Generalized Region Connection Calculus
Generalized Region Connection Calculus
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DOI：
10.1016/j.artint.2004.05.012
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发表时间：
2004-12
期刊：
影响因子：
--
通讯作者：
Sanjiang Li;M. Ying
中科院分区：
文献类型：
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作者：
Sanjiang Li;M. Ying
区域连接演算（Region Connection Calculus， RCC）是一种被广泛引用的高级（定性）空间推理系统。RCC采用连续的空间表示。这与现在从物理记录设备获得的空间信息在形式上总是数字的这一事实形成鲜明对比，因此隐含地使用了空间的离散表示。最近，高尔顿发展了一种与RCC相似的离散空间理论，但问题仍然在于，我们能否有一种定性空间推理理论，既承认离散空间模型，也承认连续空间模型？本文旨在建立一个既能容纳离散空间信息又能容纳连续空间信息的形式化理论，并对区域连接演算进行了推广。新理论GRCC采用了两个基本概念：局部的流变概念和连接的拓扑概念。离散空间的RCC理论和Galton理论都是GRCC理论的扩展。通过对GRCC模型的一些操作，阐明了连续模型与离散模型的关系。特别地，我们提出了一种构造可数RCC模型作为有限模型集合的直接极限的一般方法。与由正则连通空间产生的标准碾压混凝土模型相比，这些可数模型具有从基本区域到每个区域都可以在有限步内构造的良好性质。给出了两个有趣的可数RCC模型：一个是最小RCC模型，另一个是连续空间R2的可数子模型。
The Region Connection Calculus (RCC) is one of the most widely referenced system of high-level (qualitative) spatial reasoning. RCC assumes a continuous representation of space. This contrasts sharply with the fact that spatial information obtained from physical recording devices is nowadays invariably digital in form and therefore implicitly uses a discrete representation of space. Recently, Galton developed a theory of discrete space that parallels RCC, but question still lies in that can we have a theory of qualitative spatial reasoning admitting models of discrete spaces as well as continuous spaces? In this paper we aim at establishing a formal theory which accommodates both discrete and continuous spatial information, and a generalization of Region Connection Calculus is introduced. GRCC, the new theory, takes two primitives: the mereological notion of part and the topological notion of connection. RCC and Galton's theory for discrete space are both extensions of GRCC. The relation between continuous models and discrete ones is also clarified by introducing some operations on models of GRCC. In particular, we propose a general approach for constructing countable RCC models as direct limits of collections of finite models. Compared with standard RCC models given rise from regular connected spaces, these countable models have the nice property that each region can be constructed in finite steps from basic regions. Two interesting countable RCC models are also given: one is a minimal RCC model, the other is a countable sub-model of the continuous space R2.