Characterizing the Program Expressive Power of Existential Rule Languages
This work addresses a foundational gap in understanding how well existential rule languages can represent domain knowledge for ontology-mediated query answering, which is incremental in providing tools for definability identification.
The paper tackles the problem of characterizing the program expressive power of existential rule languages for ontology-mediated query answering, establishing novel characterizations for languages like TGDs, linear TGDs, and disjunctive TGDs using model-theoretic and automata-theoretic properties.
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.