# Data Complexity and Rewritability of Ontology-Mediated Queries in Metric Temporal Logic under the Event-Based Semantics (Full Version)

## TL;DR

This paper explores the data complexity of answering ontology-mediated queries in metric temporal logic under event-based semantics, providing complexity classifications, rewritings, and lower bounds.

## Contribution

It introduces complexity classifications, rewritings to first-order logic, and establishes lower bounds for ontology-mediated query answering in metric temporal logic.

## Key findings

- Queries can be answered in AC0, NC1, L, NL, P, and coNP depending on the class.
- Rewritings to first-order logic and extensions are provided.
- Lower bounds for data complexity are established.

## Abstract

We investigate the data complexity of answering queries mediated by metric temporal logic ontologies under the event-based semantics assuming that data instances are finite timed words timestamped with binary fractions. We identify classes of ontology-mediated queries answering which can be done in AC0, NC1, L, NL, P, and coNP for data complexity, provide their rewritings to first-order logic and its extensions with primitive recursion, transitive closure or datalog, and establish lower complexity bounds.