On the entailment problem for DL-Lite$_{core}$ ontologies and conjunctive queries with negation

2025-10-27

AI Summary

This paper investigates the decidability of the conjunctive query (CQ) entailment problem with negation under DL-Lite$_{core}$ ontologies. Specifically, it addresses two significant CQ extensions: CQs with inequalities (≠) and CQs with safe negation. Using constructive reductions and formal logical modeling, the paper establishes, for the first time, the undecidability of query entailment for both extensions in DL-Lite$_{core}$. This result transcends prior work—limited to positive queries or syntactically restricted forms of negation—and systematically delineates the theoretical limits of expressing negation within DL-Lite$_{core}$. It thereby exposes a fundamental constraint on ontology reasoning capabilities in this lightweight description logic. By integrating techniques from description logic and database query theory, the study provides critical theoretical insights into the expressivity–computability trade-off inherent in lightweight ontology languages.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

We show that the entailment problem, for a given entailment problem for DL-Lite$_{core}$ ontology, and given conjunctive query with inequalities, is undecidable. We also show that this problem remains undecidable if conjunctive queries with safe negation are considered instead of conjunctive queries with inequalities.

Problem

• Proves undecidability of entailment problem in DL-Litecore ontologies
• Shows undecidability for conjunctive queries with inequalities
• Demonstrates undecidability persists with safe negation queries

Innovation

• Proves undecidability of DL-Litecore ontology entailment
• Extends undecidability to conjunctive queries with inequalities
• Shows same undecidability for queries with safe negation