• 대한수학회논문집
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• 제25권4호
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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.

• 호남수학학술지
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• 제29권3호
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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.

• 대한수학회보
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• 제42권3호
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• pp.443-451
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• 2005

The notion of grisly deductive systems of a BL-algebra is introduced. Conditions for a deductive system to be a grisly deductive system are given. Extension property for a grisly deductive system is established

• Asia pacific journal of information systems
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• 제2권2호
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• pp.85-102
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• 1992

A deductive database consists of collection of stored facts and deductive rules. It can answer queries based on logical deduction from the stored facts and general rules. A deductive database has both a declarative meaning(semantics) and a procedural meaning. The declarative semantics of a deductive database provides a definition of the meaning of the program in a manner which is independent of procedural considerations, context-free, and easy to manipulate, exchange and reason about. This paper investigates various declarative semantics of deductive databases, dicusses related computational issues, and suggests another declarative semantics for deductive databases which is more practical than others.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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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.

• 대한수학회논문집
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• 제26권2호
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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.

• 대한수학회논문집
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• 제11권3호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권3호
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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.

• 호남수학학술지
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• 제28권1호
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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.

• 대한수학교육학회지:학교수학
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• 제4권1호
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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.