Unique Characterisability and Learnability of Temporal Instance Queries

TL;DR

This paper investigates which temporal instance queries can be uniquely characterized and learned efficiently from data, focusing on fragments of linear temporal logic and their extensions with description logics.

Contribution

It identifies classes of temporal queries that admit polynomial characterizations and extends these results to combined temporal and description logic query languages.

Findings

Certain path-shaped temporal queries are polynomially characterizable.

Polynomial characterizations can be transferred to combined temporal and description logic queries under specific conditions.

Temporal instance queries are shown to be polynomially learnable using membership queries.

Abstract

We aim to determine which temporal instance queries can be uniquely characterised by a (polynomial-size) set of positive and negative temporal data examples. We start by considering queries formulated in fragments of propositional linear temporal logic LTL that correspond to conjunctive queries (CQs) or extensions thereof induced by the until operator. Not all of these queries admit polynomial characterisations but by restricting them further to path-shaped queries we identify natural classes that do. We then investigate how far the obtained characterisations can be lifted to temporal knowledge graphs queried by 2D languages combining LTL with concepts in description logics EL or ELI (i.e., tree-shaped CQs). While temporal operators in the scope of description logic constructors can destroy polynomial characterisability, we obtain general transfer results for the case when description logic constructors are within the scope of temporal operators. Finally, we apply our characterisations to establish (polynomial) learnability of temporal instance queries using membership queries in the active learning framework.