages, irrespective of their syntax and their procedural or declarative nature? In this paper, we formalize the concept of query patterns with a variant of pattern-preserving mappings between the relational atoms of queries. This formalism allows us to analyze the relative pattern expressiveness of relational query languages and to create a hierarchy of languages with equal logical expressiveness yet different pattern expressiveness. In this analysis, relational calculus can expressive more patterns than the basic operators of relational algebra. We additionally contribute an intuitive, complete, and sound diagrammatic representation of safe relational calculus that is not only relationally complete, but can also express all logical patterns for the large and useful fragment of non-disjunctive relational calculus. Among all diagrammatic representations for relational queries that we are aware of, this is the only one that is relationally complete and that can represent all logical patterns in the non-disjunctive fragment.