Multiset semantics in SPARQL, Relational Algebra and Datalog

2026-05-01

AI Summary

This work addresses a critical gap in the formal understanding of SPARQL under multiset semantics by providing the first systematic algebraic and logical characterization of its core operators—AND, UNION, FILTER, EXCEPT, and SELECT. The paper establishes a precise correspondence between SPARQL, non-recursive Datalog with safe negation extended to support multisets, and multiset relational algebra equipped with projection, selection, natural join, arithmetic union, and difference. It rigorously proves the equivalence in expressive power among these three formalisms under multiset semantics. This result furnishes SPARQL with a unified theoretical foundation, significantly strengthening the logical and algebraic semantics underpinning query evaluation in the Semantic Web.

Abstract

The paper analyzes and characterizes the algebraic and logical structure of the multiset semantics for SPARQL patterns involving AND, UNION, FILTER, EXCEPT, and SELECT. To do this, we align SPARQL with two well-established query languages: Datalog and Relational Algebra. Specifically, we study (i) a version of non-recursive Datalog with safe negation extended to support multisets, and (ii) a multiset relational algebra comprising projection, selection, natural join, arithmetic union, and except. We prove that these three formalisms are expressively equivalent under multiset semantics.

Problem

• multiset semantics
• SPARQL
• Relational Algebra
• Datalog
• expressive equivalence

Innovation

• multiset semantics
• SPARQL
• Datalog
• Relational Algebra
• expressive equivalence