为本体查询答案责任度计算提供可处理的算法边界。
Tractable Responsibility Measures for Ontology-Mediated Query Answering
- 基于加权最小支撑的谢林值方法计算责任分数。
- 对可一阶重写的本体查询,数据复杂度为多项式时间。
- 在常见DL-Lite语言下,特定受限查询类可高效计算责任度。
近期定量解释查询答案的研究使用责任度量为事实分配得分,以量化其对特定答案的贡献。本文研究本体中介查询回答中此类责任分数的计算复杂性,聚焦于一种基于谢林值、定义为加权最小支撑(WSMS)之和的新责任度量。利用数据库领域的已有成果,我们证明:对于可一阶重写的本体查询类,该度量具有多项式数据复杂度;而当本体语言能编码可达性查询(如通过公理 ∃R.A ⊑ A)时,问题变为“shP”难。为进一步厘清可处理性边界,我们分析了联合复杂性:即使无本体,只要查询语言支持合取,原子查询即已不可行;而对于“良好行为”的合取查询并集,同样难以计算。相反,通过对结构受限的合取查询进行细致分析,我们识别出若干在常见DL-Lite方言中可实现高效计算的责任度量类。
原文摘要 · Abstract (English)
Recent work on quantitative approaches to explaining query answers employs responsibility measures to assign scores to facts in order to quantify their respective contributions to obtaining a given answer. In this paper, we study the complexity of computing such responsibility scores in the setting of ontology-mediated query answering, focusing on a very recently introduced family of Shapley-value-based responsibility measures defined in terms of weighted sums of minimal supports (WSMS). By exploiting results from the database setting, we can show that such measures enjoy polynomial data complexity for classes of ontology-mediated queries that are first-order-rewritable, whereas the problem becomes "shP"-hard when the ontology language can encode reachability queries (via axioms like $\exists R. A \sqsubseteq A$). To better understand the tractability frontier, we next explore the combined complexity of WSMS computation. We prove that intractability applies already to atomic queries if the ontology language supports conjunction, as well as to unions of `well-behaved' conjunctive queries, even in the absence of an ontology. By contrast, our study yields positive results for common DL-Lite dialects: by means of careful analysis, we identify classes of structurally restricted conjunctive queries (which intuitively disallow undesirable interactions between query atoms) that admit tractable WSMS computation.
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