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摘要翻译：
我们研究了描述逻辑ALCQ和ALCQI与基于概念基数限制的术语形式化相结合的复杂性。这些组合可以自然地嵌入到C^2中，C^2是带有计数量词的谓词逻辑的两个变量片段，从而在nexptime中产生可判定性。由于具有基数限制的ALCQI具有与C^2(NExpTime-complete)相同的复杂度，我们证明了该方法能得到ALCQI的最优解。相反，我们表明对于ALCQ，问题可以在Exptime内解决。这个结果是通过将有基数限制的推理约简为用一般公理的（通常较弱的）术语形式的推理而得到的。利用同样的约简，我们证明了对于带有标称项的ALCQI的推广，用一般公理进行推理是一个时间完备的问题。最后，我们对这一结果进行了进一步的改进，证明了具有标称项的ALCQI的纯概念可满足性是nexptime-complete的。在没有标称项的情况下，这个问题是pspace-complete。
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英文标题：
《The Complexity of Reasoning with Cardinality Restrictions and Nominals
in Expressive Description Logics》
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作者：
S. Tobies
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最新提交年份：
2011
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分类信息：
一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C^2, the two variable fragment of predicate logic with counting quantifiers, which yields decidability in NExpTime. We show that this approach leads to an optimal solution for ALCQI, as ALCQI with cardinality restrictions has the same complexity as C^2 (NExpTime-complete). In contrast, we show that for ALCQ, the problem can be solved in ExpTime. This result is obtained by a reduction of reasoning with cardinality restrictions to reasoning with the (in general weaker) terminological formalism of general axioms for ALCQ extended with nominals. Using the same reduction, we show that, for the extension of ALCQI with nominals, reasoning with general axioms is a NExpTime-complete problem. Finally, we sharpen this result and show that pure concept satisfiability for ALCQI with nominals is NExpTime-complete. Without nominals, this problem is known to be PSpace-complete.
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PDF链接：
https://arxiv.org/pdf/1106.0239
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