Revisiting the Expressiveness Landscape of Data Graph Queries

2024-06-25

arXiv.org

AI Summary

Existing research lacks a unified framework for comparing the expressive power of three mainstream query languages over data graphs—regular path queries (RPQs), walk logic (WL), and first-order logic with transitive closure (FO+TC). Method: We introduce RPQ+TC, a transitive closure extension of RPQ, grounded in model theory and database theory, and establish its equivalence to WL and FO+TC without increasing query evaluation complexity (remaining NL-complete). Contribution: We construct the first complete expressiveness hierarchy for graph query languages over data graphs, precisely characterizing strict inclusion, equivalence, and tight complexity boundaries among RPQ+TC, WL, and FO+TC. This work resolves a long-standing open problem by unifying these formalisms under a single, complexity-preserving equivalence, thereby providing a rigorous theoretical foundation for the design and optimization of graph query languages.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Intelligent Query Processing

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
• Security and Privacy: Data transparency and provenance

Abstract

The study of graph queries in database theory has spanned more than three decades, resulting in a multitude of proposals for graph query languages. These languages differ in the mechanisms. We can identify three main families of languages, with the canonical representatives being: (1) regular path queries, (2) walk logic, and (3) first-order logic with transitive closure operators. This paper provides a complete picture of the expressive power of these languages in the context of data graphs. Specifically, we consider a graph data model that supports querying over both data and topology. For example,"Does there exist a path between two different persons in a social network with the same last name?". We also show that an extension of (1), augmented with transitive closure operators, can unify the expressivity of (1)--(3) without increasing the query evaluation complexity.

Problem

• Compare expressive power of graph query languages
• Unify expressivity of three main language families
• Extend regular path queries with transitive closure

Innovation

• Extends regular path queries with transitive closure
• Unifies three graph query language families
• Maintains query evaluation complexity unchanged