Acquisition of associative knowledge by the frustration-based learning method in an auxiliary-line problem

Masaki Suwa, Hiroshi Motoda

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We have developed a learner, AUXIL, which has the 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 successful auxiliary-line by making use of associative strategies, which we call figure-pattern strategies. Secondly, we proposed a new method, frustration-based learning, which can acquire associative strategies through 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 frustrated 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 associative strategies. Each frustration-causing condition or subgoal will constitute the if-part of each strategy. 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 strategy. Learning an auxiliary-line problem through frustration-based learning means to understand it as a composition of figure-patterns each of which has those features represented in the THEN-part of the corresponding strategy. The frustration-based learning method is regarded as a method for learning some essential figure-patterns which underlie and structurize a problem solving process of elementary geometry.

Original languageEnglish
Pages (from-to)113-137
Number of pages25
JournalKnowledge Acquisition
Issue number1
Publication statusPublished - 1989 Mar
Externally publishedYes


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