• Title, Summary, Keyword: Deductive mathematics

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HYPER MV-DEDUCTIVE SYSTEMS OF HYPER MV-ALGEBRAS

  • Jun, Young-Bae;Kang, Min-Su;Kim, Hee-Sik
    • Communications of the Korean Mathematical Society
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    • v.25 no.4
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    • pp.537-545
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    • 2010
  • The notions of (weak) hyper MV-deductive systems and (weak) implicative hyper MV-deductive systems are introduced, and several properties are investigated. Relations among hyper MV-deductive systems, weak hyper MV-deductive systems, implicative hyper MV-deductive systems and weak implicative hyper MV-deductive systems are discussed. A characterization of a hyper MV-deductive system is provided. A condition for a weak hyper MV-deductive system to be a weak implicative hyper MV-deductive system is given.

STRONG DEDUCTIVE SYSTEMS OF BL-ALGEBRAS

  • Jun, Young-Bae;Park, Chul-Hwan;Doh, Myung-Im
    • Honam Mathematical Journal
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    • v.29 no.3
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    • pp.445-453
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    • 2007
  • The notion of strong deductive system of a BL-algebra is introduced, and a characterization of a strong deductive system is given. A relation between a strong deductive system and a deductive system is given. It will be seen that every strong deductive system can be expressed as the union of special sets.

VAGUE DEDUCTIVE SYSTEMS OF SUBTRACTION ALGEBRAS

  • Park, Chul-Hwan
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.427-436
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    • 2008
  • The notion of vague deductive systems in subtraction algebras is introduced, and several properties are investigated. Conditions for a vague set to be a vague deductive system are provided. Characterizations of a vague deductive system are established.

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DEDUCTIVE SYSTEMS OF BL-ALGEBRAS

  • JUN, YOUNG BAE;KO, JUNG MI
    • Honam Mathematical Journal
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    • v.28 no.1
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    • pp.45-56
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    • 2006
  • We give characterizations of a deductive system of a BL-algebra, and discuss how to generate a deductive system by a set.

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CENTRAL HILBERT ALGEBRAS

  • Jun, Young-Bae;Park, Chul-Hwan
    • The Pure and Applied Mathematics
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    • v.15 no.3
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    • pp.309-313
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    • 2008
  • The notion of central Hilbert algebras and central deductive systems is introduced, and related properties are investigated. We show that the central part of a Hilbert algebra is a deductive system. Conditions for a subset of a Hilbert algebra to be a deductive system are given. Conditions for a subalgebra of a Hilbert algebra to be a deductive system are provided.

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On deductive systems of hilbert algebras

  • Hong, Sung-Min;Jun, Young-Bae
    • Communications of the Korean Mathematical Society
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    • v.11 no.3
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    • pp.595-600
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    • 1996
  • We give a characterization of a deductive system. We introduce the concept of maximal deductive systems and show that every bounded Hilbert algebra with at least two elements contains at least one maximal deductive system. Moreover, we introduce the notion of radical and semisimple in a Hilbert algebra and prove that if H is a bounded Hilbert algebra in which every element is an involution, then H is semisimple.

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A Study on Teaching How to Draw Auxiliary Lines in Geometry Proof (보조선 지도법 연구)

  • Yim, Jae-Hoon;Park, Kyung-Mee
    • School Mathematics
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    • v.4 no.1
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    • pp.1-13
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    • 2002
  • The purpose of this study is to investigate the reasons and backgrounds of drawing auxiliary lines in the proof of geometry. In most of proofs in geometry, drawing auxiliary lines provide important clues, thus they play a key role in deductive proof. However, many student tend to have difficulties of drawing auxiliary lines because there seems to be no general rule to produce auxiliary lines. To alleviate such difficulties, informal activities need to be encouraged prior to draw auxiliary lines in rigorous deductive proof. Informal activities are considered to be contrasting to deductive proof, but at the same time they are connected to deductive proof because each in formal activity can be mathematically represented. For example, the informal activities such as fliping and superimposing can be mathematically translated into bisecting line and congruence. To elaborate this idea, some examples from the middle school mathematics were chosen to corroborate the relation between informal activities and deductive proof. This attempt could be a stepping stone to the discussion of how to teach auxiliary lines and deductive reasoning.

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A study of the types of students' justification and the use of dynamic software (학생들의 정당화 유형과 탐구형 소프트웨어의 활용에 관한 연구)

  • 류희찬;조완영
    • Journal of Educational Research in Mathematics
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    • v.9 no.1
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    • pp.245-261
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    • 1999
  • Proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. But, teaching proof in school mathematics have been unsuccessful for many students. The traditional approach to proofs stresses formal logic and rigorous proof. Thus, most students have difficulties of the concept of proof and students' experiences with proof do not seem meaningful to them. However, different views of proof were asserted in the reassessment of the foundations of mathematics and the nature of mathematical truth. These different views of justification need to be reflected in demonstrative geometry classes. The purpose of this study is to characterize the types of students' justification in demonstrative geometry classes taught using dynamic software. The types of justification can be organized into three categories : empirical justification, deductive justification, and authoritarian justification. Empirical justification are based on evidence from examples, whereas deductive justification are based logical reasoning. If we assume that a strong understanding of demonstrative geometry is shown when empirical justification and deductive justification coexist and benefit from each other, then students' justification should not only some empirical basis but also use chains of deductive reasoning. Thus, interaction between empirical and deductive justification is important. Dynamic geometry software can be used to design the approach to justification that can be successful in moving students toward meaningful justification of ideas. Interactive geometry software can connect visual and empirical justification to higher levels of geometric justification with logical arguments in formal proof.

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FUZZY ABYSMS OF HILBERT ALGEBRAS

  • Jun, Young-Bae;Lee, Kyoung-Ja;Park, Chul-Hwan
    • 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.

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