Specification of Figure Processing System basedon Multi-agent oriented Ontology

由于图形表示和运算的方法是单独和经验性地发展起来的，所以很难比较这些方法的性质，确保各种表示之间的兼容性，以及显示图形运算的正确性。为了解决这一问题，我们建立了图形本体，并提出了图形处理系统的描述方法。1.利用多智能体自认知逻辑(MAEL)将图形看作智能体，建立了点、线、矩形、圆等图形和加法、移动、变色、删除等图形操作的形式化方法。其核心思想如下：(1)图的属性被认为是智能体的知识；(2)图之间的概念层次用关于智能体之间通信的元知识来描述；(3)图操作被形式化为关于操作前后图之间关系的元知识，特别是给出了一个公理来表示性质：对图的整体的操作将被应用到图的各个部分。显示了绘图系统Sync/DRAW中图形操作的正确性。为此，重新形式化地定义了Sync/Drawing调用对象中的图形表示，并定义了以下函数来表示它们之间的交换性：(1)从对象到Mael公式的解释函数；(2)重写对象集合之间的规则以形式化图形运算；(3)Mael公式集合之间的转换函数以形式化图形运算的含义。

Since the methods to represent and operate figures have been developed individually and empirically, it is not easy to compare the properties of the methods, to assure compatibility among various kinds of representations, and to show correctness of the figure operations. To solve the problem, we establish ontology for figures and a method for specification of figure processing systems. In this research, the followings are shown :1.A method to formalize figures such as points, lines, rectangles, and circles and figure operations such as addition, movement, color change, and deletion is established, where multi-agent autoepistemic logic(MAEL) is employed to regard the figures as agents. The key ideas are as follows : (1)Attributes of figures are considered to be knowledge of the agents, (2)Concept hierarchy among the figures is described in terms of meta-knowledge about communications among the agents, and (3)Figure operations are formalized as meta-knowledge about relations between figures before and after the operations, especially giving an axiom which represents the property "operations to the whole of a figure are to be applied to the parts of it." to the parts.2.Correctness of figure operations in the drawing system Sync/Draw is shown. To do so, figure representation in Sync/Draw called objects is re-defined formally and the following functions are defined to show commutativity among them : (1)An interpretation function from objects to MAEL formulas, (2)Rewrite rules between sets of objects which formalize figure operations, and (3)Transformation functions between sets of MAEL formulas which formalize meanings of figure operations.