TY - JOUR

T1 - Acquisition of associative knowledge by the frustration-based learning method in an auxiliary-line problem

AU - Suwa, Masaki

AU - Motoda, Hiroshi

PY - 1989

Y1 - 1989

N2 - 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.

AB - 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.

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U2 - 10.1016/S1042-8143(89)80008-1

DO - 10.1016/S1042-8143(89)80008-1

M3 - Article

AN - SCOPUS:3543057574

VL - 1

SP - 113

EP - 137

JO - Knowledge Acquisition

JF - Knowledge Acquisition

SN - 1042-8143

IS - 1

ER -