• 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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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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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• v.2 no.2
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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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• 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.

• 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.

• 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.

• 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.

• 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.

• 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.