• Journal for History of Mathematics
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• v.35 no.2
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• pp.43-56
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• 2022

The 21st century world has experienced all-around changes from the 4th industrial revolution. In this developmental changes, artificial intelligence is at the heart, with data science adopting certain scientific methods and tools on data. It is necessary to investigate on the logic lying underneath the methods and tools. We look at the origins of logic, deduction and induction, and scientific methods, together with mathematical induction, probabilistic method and data science, and their meaning.

• Korean Journal of Logic
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• v.19 no.1
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• pp.83-106
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• 2016

We compare the approaches to natural numbers and the induction principles in Frege's Grundgesetze and in systems thereafter. We start with an illustration of Frege's approach and then explain the use of induction principles in Zermelo-Fraenkel set theory and in modern type theories such as Calculus of Inductive Constructions. A comparison among the different approaches to induction principles is also given by analyzing them in respect of predicativity and impredicativity.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.123-135
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• 2008

This study analysed the schemata which are requisite to understand and prove examples of mathematical induction, and examined students' construction of the schemata. We verified that the construction of implication-valued function schema and modus ponens schema needs function schema and proposition-valued function schema, and needs synthetic coordination for successive mathematical induction schema. Given this background, we establish $1{\sim}4$ levels for students' understanding of the mathematical induction. Further, we analysed cognitive difficulties of students who studying mathematical induction in connection with these understanding levels.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.3
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• pp.619-626
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• 2007

Constructive induction is a technique to draw useful attributes from given primitive attributes to classify given examples more efficiently. Useful attributes are obtained from given primitive attributes by applying appropriate operators to them. The paper proposes a constructive induction approach for a GA-based inductive learning environment that learns classification rules that ate similar to rules used in PROSPECTOR from given examples. The paper explains our constructive induction approach in details, centering on operators to combine primitive attributes and methods to evaluate the usefulness of derived attributes, and presents the results of various experiments performed to evaluate the effect of our constructive induction approach on the GA-based learning environment.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.23-48
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• 2007

This study begins from posing a problem, 'formal introduction of mathematical induction in school mathematics'. Most students may learn the mathematical induction at the level of instrumental understanding without meaningful understanding about its meaning and structure. To improve this didactical situation, we research on the historical progress of mathematical induction from implicit use in greek mathematics to formalization by Pascal and Fermat. And we identify various types of thinking included in the developmental process: recursion, regression, analytic thinking, synthetic thinking. In special, we focused on the role of regression in mathematical induction, and then from that role we induce the implications for teaching mathematical induction in school mathematics.

• The Journal of Korean Institute for Practical Engineering Education
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• v.5 no.1
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• pp.1-13
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• 2013

For a basic engineering education the confirmation and verification of the deductive Inference was studied and the principle of probability inference was applied. The background of introduction of deductive Inference and its test method was mentioned, and historic arguments on the compatibility of deductive statistical inference was summarized and analyzed. Philosophical arguments on the deductive confirmation for engineering experiments was introduced. Premise, procedure, and control of the experiments are studied. As an example of the deductive probability inference three groups of experimental data were used in order to find successful inferences respectively.

• Proceedings of the Korean Information Science Society Conference
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• 2004.10a
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• pp.193-195
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• 2004

기존의 규칙 귀납법(Rule Induction)은 양성적 추론(positive reasoning)과 음성적 추론(negative reasoning)을 잘 반영하지 못하고 있지만 의학 분야의 추론은 양성적 추론과 음성적 추론을 모두 포함하고 있다. 이것이 의학 전문가들이 귀납된 규칙을 해석하는데 어려움을 가지게 되며, 진단 과정을 위해서 규칙을 해석하는 것을 쉽게 진행할 수 없는 이유이기도 하다. 본 연구에서는 양성적 규칙들과 음성적 규칙들의 귀납법을 위한 두 가지 알고리즘을 적용한 진단 시스템인 DS-ARI(Diagnosis System using Algorithms for Rule Induction)물 제안한다. 제안하는 시스템과 기존 시스템을 비교해 보았을 때 제안하는 시스템에서 전문가의 지식을 보다 정확하게 표현하여 정확성을 높이게 되었다.

• Journal of KIISE
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• v.43 no.12
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• pp.1342-1350
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• 2016

Induction and coinduction are well-established proof principles, which are widely used in mathematics and computer science. In particular, induction is taught in most undergraduate programs and well understood in the field of computer science. In contrast, coinduction is not as widespread or well understood as induction. In this paper, we introduce coinduction by defining a subtype system for recursive and union types and proving the transitivity property of the system. This paper will help to promote familiarity with coinduction and provides a basis for a subtype system for recursive types with other advanced type constructors and connectives.

• Journal for History of Mathematics
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• v.34 no.6
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• pp.195-204
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• 2021

Mathematical induction is one of the deductive methods used for proving mathematical theorems, and also used as an inductive method for investigating and discovering patterns and mathematical formula. Proper understanding of the mathematical induction provides an understanding of deductive logic and inductive logic and helps the developments of algorithm and data science including artificial intelligence. We look at the origin of mathematical induction and its usage and educational aspects.

• Proceedings of the Korean Society for History of Mathematics Conference
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• 2001.11a
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• pp.9-9
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• 2001