Materialization is an important reasoning service for many ontology-based applications, but the rapid growth of semantic data poses the challenge to efficiently perform materialization on large-scale ontologies. Parallel materialization algorithms work well for some ontologies, although the reasoning problem for the used ontology language is not in NC, i.e., the theoretical complexity class for parallel tractability. This motivates us to study the problem of parallel tractability of ontology materialization from a theoretical perspective. We focus on the datalog rewritable ontology languages DL-Lite and Description Horn Logic (DHL) and propose algorithms, called NC algorithms, to identify classes of ontologies for which materialization is tractable in parallel. To verify the practical usability of the above results, we analyze different benchmarks and real-world datasets, including LUBM and the YAGO ontology, and show that for many ontologies expressed in DHL materialization is tractable in parallel. The implementation of our optimized parallel algorithm shows performance improvements over the highly optimized state-of-the-art reasoner RDFox on ontologies for which materialization is tractable in parallel.

物化是许多基于本体的应用程序的重要推理服务，但是语义数据的快速增长提出了在大规模本体上有效执行物化的挑战。尽管所用本体语言的推理问题不在NC中，即并行可处理性的理论复杂度类别，但并行实现算法在某些本体上仍能很好地工作。这促使我们从理论的角度研究本体实现的并行可处理性问题。我们专注于数据记录可重写本体语言DL-Lite和描述喇叭逻辑（DHL），并提出了称为NC的算法算法，以识别可并行实现的本体类别。为了验证上述结果的实际可用性，我们分析了不同的基准和现实世界的数据集，包括LUBM和YAGO本体，并表明对于DHL实现而言，许多本体可并行处理。我们优化的并行算法的实现显示了在本体上可并行处理的高度优化的最新推理机RDFox的性能提升。