[Paper Review] SPARQL for a Web of Linked Data: Semantics and Computability (Extended Version)

Olaf Hartig|arXiv (Cornell University)|Mar 7, 2012

Semantic Web and Ontologies16 references3 citations

TL;DR

This paper formally investigates SPARQL's suitability for querying the Web of Linked Data by introducing two novel semantics: full-Web semantics and reachability-based semantics. It establishes theoretical foundations through a data and computation model, proving that SPARQL queries under constant reachability criteria are computable and yield finite results, even in infinitely large Web of Linked Data environments.

ABSTRACT

The World Wide Web currently evolves into a Web of Linked Data where content providers publish and link data as they have done with hypertext for the last 20 years. While the declarative query language SPARQL is the de facto for querying a-priory defined sets of data from the Web, no language exists for querying the Web of Linked Data itself. However, it seems natural to ask whether SPARQL is also suitable for such a purpose. In this paper we formally investigate the applicability of SPARQL as a query language for Linked Data on the Web. In particular, we study two query models: 1) a full-Web semantics where the scope of a query is the complete set of Linked Data on the Web and 2) a family of reachability-based semantics which restrict the scope to data that is reachable by traversing certain data links. For both models we discuss properties such as monotonicity and computability as well as the implications of querying a Web that is infinitely large due to data generating servers.

Motivation & Objective

• To address the lack of theoretical foundations for querying the Web of Linked Data using SPARQL.
• To define a formal data model capturing the infinite, interconnected nature of the Web of Linked Data.
• To introduce a computation model based on Turing machines that reflects limited Web data access capabilities.
• To propose and analyze two query semantics: full-Web and reachability-based, for SPARQL over dynamic, distributed data.
• To investigate key properties such as satisfiability, monotonicity, and computability under these semantics.

Proposed method

• Proposes a theoretical framework based on an infinite data model representing the Web of Linked Data as a network of interlinked RDF documents.
• Introduces a computation model using a restricted type of Turing machine to formalize limited data access during Web queries.
• Defines full-Web semantics, where SPARQL queries evaluate over the entire set of available Linked Data on the Web.
• Introduces a family of reachability-based semantics that restrict query scope to data reachable via specific data links.
• Defines four types of constant reachability criteria: U-constant, T-constant, (U∧T)-constant, and (U∨T)-constant, based on sets of URIs and RDF triples.
• Uses formal definitions and proofs to analyze properties like monotonicity, satisfiability, and computability under each semantics.

Experimental results

Research questions

• RQ1 Can SPARQL be formally adapted as a query language for the entire Web of Linked Data, given its dynamic and potentially infinite nature?
• RQ2 What are the theoretical properties—such as monotonicity and satisfiability—of SPARQL queries under full-Web and reachability-based semantics?
• RQ3 Is it possible to ensure computability of SPARQL queries when the Web of Linked Data is infinitely large?
• RQ4 How do different reachability criteria (U-constant, T-constant, etc.) affect the finiteness and tractability of query results?
• RQ5 What is the relationship between different reachability criteria in terms of restrictiveness and computational feasibility?

Key findings

• The full-Web semantics allows SPARQL queries to consider all available Linked Data on the Web, but raises challenges regarding computability due to potential infiniteness.
• Reachability-based semantics restrict query scope to data reachable via defined criteria, enabling finite and computable query results.
• All constant reachability criteria—U-constant, T-constant, (U∧T)-constant, and (U∨T)-constant—ensure finiteness of reachable data, as proven via bounded sets of URIs and triples.
• The (U∨T)-constant criterion is the least restrictive, while (U∧T)-constant is the most restrictive, with monotonicity properties preserved across the hierarchy.
• The paper proves that SPARQL queries under any of the constant reachability criteria are computable, even in the presence of infinitely large Web of Linked Data.
• The theoretical framework provides a solid foundation for reasoning about query semantics, computability, and correctness in dynamic, distributed Linked Data environments.