• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.211-217
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• 2006

Topos is a set-like category. In topos, the axiom of choice can be expressed as (AC1), (AC2) and (AC3). Category Fuz of fuzzy sets has a similar function to the topos Set and it forms weak topos. But Fuz does not satisfy (AC1), (AC2) and (AC3). So we define (WAC1), (WAC2) and (WAC3) in weak topos Fuz. And we show that they are equivalent in Fuz.

• Journal for History of Mathematics
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• v.31 no.6
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• pp.315-337
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• 2018

Pythagorean thoerem exists in several equivalent forms in the Euclidean plane, that is, the Hilbert plane which in addition satisfies the parallel axiom. In this article, we investigate the truthness and mutual relationships of those propositions in various non-Hilbert planes which satisfy the parallel axiom and all the Hilbert axioms except the SAS axiom.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.115-128
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• 2009

In this paper, we modify the axiom of infinity of von Neumann's axioms modified by Pinter([5]), and then discuss an existence of an unknowable class in the system and a relationship between the unknowable class and the axiom of choice.

• Journal of KIISE:Software and Applications
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• v.35 no.6
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• pp.366-373
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• 2008

The web ontology language(OWL) has been used by ontology designers to construct ontology. In order to derive hidden information(concept subsumption, concept satisfiability and realization) of OWL ontology, a number of OWL reasoners have been introduced. But most reasoners simply report these information without process for any arbitrary entailment and unsatisfiable concept derived from a OWL ontologies. In this paper, we propose Minimum Expression Axiom Set(MEXS) detection and storing for debugging unsatisfiable concepts in ontology. In order to detect MEXS, we need to find axiom to cause inconsistency in ontology. Therefore, our work focused on two key aspects: given a inconsistency ontology, identifying the roots of axioms to occur unsatisfiable and derived axioms from among them; and extracting MEXS. Our results can be applicable to all application, which is at the basis of the description logic.

• Kyungpook Mathematical Journal
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• v.19 no.2
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• pp.159-163
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• 1979

In this paper $T_0$-identification spaces are used to prove that the semi-$R_1$ separation axiom is not a generalization of the $R_1$ separation axiom and to determine conditions, which together with $R_1$, do and do not imply semi-$R_1$.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.201-205
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• 2015

We show that if a regular map belongs to the $C^1$-interior of the set of all Kupka-Smale differentiable maps then it satisfis Axiom A and the strong transverality condition.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.191-195
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• 2001

In this paper, a simple axiom system of lattice implication algebras is presented, it is convenient for verifying whether an algebra of type (2,2,2,1,0,0) becomes a lattice implication algebra.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.473-490
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• 2000

Removal independence is a translation of Arrow's axiom of independence of irrelevant alternatives for social welfare functions to an axiom about consensus functions involving n-trees. It is shown that a consensus function is removal independent if and only if it is expressible as th union of three types of functions.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2007.06a
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• pp.593-594
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• 2007

• Journal of the Korean Society for Library and Information Science
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• v.46 no.2
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• pp.157-174
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• 2012

This study tries to describe personal name access point control ontology for the American novelist Mark Twain using RDF/OWL axiom to control access point based on the ontology. The Axiom used in this study are disjoint with class, domain and range, property cardinality, inverse functional property, individual and literal data property. As a result, in the ontology environment we can accept various access points as equal access points exclusive of authority heading and heading concept. It can successfully describe Mark Twain's personal name access point control ontology and display using the OntoGraf.