We study ontology-mediated querying in the case where ontologies are formulated in the guarded fragment of first-order logic (GF) or extensions thereof with counting and where the actual queries are (unions of) conjunctive queries. Our aim is to classify the data complexity and Datalog rewritability of query evaluation depending on the ontology O , where query evaluation w.r.t. O is in PT ime (resp. Datalog rewritable) if all queries can be evaluated in PT ime w.r.t. O (resp. rewritten into Datalog under O ), and co NP-hard if at least one query is co NP-hard w.r.t. O . We identify several fragments of GF that enjoy a dichotomy between Datalog-rewritability (which implies PT ime ) and co NP-hardness as well as several other fragments that enjoy a dichotomy between PT ime and co NP-hardness, but for which PT ime does not imply Datalog-rewritability. For the latter, we establish and exploit a connection to constraint satisfaction problems. We also identify fragments for which there is no dichotomy between PT ime and co NP. To prove this, we establish a non-trivial variation of Ladner’s theorem on the existence of NP-intermediate problems. Finally, we study the decidability of whether a given ontology enjoys PT ime query evaluation, presenting both positive and negative results, depending on the fragment.

中文翻译：

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带有保护片段的本体介导查询中的二分法

我们研究了本体介导的查询，其中本体是在一阶逻辑（GF）的受保护片段中制定的，或者具有计数的扩展，并且实际查询是连接查询（的联合）。我们的目标是根据本体对查询评估的数据复杂性和 Datalog 可重写性进行分类○, 其中查询评估 wrt○在 PT我(resp. Datalog rewritable) 如果所有查询都可以在 PT 中进行评估我写○（分别重写到 Datalog 下○）， 和合作如果至少有一个查询是 NP-hard合作NP-hard wrt○. 我们确定了几个 GF 片段，它们在 Datalog 可重写性（这意味着 PT我） 和合作NP 硬度以及其他几个在 PT 之间具有二分法的片段我和合作NP 硬度，但对于 PT我并不意味着 Datalog 可重写。对于后者，我们建立并利用与约束满足问题的联系。我们还确定了 PT 之间没有二分法的片段我和合作NP。为了证明这一点，我们建立了关于存在 NP 中间问题的 Ladner 定理的非平凡变体。最后，我们研究给定本体是否享有 PT 的可判定性我查询评估，根据片段显示正面和负面结果。