Unique Characterisability and Learnability of Temporal Queries Mediated by an Ontology

TL;DR

The paper develops a principled framework to transfer results on unique characterisation and exact learnability from atemporal ontology-mediated queries to temporal data queries. By introducing temporalised query languages based on $LTL$ and combining them with DL ontologies (e.g., DL-Lite, ALCHI, ELHIF), it derives transfer theorems that preserve (polynomial) learnability under containment-reduction and safety assumptions, and identifies conditions under which polysize or exponential unique characterisations are achievable. It also presents learning algorithms that exploit these characterisations to identify target queries from membership queries, linking explainability and synthesis to temporal ontology-mediated querying. The results advance practical avenues for automating query construction and explanation over temporal data, while outlining clear boundaries and open questions for future work.

Abstract

Algorithms for learning database queries from examples and unique characterisations of queries by examples are prominent starting points for developing automated support for query construction and explanation. We investigate how far recent results and techniques on learning and unique characterisations of atemporal queries mediated by an ontology can be extended to temporal data and queries. Based on a systematic review of the relevant approaches in the atemporal case, we obtain general transfer results identifying conditions under which temporal queries composed of atemporal ones are (polynomially) learnable and uniquely characterisable.

Theorems & Definitions (72)

• Lemma 1
• proof
• Lemma 2
• Theorem 1
• Theorem 2
• Example 1
• Theorem 3
• Theorem 4
• Theorem 5
• Theorem 6