Our concern is the problem of efficiently determining the data complexity of answering queries mediated by description logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology-based data access and datalog optimisation, this problem is known to be computationally very complex in general, with no explicit syntactic characterisations available. In this article, aiming to understand the fundamental roots of this difficulty, we strip the problem to the bare bones and focus on Boolean conjunctive queries mediated by a simple covering axiom stating that one class is covered by the union of two other classes. We show that, on the one hand, these rudimentary ontology-mediated queries, called disjunctive sirups (or d-sirups), capture many features and difficulties of the general case. For example, answering d-sirups is Pi^p_2-complete for combined complexity and can be in AC0 or LogSpace-, NL-, P-, or coNP-complete for data complexity (with the problem of recognising FO-rewritability of d-sirups being 2ExpTime-hard); some d-sirups only have exponential-size resolution proofs, some only double-exponential-size positive existential FO-rewritings and single-exponential-size nonrecursive datalog rewritings. On the other hand, we prove a few partial sufficient and necessary conditions of FO- and (symmetric/linear-) datalog rewritability of d-sirups. Our main technical result is a complete and transparent syntactic AC0/NL/P/coNP tetrachotomy of d-sirups with disjoint covering classes and a path-shaped Boolean conjunctive query. To obtain this tetrachotomy, we develop new techniques for establishing P- and coNP-hardness of answering non-Horn ontology-mediated queries as well as showing that they can be answered in NL.
翻译：我们关心的问题是,如何有效地确定以描述逻辑的逻辑和构建对标准数据库查询的最佳改写,来解答问题的数据复杂性。我们从基于本体的数据访问和数据优化中发现,这个问题一般而言在计算上非常复杂,没有明确的合成特性。在本篇文章中,为了了解这一困难的根本根源,我们将问题分解到赤骨上,并关注通过简单覆盖轴心来调解的布尔伦调调质查询,指出一个班由另外两个班的结合所覆盖。我们表明,一方面,这些以本体为基础的基于本体的数据访问和数据优化,称为不相干调试的调子(或dirsirsirups), 捕捉到一般案例的许多特点和困难。例如,解答 dirups(píp_2-compilation), 可以在 AC0 或 Log Space-、NL-、P-或 CoNP-com-commissional 调解析中(我们只能识别完全的OFO-rent-rick-lational-deal-lational-deal-deal-deal-deal-deal-lational-lational-lational-lational-lational-lational-lational-lational-lational-lational-lational-lational-lational-lational-al-lational-lational-lis-lis-lislation-lation-lation-lation-lation-lation-lation-lation-lation-lation-lation-lation-lation-lation-de-de-l-lation-de-de-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-lick-l-l-lation-l-l-lick-lation-l-l-l
相关内容
微信扫码咨询专知VIP会员