• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.169-182
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• 2011

The notions of bipolar fuzzy hyper MV-subalgebras, (weak) bipolar fuzzy hyper MV-deductive system and precisely weak bipolar fuzzy hyper MV-deductive system are introduced, and their relations are investigated. Characterizations of bipolar fuzzy hyper MV-subalgebras and weak bipolar fuzzy hyper MV-deductive systems are provided.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.57-64
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• 2014

It is known that the class of CI-algebras is a generalization of the class of BE-algebras [5]. Recently, K. H. Kim introduced the notion of a CS-algebra [4]. In this paper we discuss a closed deductive system of a CS-algebra, and we find some fundamental properties. Moreover, we study a CS-algebra homomorphism and a congruence relation.

• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.377-385
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• 2008

The notion of fuzzy abysms in Hilbert algebras is introduced, and several properties are investigated. Relations between fuzzy subalgebra, fuzzy deductive systems, and fuzzy abysms are considered.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.313-324
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• 2008

Molodtsov [8] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of subtraction algebras. The notion of soft WS-algebras, soft subalgebras and soft deductive systems are introduced, and their basic properties are derived.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.47-58
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• 2007

In this paper, we shall try to give a comparative study of mathematics developments in ancient Greece and ancient Oriental mathematics. We have found that the Oriental Mathematics. is quantitative, computational and algorithmetic, but the ancient Greece is axiomatic and deductive mathematics in character. The two region mathematics should be unified to give impetus to further development of mathematics in future times.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.325-344
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• 2010

The purpose of this study is to investigate what influences students' preferences on empirical and deductive proofs and find their relations. Although empirical and deductive proofs have been seen as a significant aspect of school mathematics, literatures have indicated that students tend to have a preference for empirical proof when they are convinced a mathematical statement. Several studies highlighted students'views about empirical and deductive proof. However, there are few attempts to find the relations of their views about these two proofs. The study was conducted to 47 students in 7~9 grades in the transition from empirical proof to deductive proof according to their mathematics curriculum. The data was collected on the written questionnaire asking students to choose one between empirical and deductive proofs in verifying that the sum of angles in any triangles is $180^{\circ}$. Further, they were asked to provide explanations for their preferences. Students' responses were coded and these codes were categorized to find the relations. As a result, students' responses could be categorized by 3 factors; accuracy of measurement, representative of triangles, and mathematics principles. First, the preferences on empirical proof were derived from considering the measurement as an accurate method, while conceiving the possibility of errors in measurement derived the preferences on deductive proof. Second, a number of students thought that verifying the statement for three different types of triangles -acute, right, obtuse triangles - in empirical proof was enough to convince the statement, while other students regarded these different types of triangles merely as partial examples of triangles and so they preferred deductive proof. Finally, students preferring empirical proof thought that using mathematical principles such as the properties of alternate or corresponding angles made proof more difficult to understand. Students preferring deductive proof, on the other hand, explained roles of these mathematical principles as verification, explanation, and application to other problems. The results indicated that students' preferences were due to their different perceptions of these common factors.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.61-71
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• 2011

The notion of a complicated pre-logic is introduced and investigated some properties of it. A special set in a pre-logic is established and some related its properties are discussed. Also more extended special sets in a pre-logic are introduced and some relations with deductive systems are obtained.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.3
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• pp.286-291
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• 2001

We inverstigate the properties of BL-hommorphisms on BL-algebras. In particular, we find the BL-algebra in duced by lattice-isomorphism. From these facts, we obtain the generalized Lukasiewicz structure. More-over, we study the properties of quotient BL-algebras and deductive systems.

• 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.

• The Mathematical Education
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• v.37 no.1
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• pp.73-85
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• 1998

The purpose of this study is to investigate the understanding of middle school students on the meaning of proof and to suggest a teaching method to improve their understanding based on three levels identified by Kunimune as follows: Level I to think that experimental method is enough for justifying proof, Level II to think that deductive method is necessary for justifying proof, Level III to understand the meaning of deductive system. The conclusions of this study are as follows: First, only 13% of 8th graders and 22% of 9th graders are on level II. Second, although about 50% students understand the meaning of hypothesis, conclusion, and proof, they can't understand the necessity of deductive proof. This conclusion implies that the necessity of deductive proof needs to be taught to the middle school students. One of the teaching methods on the necessity of proof is to compare the nature of experimental method and deductive proof method by providing their weak and strong points respectively.