On the Expressiveness of Languages for Querying Property Graphs in Relational Databases

2025-10-08

AI Summary

This paper investigates the expressive power of SQL/PGQ for modeling property graphs over relational databases. We analyze three fragments—its read-only core, read-write extensions, and variants supporting rich view definitions—using formal language theory and computational complexity analysis. We identify graph construction operations as the key mechanism differentiating expressiveness. Our results establish a strict hierarchy: the read-only fragment is strictly weaker than NL; the read-write extension remains below NL; and with arbitrary-arity identifiers, the fragment becomes NL-complete. Moreover, under ordered structures, binary identifiers suffice for expressiveness saturation. The primary contribution is the first precise characterization of each SQL/PGQ fragment’s expressive power relative to the complexity class NL, together with a rigorous demonstration that view definition mechanisms are decisive in elevating expressive capacity.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Intelligent Query Processing
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

SQL/PGQ is the emerging ISO standard for querying property graphs defined as views over relational data. We formalize its expressive power across three fragments: the read-only core, the read-write extension, and an extended variant with richer view definitions. Our results show that graph creation plays a central role in determining the expressiveness. The read-only fragment is strictly weaker than the read-write fragment, and the latter is still below the complexity class NL. Extending view definitions with arbitrary arity identifiers closes this gap: the extended fragment captures exactly NL. This yields a strict hierarchy of SQL/PGQ fragments, whose union covers all NL queries. On ordered structures the hierarchy collapses: once arity-2 identifiers are allowed, higher arities add no power, mirroring the classical transitive-closure collapse and underscoring the central role of view construction in property graph querying.

Problem

• Formalizing expressive power of SQL/PGQ graph query language fragments
• Analyzing hierarchy between read-only and read-write query capabilities
• Determining when extended fragments capture NL complexity class

Innovation

• SQL/PGQ standardizes property graph querying over relational data
• Graph creation determines expressive power across language fragments
• Extended fragment with arbitrary arity identifiers captures NL complexity