• International Journal of Contents
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• v.7 no.4
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• pp.56-63
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• 2011

Quantum mechanics is a branch of physics for a mathematical description of the particle wave, and it is applied to information technology such as quantum computer, quantum information, quantum network and quantum cryptography, etc. In 1936, Garrett Birkhoff and John von Neumann introduced the logic of quantum mechanics (quantum logic) in order to investigate projections on a Hilbert space. As another type of quantum logic, orthomodular implication algebra was introduced by Chajda et al. This algebra has the logical implication as a binary operation. In pure mathematics, there are many algebras such as Hilbert algebras, implicative models, implication algebras and dual BCK-algebras (DBCK-algebras), which have the logical implication as a binary operation. In this paper, we introduce the definitions and some properties of those algebras and clarify the relations between those algebras. Also, we define the implicative poset which is a generalization of orthomodular implication algebras and DBCK-algebras, and research properties of this algebraic structure.

• Journal of the Korean Operations Research and Management Science Society
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• v.39 no.3
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• pp.7-22
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• 2014

By the publications of RDF and OWL, the Semantic Web is confirmed as a technology through which information in the Internet can be processed by machines. The focus of the Semantic Web study after then has moved to how to provide more useful information to users for their decision making beyond simple use of the structured data in ontologies. SWRL that makes logical inference possible by rules, and SWCL that formulates constraints under the Semantic Web environment are some of many efforts toward the achievement of that goal. Constraint represents a connection or a relationship between individual data in ontology. Based on SWCL, this paper tries to extend the language by adding one more type of constraint, implication constaint, in its repertoire. When users use binary variables to represent logical relationships in mathematical models, it requires and knowledge on the solver to solve the models. The use of implication constraint ease this difficulty. Its need, definition and relevant technical description is presented by the use of the optimal common attribute selection problem in product design.

• School Mathematics
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• v.1 no.1
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• pp.95-107
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• 1999

In this study, we tried to make clear the meaning of implication, and inquired into Piaget's theory on the development of children's logical thinking focussing on implication. Because the progressive development of the notion of implication is very important to learn the meaning of conditional proposition, we searched a sequence for the learning implication on basis of Piaget's theory.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.193-198
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• 1997

In order to research the logical system whose propositional value is given in a lattice, Y. Xu [4] proposed the concept of lattice implication algebras, and discussed their some properties in [3] and [4]. Y. Xu and K. Qin [5] introduced the notions of filter and implicative filter in a lattice implication algebra, and investigated their properties. In this paper, in the first place, we give an equivalent condition of a filter, and provide some equivalent conditions that a filter is an implicative filter in a lattice implication algebra. By using these results, we construct an extension property for implicative filter.

• Korean Journal of Logic
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• v.7 no.2
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• pp.105-120
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• 2004

In this paper, we provide Routley-Meyer semantics for the many-valued logics ${\L}C$ and LC, and give completeness for each of them. This result shows the following two: 1) Routley-Meyer semantics is very powerful in the sense that it can be used as the semantics for several sorts of logics, i.e., many-valued logic, not merely relevance logic and substructural logic. Note that each implication of ${\L}C$ and LC does not (partially) result in "paradoxes of material implication" 2) This implies that Routley-Meyer semantics can be also used not merely for relevance systems but also for other logical systems such as ${\L}C$ and LC, each of which has its own implication by which we can overcome (partially) the problem of "paradoxes of material implication".

• Journal for History of Mathematics
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• v.26 no.5_6
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• pp.401-416
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• 2013

There has been increasing interest in recent years in the pedagogical importance of counter-examples that focuses on pedagogical perspectives. But there is no research that undergraduate students' generating counter-examples and proposing the true statements. This study analyze 6 undergraduate students' response to interview tasks and the process of their generating counter-examples and proposing true statements. The results of interviews are that the more undergraduate students generate various counter-examples, the more valid they propose true statements. If undergraduate students have invalid understanding of logical implication and generate only one counter-example, they would not propose true statements that modify the given statement, preserving the antecedent. In pre-service teacher's education and school mathematics class, we need to develop materials and textbooks about counter-examples and false statements.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.146-151
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• 1994

An empirical comparison of static fuzzy relational models which are identified with different fuzzy implication operators and inferred by different composition operators is made in case that all the information is represented by the fuzzy discretization. Four performance measures (integral of mean squared error, maximal error, fuzzy equality index and mean lack of sharpness) are adopted to evaluate and compare the quality of the fuzzy relational models both at the numerical level and logical level. As the results, the fuzzy implication operators useful in various fuzzy modeling problems are discussed and it is empirically shown that the selection of data pairs is another important factor for identifying the fuzzy model with high quality.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.449-449
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• 2000

Many researchers have studied architectures for non-Neumann's computers because of escaping its bottleneck. To avoid the bottleneck, a neuron-based computer has been developed. The computer has only neurons and their connections, which are constructed of the learning. But still it has information processing facilities, and at the same time, it is like as a simplified brain to make inference; it is called "neuron-computer". No instructions are considered in any neural network usually; however, to complete complex processing on restricted computing resources, the processing must be reduced to primitive actions. Therefore, we introduce the instructions to the neuron-computer, in which the most important function is implications. There is an implication represented by binary-operators, but general implications for multi-value or fuzzy logics can't be done. Therefore, we need to use Lukasiewicz' operator at least. We investigated a neuron-computer having instructions for general implications. If we use the computer, the effective inferences base on multi-value logic is executed rapidly in a small logical unit.

• Journal of Convergence for Information Technology
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• v.7 no.3
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• pp.65-71
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• 2017

The quantum logic was introduced by G. Birkhoff and 1. von Neumann in order to study projections of a Hilbert space for a formulation of quantum mechanics, and Husimi proposed orthomodular law and orthomodular lattices to complement the quantum logic. Abott introduced orthoimplication algebras and its properties to investigate an implication of orthomodular lattice. The commuting relation is an important property on orthomodular lattice which is related with the distributive law and the modular law, etc. In this paper, we define a binary operation on orthoimplication algebra and the greatest lower bound by using this operation and research some properties of this operation. Also we define a homomorphism and characterize the commuting relation of orthoimplication algebra by the homomorphism.

• Proceedings of the Korea Contents Association Conference
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• 2017.05a
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• pp.431-432
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• 2017

고전 논리의 연산이 집합의 연산과 밀접하게 관련되어 있는 것과 같이 양자논리(quantum logic)는 힐버트 공간(Hilbert space)의 닫힌부분공간(closed subspace)의 연산과 관련되어 있다. 닫힌부분공간들의 집합은 직교모듈로 격자(orthomodular lattice)를 이루고, von Neumann과 Birkhoff를 포함하여 많은 수학자들은 양자논리의 수학적 체계를 만들기 위해 직교모듈로 격자를 이용하였다. 일반 격자(lattice)에서 논리적 함의(implication)는 $x{\rightarrow}y={\neg}x{\vee}y$에 의해 일의적으로 정의되지만 직교모듈로 격자에서는 6개의 서로 다른 논리적 함의가 정의되는 것으로 알려져 있다. 본 논문에서는 직교모듈로 격자에서 정의되는 3개의 논리적 함의를 소개하고 이들 사이의 관계를 조사한다.