Properties of Euler Diagrams
Properties of Euler Diagrams
复制标题
欧拉图的性质
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
John Taylor
中科院分区：
文献类型：
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作者：
Gem Stapleton;P. Rodgers;J. Howse;John Taylor
欧拉图有许多应用领域，基于它们的语言种类繁多。在软件工程方面，这些领域包括建模和规范，包括从正式的角度。在所有这些应用领域中，理想情况下以一种好的方式提供布局欧拉图的工具是可取的。各种各样的“美好”概念可以与欧拉图可能具有或不具有的某些性质相关联。事实上，迄今为止开发的相关布局算法产生的欧拉图具有某些属性集，有时称为良构性条件。然而，欧拉图并没有一个普遍认同的定义，其上的性质也很少被精确地描述。在本文中，我们提供了一个非常一般的定义的欧拉图，它可以以不同的方式进行约束，以匹配各种定义，存在于文献中。实际上，所施加的约束对应于图可能拥有的属性。本文的一个贡献是提供这些属性的正式定义，我们讨论这些属性可能是可取的。我们的欧拉图的定义和这些属性的形式化提供了一个通用的语言欧拉图社区利用。使用共同语言的一个结果是更好地整合研究成果，使研究成果更容易获得。
Euler diagrams have numerous application areas, with a large variety of languages based on them. In relation to software engineering, such areas encompass modelling and specification including from a formal perspective. In all of these application areas, it is desirable to provide tools to layout Euler diagrams, ideally in a nice way. Various notions of `niceness' can be correlated with certain properties that an Euler diagram may or may not possess. Indeed, the relevant layout algorithms developed to date produce Euler diagrams that have certain sets of properties, sometimes called well-formedness conditions. However, there is not a commonly agreed definition of an Euler diagram and the properties imposed on them are rarely stated precisely. In this paper, we provide a very general definition of an Euler diagram, which can be constrained in varying ways in order to match the variety of definitions that exist in the literature. Indeed, the constraints imposed correspond to properties that the diagrams may possess. A contribution of this paper is to provide formal definitions of these properties and we discuss when these properties may be desirable. Our definition of an Euler diagram and the formalization of these properties provides a general language for the Euler diagram community to utilize. A consequence of using a common language will be better integration of, and more accessible, research results.