Exploring Parallel Tractability of Ontology Materialization

Materialization is an important reasoning service for applications built on the Web Ontology Language (OWL). To make materialization efficient in practice, current research focuses on deciding tractability of an ontology language and designing parallel reasoning algorithms. However, some well-known large-scale ontologies, such as YAGO, have been shown to have good performance for parallel reasoning, but they are expressed in ontology languages that are not parallelly tractable, i.e., the reasoning is inherently sequential in the worst case. This motivates us to study the problem of parallel tractability of ontology materialization from a theoretical perspective. That is, we aim to identify the ontologies for which materialization is parallelly tractable, i.e., in NC complexity. In this work, we focus on datalog rewritable ontology languages. We identify several classes of datalog rewritable ontologies (called parallelly tractable classes) such that materialization over them is parallelly tractable. We further investigate the parallel tractability of materialization of a datalog rewritable OWL fragment DHL (Description Horn Logic) and an extension of DHL that allows complex role inclusion axioms. Based on the above results, we analyze real-world datasets and show that many ontologies expressed in DHL or its extension belong to the parallelly tractable classes.