In contrast to qualitative linear temporal logics, which can be used to state that some property will eventually be satisfied, metric temporal logics allow us to formulate constraints on how long it may take until the property is satisfied. While most of the work on combining description logics (DLs) with temporal logics has concentrated on qualitative temporal logics, there is a growing interest in extending this work to the quantitative case. In this article, we complement existing results on the combination of DLs with metric temporal logics by introducing interval-rigid concept and role names. Elements included in an interval-rigid concept or role name are required to stay in it for some specified amount of time. We investigate several combinations of (metric) temporal logics with A ℒ C by either allowing temporal operators only on the level of axioms or also applying them to concepts. In contrast to most existing work on the topic, we consider a timeline based on the integers and also allow assertional axioms. We show that the worst-case complexity does not increase beyond the previously known bound of 2-E xp S pace and investigate in detail how this complexity can be reduced by restricting the temporal logic and the occurrences of interval-rigid names.

中文翻译：

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具有区间刚性名称的度量时间描述逻辑

与可用于说明某些属性最终将得到满足的定性线性时间逻辑相比，度量时间逻辑允许我们制定关于直到满足该属性可能需要多长时间的约束。虽然将描述逻辑 (DL) 与时间逻辑相结合的大部分工作都集中在定性时间逻辑上，但人们越来越有兴趣将这项工作扩展到定量案例。在本文中，我们通过引入 DL 与度量时间逻辑来补充现有的结果区间刚性概念和角色名称。包含在区间刚性概念或角色名称中的元素需要在其中停留一段时间。我们研究了（度量）时间逻辑的几种组合一种ℒC通过仅在公理级别上允许时间运算符或将它们应用于概念。与该主题的大多数现有工作相比，我们考虑基于整数的时间线，并且还允许断言公理。我们表明，最坏情况的复杂性不会增加超出先前已知的 2-E 界限经验小号步伐并详细研究如何通过限制时间逻辑和间隔刚性名称的出现来降低这种复杂性。