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摘要翻译：
定性空间推理中的一个重要问题是相对方向的表示。在本文中，我们给出了简单的几何规则，使有向点之间的相对方向推理成为可能。这个框架，面向点代数OPRA_m，具有可伸缩的粒度M。我们提出了一个简单的计算OPRA_m组合表的算法，并证明了该算法的正确性。利用一个组合表，对一组OPRA语句进行代数闭包就足以解决空间导航任务。事实证明，可伸缩粒度在这些导航任务中很有用。
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英文标题：
《Qualitative Reasoning about Relative Direction on Adjustable Levels of
Granularity》
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作者：
Till Mossakowski, Reinhard Moratz
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最新提交年份：
2010
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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：
An important issue in Qualitative Spatial Reasoning is the representation of relative direction. In this paper we present simple geometric rules that enable reasoning about relative direction between oriented points. This framework, the Oriented Point Algebra OPRA_m, has a scalable granularity m. We develop a simple algorithm for computing the OPRA_m composition tables and prove its correctness. Using a composition table, algebraic closure for a set of OPRA statements is sufficient to solve spatial navigation tasks. And it turns out that scalable granularity is useful in these navigation tasks.
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PDF链接：
https://arxiv.org/pdf/1011.0098
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