We introduce and investigate the expressive description logic (DL) ALCSCC++, in which the global and local cardinality constraints introduced in previous papers can be mixed. On the one hand, we prove that this does not increase the complexity of satisfiability checking and other standard inference problems. On the other hand, the satisfiability problem becomes undecidable if inverse roles are added to the languages. In addition, even without inverse roles, conjunctive query entailment in this DL turns out to be undecidable. We prove that decidability of querying can be regained if global and local constraints are not mixed and the global constraints are appropriately restricted. The latter result is based on a locally-acyclic model construction, and it reduces query entailment to ABox consistency in the restricted setting, i.e., to ABox consistency w.r.t. restricted cardinality constraints in ALCSCC, for which we can show an ExpTime upper bound.

中文翻译：

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具有全局和局部基数约束的描述逻辑中的可满足性和查询应答

我们介绍并研究了表达描述逻辑 (DL) ALCSCC++，其中可以混合之前论文中介绍的全局和局部基数约束。一方面，我们证明这不会增加可满足性检查和其他标准推理问题的复杂性。另一方面，如果将反向角色添加到语言中，可满足性问题将变得不可判定。此外，即使没有反向角色，这个 DL 中的联合查询蕴涵也证明是不可判定的。我们证明，如果全局和局部约束不混合并且全局约束得到适当限制，则可以重新获得查询的可判定性。后一个结果基于局部非循环模型构建，并且在受限设置中减少了对 ABox 一致性的查询蕴涵，即，