Someone slept in my bed! On the entailment problem for conjunctive queries with safe negation over DL-Lite$_{core}$ knowledge bases

2026-07-06

AI Summary

The decidability of answering conjunctive queries with safe negation over DL-Lite$_{core}$ knowledge bases has long remained an open problem. This work resolves this longstanding theoretical question in knowledge representation and reasoning by establishing the undecidability of the query entailment problem through a rigorous reduction from the halting problem for Turing machines. By demonstrating that even under the syntactic restriction of safe negation, query answering in DL-Lite$_{core}$ is undecidable, the paper precisely delineates the boundary of the language’s reasoning capabilities. This result provides a crucial theoretical foundation for future investigations into tractable fragments and extensions of description logics accommodating negation.

Abstract

We solve a long standing open problem, showing that the query answering for conjunctive queries with safe negation, over DL-Lite$_{core}$ knowledge bases, is undecidable.

Problem

• conjunctive queries
• safe negation
• DL-Lite$_{core}$
• query answering
• undecidability

Innovation

• conjunctive queries
• safe negation
• DL-Lite$_{core}$
• undecidability
• query answering