• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.311-312
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• 2008

Fuzzy logic is introduced by Zadeh in 1965. It has been continuously developed by many mathematicians and knowledge engineers all over the world. A lot of papers concerning with the history of mathematics and the mathematical education related with fuzzy logic, but there is no paper concerning with Zadeh. In this article, we investigate his life and papers about fuzzy logic. We also compare two-valued logic, three-valued logic, fuzzy logic, intuisionistic logic and intuitionistic fuzzy sets. Finally we discuss about the expression of intuitionistic fuzzy sets.

• Journal for History of Mathematics
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• v.21 no.1
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• pp.29-44
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• 2008

Fuzzy logic is introduced by Zadeh in 1965. It has been continuously developed by many mathematicians and knowledge engineers all over the world. A lot of papers concerning with the history of mathematics and the mathematical education related with fuzzy logic, but there is no paper concerning with Zadeh. In this article, we investigate his life and papers about fuzzy logic. We also compare two-valued logic, three-valued logic, fuzzy logic, intuisionistic logic and intuitionistic fuzzy sets. Finally we discuss about the expression of intuitionistic fuzzy sets.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 2009.05a
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• pp.101-106
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• 2009

수학적 사고의 입장에서 중등학생들이 수학적 문제해결에 논리적 사고와 직관적 사고가 어떻게 작용하는지를 연구하는 것은 수학교육에서 중요하고도 흥미로운 과제의 하나이다. 본 연구의 주된 목적은 중등학교 영재학생을 대상으로 이러한 문제를 조사하는 것이다. 특히 이들 중등영재학생들의 논리적 사고와 직관적 사고에 대한 선호도와 논리적 문제의 문제해결능력 사이의 관계를 조사한다.

• Korean Journal of Logic
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• v.12 no.1
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• pp.1-24
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• 2009

이 논문에서 우리는 집합의 두 점 사이의 관계를 소개하고, '가깝다'와 '충분히 가깝다'의 위상적인 개념을 다양하게 정의할 수 있음을 보인다. 또한 직관주의 논리와 관계가 있는 De Morgan frame을 소개하고 pre-order에 의하여 정의된 동치관계로 만들어진 동치류들의 집합을 기저로 생성된 위상 공간이 extremally disconnected 임을 보인다.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.23-30
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• 2005

Intuition has played an important role in process of invention of mathematics and given understanding of mathematical truth and the direction of solution. So, I review about intuition in history of mathematical philosophy and mathematics because we need systematic research about intuition for search of the methods for enhancement of intuition in mathematics education. According to the research of scholars who emphasize intuitive education, intuition is common feature which everybody hold and is not special feature which particular person hold. In addition, intuition is universal ability that can enhance by proper instruction. So, we have to emphasize the importance of the development of intuition and education which emphasize creative thought via intuition.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10b
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• pp.404-406
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• 1998

확정절 문법은 구 구조문법을 명시하는데 사용된 후 계산이론적 언어학자들이 많은 연구를 하는 분야이다. 확정절 문법은 혼절에 근거하고 있기 때문에 관계절 공간연결 파서를 구성할 때 메우개-공간 의존을 자연스럽게 설명할 수 없다. 본 논문에서는 메우개-공간 의존을 처리할 수 있는 일반 구 구조문법 GPSG의 특성에 대해서 논하고 일반 구 구조 문법을 논리 문법으로 확장할 수 있는 방법에 대해서 기술하였다. [7]에서는 메우개-공간 의존을 설명하기 위해서 직관적 논리를 이용하였다. 여기에서는[7]의 직관적 논리 문법의 한계에 대해서 논하였다. 또 [5]에서는 일차 선형 논리를 이용하였는데, 이는 공간연결 파서로 자연어 문장을 논리식으로 번역하는데 사용될 수 없다. 따라서 본 연구에서는 고차 선형 논리문법을 이용하여 자연어 파서를 구성하였다.

• Journal of The Korean Association For Science Education
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• v.37 no.3
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• pp.523-537
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• 2017

The purpose of this study is to investigate the features of elementary students' intuitive thinking emerged during problem solving activities as it related to thermal phenomena, focusing on when intuitive thinking appears and how it is related to logical thinking. For this, we presented a problem related to thermal phenomena to nine 5th-grade students, and examined how students' thinking emerged in the activities. We conducted clinical interviews to investigate the thinking process of students. The results of this study are as follows. First, students made their own solutions and justified it later during the emergence process of intuitive thinking. It was also found that students connected concrete materials and abstract concepts intuitively. They solved the problem by making predictions even when information is insufficient. Second, it was shown that intuitive thinking can emerge through the intended strategies such as drawing a mental image, thinking from a different perspective, and integrating methods. These results, which are related to the students' intuitive thinking has received little attention and will be the basis for helping students in the context of discovery of their problem solving activities.

• Korean Journal of Logic
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• v.14 no.2
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• pp.39-76
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• 2011

We explain some basic elements of Martin-L$\ddot{o}$f's type theory and examine the distinction between propositions and judgments. In section 1, we introduce the problem. In section 2, we explain the concept of proposition in the intuitionistic type theory as a development of the intuitionistic conception of proposition. In section 3, we explain the concept of judgment in the intuitionistic type theory. In section 4, we explain some basic inference rules and examine a particular derivation in the theory. In section 5, we examine one route from the Fregean distinction between propositions and judgments to the distinction between them in the intuitionistic type theory, paying attention to the alleged necessity for introducing different forms of judgments.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.565-581
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• 2016

Intuition in the mathematical problem solving has been stressed the importance with the logic because intuition is the cognition that give significant clue or idea to problem solving. Fischbein classified intuition by the origin; primary intuition and secondary intuition And he said the role of the personal experience and school education. Through these precedent research, we can understand the social influence. This study attempt to investigate social intuition model of Haidt, moral psychologist that has surfaced social property of intuition in terms of the mathematical problem solving. The major suggestions in problem solving and the education of intuition are followed. First, I can find the social property of intuition in the mathematical problem solving. Second, It is possible to make the mathematical problem solving model by transforming the social intuitionist model. Third, the role of teacher is important to give the meaningful experience for intuition to their students. Fourth, for reducing the errors caused by the coerciveness and globality of intuition, we need the education of checking their own intuition. In other words, we need intuition education emphasized on metacognition.

• Korean Journal of Logic
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• v.21 no.1
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• pp.59-96
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• 2018

${\bot}$It is often said that in a purely formal perspective, intuitionistic logic has no obvious advantage to deal with the liar-type paradoxes. In this paper, we will argue that the standard intuitionistic natural deduction systems are vulnerable to the liar-type paradoxes in the sense that the acceptance of the liar-type sentences results in inference to absurdity (${\perp}$). The result shows that the restriction of the Double Negation Elimination (DNE) fails to block the inference to ${\perp}$. It is, however, not the problem of the intuitionistic approaches to the liar-type paradoxes but the lack of expressive power of the standard intuitionistic natural deduction system. We introduce a meta-level negation, ⊬$_s$, for a given system S and a meta-level absurdity, ⋏, to the intuitionistic system. We shall show that in the system, the inference to ${\perp}$ is not given without the assumption that the system is complete. Moreover, we consider the Double Meta-Level Negation Elimination rules (DMNE) which implicitly assume the completeness of the system. Then, the restriction of DMNE can rule out the inference to ${\perp}$.