A program that acquires how to solve problems in mathematics

  • Authors:
  • Machiko Fujiwara;Kenzo Iwama

  • Affiliations:
  • Engicom Corporation, Kita-ku, Tokyo, Japan;Engicom Corporation, Kita-ku, Tokyo, Japan

  • Venue:
  • ICCOMP'09 Proceedings of the WSEAES 13th international conference on Computers
  • Year:
  • 2009

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Abstract

In mathematics, a sequence of sentences describes how to solve a problem; for instance, sentences, "Calculate the least common multiple of 10 and 15. Firstly divide 10 and 15 by 2. Divide 10 by 2. The result is 5. Divide 15 by 2. Cannot divide." and so on, describe how to calculate the least common multiple of 10 and 15. While example sequences of sentences are given to our initial program, the initial program generalizes the example sentences and generates a program, pG, to solve a problem. For instance, the generated program, pG, calculates the least common multiple of 110 and 165 although 110 and 165 have not been given in an example sequence. This paper argues when one can say a program acquires how to solve a problem, and then explains such a program. The paper also argues, as a result of generating a program, pG, the meaning of a sentence is represented in the generated program, pG.