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

TL;DR

This paper proves that the entailment problem for DL-Lite$_{core}$ ontologies with conjunctive queries involving negation or inequalities is undecidable, highlighting fundamental limitations in reasoning capabilities.

Contribution

It establishes the undecidability of the entailment problem in DL-Lite$_{core}$ with certain complex query features, extending understanding of logical reasoning boundaries.

Findings

Entailment with inequalities is undecidable.

Entailment with safe negation is undecidable.

Results highlight reasoning limitations in DL-Lite$_{core}$.

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.