扩展对象间基数方向的推理

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摘要翻译：
扩展空间对象之间的方向关系是重要的常识知识。最近，Goyal和Egenhofer提出了一种形式模型，称为基数方向演算(CDC)，用于表示连通平面区域之间的方向关系。CDC可能是对方向信息最具表达能力的定性演算，并引起了人工智能、地理信息科学和图像检索等领域越来越多的兴趣。给定一个具有CDC约束的网络，一致性问题是确定该网络是否可由实际平面上的连通区域实现。本文给出了一个检验基本CDC约束网络一致性的三次算法，证明了CDC约束网络推理一般是一个NP完全问题。对于一个基本CDC约束的一致网络，我们的算法也在三次时间内返回一个“规范”解。这种三次算法也适用于处理可能不连通区域之间的基数方向，在这种情况下，目前最好的算法是时间复杂度为O(n^5)。
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英文标题：
《Reasoning about Cardinal Directions between Extended Objects》
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作者：
Xiaotong Zhang, Weiming Liu, Sanjiang Li, Mingsheng Ying
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最新提交年份：
2009
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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：
  Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between connected plane regions. CDC is perhaps the most expressive qualitative calculus for directional information, and has attracted increasing interest from areas such as artificial intelligence, geographical information science, and image retrieval. Given a network of CDC constraints, the consistency problem is deciding if the network is realizable by connected regions in the real plane. This paper provides a cubic algorithm for checking consistency of basic CDC constraint networks, and proves that reasoning with CDC is in general an NP-Complete problem. For a consistent network of basic CDC constraints, our algorithm also returns a 'canonical' solution in cubic time. This cubic algorithm is also adapted to cope with cardinal directions between possibly disconnected regions, in which case currently the best algorithm is of time complexity O(n^5).
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PDF链接：
https://arxiv.org/pdf/0909.0138

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