| Budget Amount *help |
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Research Abstract |
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.
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