Characterizing the Program Expressive Power of Existential Rule Languages

TL;DR

This paper investigates the expressive power of various existential rule languages used in ontology-mediated query answering, providing new characterizations through model-theoretic and automata-theoretic methods.

Contribution

It introduces novel characterizations of the program expressive power for key existential rule languages, enhancing understanding of their domain knowledge representation capabilities.

Findings

Characterizations for TGDs, linear TGDs, and disjunctive TGDs

Use of model-theoretic and automata-theoretic properties

Tools for identifying definability in OMQA

Abstract

Existential rule languages are a family of ontology languages that have been widely used in ontology-mediated query answering (OMQA). However, for most of them, the expressive power of representing domain knowledge for OMQA, known as the program expressive power, is not well-understood yet. In this paper, we establish a number of novel characterizations for the program expressive power of several important existential rule languages, including tuple-generating dependencies (TGDs), linear TGDs, as well as disjunctive TGDs. The characterizations employ natural model-theoretic properties, and automata-theoretic properties sometimes, which thus provide powerful tools for identifying the definability of domain knowledge for OMQA in these languages.