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arXiv 1611.02453cs.AI
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描述逻辑本体论的数据复杂度

The Data Complexity of Description Logic Ontologies

University of Bremen(不来梅大学);University of Liverpool(利物浦大学)

Carsten Lutz, Frank Wolter

AI总结:

本文分析ALC族描述逻辑本体的数据复杂度,证明深度为一的ALCFI及无深度限制的ALC/ALCI本体存在PTime/coNP二分法,而ALCF本体无此二分法且PTime求值判定不可判定,并探讨与Datalog重写的关联。

摘要:

我们分析了本体中介查询的数据复杂度,其中本体以ALC家族的描述逻辑(DL)表述,查询为合取查询、正存在查询或无环合取查询。我们的方法是非均匀的,即旨在理解每个单独本体的复杂度,而非针对以某种语言表述的所有本体。在此过程中,我们对查询进行量化,并关注例如给定本体是否所有查询都能在多项式时间内求值的问题。我们的结果包括:深度为一的ALCFI本体存在PTime/coNP二分法,深度不受限的ALC和ALCI本体存在相同的二分法,而ALCF本体则不存在此类二分法。对于后者,我们还进一步证明,判定给定本体是否允许PTime查询求值是不可判定的。我们还考虑了PTime查询求值与(一元)Datalog重写之间的联系。

英文摘要:

We analyze the data complexity of ontology-mediated querying where the ontologies are formulated in a description logic (DL) of the ALC family and queries are conjunctive queries, positive existential queries, or acyclic conjunctive queries. Our approach is non-uniform in the sense that we aim to understand the complexity of each single ontology instead of for all ontologies formulated in a certain language. While doing so, we quantify over the queries and are interested, for example, in the question whether all queries can be evaluated in polynomial time w.r.t. a given ontology. Our results include a PTime/coNP-dichotomy for ontologies of depth one in the description logic ALCFI, the same dichotomy for ALC- and ALCI-ontologies of unrestricted depth, and the non-existence of such a dichotomy for ALCF-ontologies. For the latter DL, we additionally show that it is undecidable whether a given ontology admits PTime query evaluation. We also consider the connection between PTime query evaluation and rewritability into (monadic) Datalog.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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