Geometric Programming System

几何规划系统

• 批准号: 03452171
• 负责人: MATSUYAMA Takashi
• 金额: $ 4.35万
• 依托单位: OKAYAMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1991
• 资助国家: 日本
• 起止时间: 1991 至 1992
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-03452171/
• 关键词: Algebraic Constraint; Constraint Programming; Geometric Reasoning; Grobner Basis Method; Geometric Theorem Proving; Graphic Software; Image Processing Software; Grobner基底法

(1)Design and Implementation of Geometric Programming Language ・ We designed and implemented an algebraic constraint programming language named GPL. Major characteristics of GPL are - Functional Programming Language with Global Variables - Function Overloading - Array of Indefinite Size - Constraint Inheritance - Automatic Type Conversion ・ We showed that various geometric objects such as images, points, lines, polygons and so on can be compactly described in GPL, and that facilities of function overloading, constraint inheritance, and type conversion are very useful to describe operators to process those geometric objects. ・ As a future problem, we should develop a compiler of GPL.(2)Development of Geometric Reasoning System by Integrated Logical and Algebraic Reasoning ・ We devised a new geometric reasoning method which integrates both logical reasoning based on the first order predicate calculus and algebraic reasoning using Grobner basis method. ・ We developed a geometric theorem prover and showed that the new reasoning method is more powerful than ordinary ones.

（1）几何程序设计语言的设计与实现·设计并实现了一种代数约束程序设计语言GPL。GPL的主要特点是：全局变量函数式程序设计语言函数重载不定大小数组约束继承自动类型转换。我们证明了图像、点、线、多边形等各种几何对象都可以用GPL来描述，函数重载、约束继承、和类型转换是非常有用的描述操作处理这些几何对象。·作为未来的问题，我们应该开发一个GPL的编译器。（2）逻辑与代数推理相结合的几何推理系统的开发。我们设计了一种新的几何推理方法，它将基于一阶谓词演算的逻辑推理和基于Grobner基方法的代数推理相结合。·我们开发了一个几何定理证明器，并表明新的推理方法比普通的方法更强大。

项目成果

T.Tanaka, H.Tokunaga, and T.Matsuyama: "GPL: A Geometric Programming Language Based on Algebraic Constraint Specification" Proc. of 3rd Symposium on Functional Figure Processing. 107-112 (1992)

T.Tanaka、H.Tokunaga 和 T.Matsuyama：“GPL：基于代数约束规范的几何编程语言”Proc。

松山 隆司,新田 知明: "論理的推論と代数的推論の融合による幾何推論" 人工知能学会誌. 8. (1993)

Takashi Matsuyama、Tomoaki Nitta：“结合逻辑推理和代数推理的几何推理”日本人工智能学会杂志 8。（1993）。

田中 智之,徳永 博之,松山 隆司: "GPL:代数的制約記述に基づく幾何プログラミング言語" 第3回機能図形情報システムシンポウジウム論文集. 107-112 (1992)

Tomoyuki Tanaka、Hiroyuki Tokunaga、Takashi Matsuyama：“GPL：基于代数约束描述的几何编程语言”第三届功能图形信息系统研讨会论文集107-112（1992）。

T.Matsuyama and T.Nitta: "Geometric Theorem Proving by Integrated Logical and Algebraic Reasoning" Journal of Japanese Society for Artificial Intelligence. Vol.8, No.3. (1993)

T.Matsuyama 和 T.Nitta：“综合逻辑和代数推理的几何定理证明”日本人工智能学会杂志。