# 初等幾何学の補助線問題におけるフラストレーションに基づく学習Frustration-Based Learning in Auxiliary-Line Problems in Elementary Geometry

## 抄録

We have developed a learning system, AUXIL, which has an ability to solve auxiliary-line problems in geometry in an intelligent way. First, we show that a basic mechanism for producing auxiliary-lines is to associate a certain condition or subgoal in the problem with an appropriate figure-pattern and that AUXIL can produce a right auxiliary-line by making use of associative knowledge, which we call figure-pattern strategies. Secondly, we proposed a new method, frustration-based learning, which can learn associative knowledge from experiences of solving a variety of auxiliary-line problems. AUXIL simulates the following expert behavior. When an expert tries to solve such a problem, he feels frustration because enough information is not given in a problem space for him to proceed an inference and to find a correct path from given conditions to the goal. Here, he concentrates himself on the conditions or subgoals which have caused frustration. After he has produced an auxiliary-line and made a complete proof-tree, he would learn several pieces of associative knowledge. Each frustration-causing condition or subgoal will constitute the if-part of each knowledge. He will then recognize several lumps of figure-patterns in the proof-tree, each of which has contributed to resolving each frustration. All pieces of geometrical information of each figure-pattern will constitute the then-part of each knowledge. A figure-pattern strategy has two characteristics as an associative knowledge. One is that its application to problems does not necessarily contribute to successful paths of the problems because it is a mere successful instance in the past experiences. The other is that it can enjoy flexible application to problems under no constraint of their goal-structures because its if-part can be unified, if unifiable, to any partial element of the problems. The second characteristic enables AUXIL to produce an appropriate auxiliary-line by a multiple use of figure-pattern strategies in response to several frustrations occurring in a problem, which is sufficient for making up for the first undesirable characteristic.

## 収録刊行物

• 人工知能学会誌 = Journal of Japanese Society for Artificial Intelligence

人工知能学会誌 = Journal of Japanese Society for Artificial Intelligence 4(3), 308-320, 1989-05-20

## 被引用文献:  7件中 1-7件 を表示

• 平面幾何学の推論と学習への視覚的イメージの導入

守屋 哲朗 , 沼尾 正行

人工知能学会全国大会論文集 = Proceedings of the Annual Conference of JSAI 7, 101-104, 1993-07-20

参考文献6件

• 新しいAI研究を目指して

中島 秀之 , 有馬 淳 , 佐藤 理史 , 諏訪 正樹 , 橋田 浩一 , 浅田 稔 , Hideyuki Nakashima , Jun Arima , Satoshi Sato , Masaki Suwa , Koiti Hasida , Minoru Asada , 電子技術総合研究所協調アーキテクチャ計画室:電子技術総合研究所通信知能研究室 , (株)富士通研究所 , 北陸先端科学技術大学院大学情報科学研究科 , (株)日立製作所基礎研究所 , 電子技術総合研究所知能情報部自然言語研究室 , 大阪大学工学部

人工知能学会誌 = Journal of Japanese Society for Artificial Intelligence 11(5), 713-724, 1996-09-01

人工知能学会 参考文献35件 被引用文献8件

• 明示的理解に魅せられて

元田 浩 , Hiroshi Motoda , 大阪大学産業科学研究所 , Institute of Scientific and Industrial Research Osaka University

人工知能学会誌 = Journal of Japanese Society for Artificial Intelligence 14(4), 615-625, 1999-07-01

人工知能学会 参考文献72件 被引用文献4件

• 2次関数問題解答システム

村田 剛志 , 細谷 蘭 , 河辺 信吾 , 志村 正道

電子情報通信学会論文誌. D-1, 情報・システム 1-情報処理 00082(00009), 1181-1190, 1999-09-25

参考文献16件

• 帰納的学習と演繹的説明づけに駆動された知識獲得システム : KAISER

辻野 克彦 , 西田 正吾 , Katsuhiko Tsujino , Shogo Nishida , 三菱電機(株)中央研究所システム基礎研究部 , 三菱電機(株)中央研究所システム基礎研究部 , Information and System Science Dept. Central Research Lab. Mitsubishi Electric Corp. , Information and System Science Dept. Central Research Lab. Mitsubishi Electric Corp.

人工知能学会誌 = Journal of Japanese Society for Artificial Intelligence 7(1), 149-159, 1992-01-01

人工知能学会 参考文献20件 被引用文献16件

• 図情報による推論・学習制御 (<特集>「図による推論」)

諏訪 正樹 , Masaki Suwa , (株)日立製作所基礎研究所 , Advanced Research Laboratory Hitachi Ltd.

人工知能学会誌 = Journal of Japanese Society for Artificial Intelligence 9(2), 196-200, 1994-03-01

人工知能学会 参考文献11件 被引用文献2件

• 認知的方略(perceptual-chunks)の学習 : 学習プロセスの視覚的制御

諏訪 正樹 , 元田 浩 , Masaki Suwa , Hiroshi Motoda , (株)日立製作所基礎研究所 , (株)日立製作所基礎研究所 , Advanced Research Laboratory Hitachi Ltd. , Advanced Research Laboratory Hitachi Ltd.

人工知能学会誌 = Journal of Japanese Society for Artificial Intelligence 9(4), 548-558, 1994-07-01

人工知能学会 参考文献21件 被引用文献4件

## 各種コード

• NII論文ID(NAID)
110002807218
• NII書誌ID(NCID)
AN10067140
• 本文言語コード
JPN
• 資料種別
Article
• ISSN
09128085
• データ提供元
CJP引用  NII-ELS  JSAI

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