• Proceedings of the Korean Society for Language and Information Conference
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• 2006.06a
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• pp.123-138
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• 2006

• The Mathematical Education
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• v.50 no.1
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• pp.41-59
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• 2011

Given the importance of algebra in the early grades, this paper analyzed the contents of whole numbers and their operations from the perspectives of generalized arithmetic. In particular, the focus of analysis was given to the properties of 0 and 1, those of operations such as commutativity, associativity, and distributivity, and the relations between operations. As such, this paper analyzed in detail how such properties and relations were introduced and expanded across different grades. It is expected that many issues in this paper will serve basic information to develop instructional materials in a way to fostering students' algebraic thinking in the elementary grades.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.415-421
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• 2020

In the proof of Theorem 3 on p.253 in [4], both right and left distributivity are assumed simultaneously which makes the proof invalid. We give a corrected proof for this theorem by introducing an extension of Lemma 2.2 in [2].

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.97-118
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• 2006

We obtain a property of distributivity in the equivalence form over LR fuzzy intervals. As an application and main result of the paper, we give a determinant method to solve systems of linear equivalentions. The expected value of the obtained solution is equal to the corresponding solution of the classical system of linear equations considering the expected values as data.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.523-535
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• 2010

There are different categorifications of the notion of a ring such as Ann-category due to N. T. Quang, ring category due to M. M. Kapranov and V. A. Voevodsky. The main result of this paper is to prove that every axiom in the definition of a ring category, but the axiom $x_0 = y_0$, can be deduced from the axiomatics of an Ann-category.

• The Journal of the Korea Contents Association
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• v.6 no.11
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• pp.202-216
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• 2006

A number of process algebras are not well suitable for real-time navigation/delivery systems due to the following reasons: 1) lack of representation of process distributivity over some geographical space and 2) the indistinction of representation of process mobility from process distributivity over the space. To make the process algebra suitable to the systems, it seems to be necessary to separate the space representation from the mobility representation. This paper presents a formal method for this purpose, namely, Calculus of Abstract Real-Time Distribution, Mobility, and Interaction (CARDMI). For analysis and verification of behavioral properties, CARDMI defines a set of the spatial, temporal and the interactive deduction rules and a set of equivalence relations. The rules and equivalences can be abstracted hierarchically due to the spatial abstraction, too. CARDMI can be applied to virtual navigation/delivery system for contents, too.

• KIPS Transactions on Computer and Communication Systems
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• v.11 no.9
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• pp.289-304
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• 2022

It is necessary to apply process algebra and logic in order to analyze and verify safety requirements for Smart IoT Systems due to distributivity and mobility of the systems over some predefined geo-temporal space. However the analysis and verification cannot be fully intuitive over the space due to the fact that the existing process algebra and logic are very limited to express the distributivity and the mobility. In order to overcome the limitations, the paper presents a new logic, namely for GTS-VL (Geo-Temporal Space-Visual Logic), visualization of the analysis and verification over the space. GTS-VL is the first order logic that deals with relations among the different types of blocks over the space, which is the graph that visualizes the system behaviors specified with the existing dTP-Calculus. A tool, called SAVE, was developed over the ADOxx Meta-Modeling Platform in order to demonstrate the feasibility of the approach, and the advantages and practicality of the approach was shown with the comparative analysis of PBC (Producer-Buffer-Consumer) example between the graphical analysis and verification method over the textual method with SAVE tool.

• Proceedings of the Korean Society for Cognitive Science Conference
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• 2000.05a
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• pp.121-127
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• 2000

지금까지 상호 표현(reciprocal expressions)이나 상호성(reciprocity)의 개념에 대한 연구는 영어의 'each other'를 중심으로 이뤄졌다. 그런데 한국어의 상호 대명사 '서로'는 'each other'와 달리, 그 자체로 배분성(distributivity)을 갖지 않는다. 오히려 다양한 배분 표현들과 공기함으로써 상호성을 구체화한다. 특히, 배분적 양화사는 상호 표현이 쓰인 문장에 강한 상호성(strong reciprocity)을 부여한다. 이외에도 한국어의 상호성 실현에는 함께 쓰인 술어가 중요한 역할을 한다. 우선, 술어가 대칭적(symmetric)이거나, 상호 대명사(reciprocal)'서로'를 논항으로 취하면, 문장은 일차적으로 상호성을 갖게된다. 또한, 술어가 반가법(anti-additive)함수로서의 의미 특성을 갖는 경우는, 논항이 복수 연접 명사구로 구성되었을 때, 논항을 그룹(group)으로 해석하는 것을 선호한다. 본고는 상호성 술어(reciprocated predicates)와 배분적 양화사의 의미 기여를 중심으로, 한국어 상호 표현의 다양한 의미·통사적 특징을 밝히는 것을 목표로 하며, 이를 통해 상호성의 개념이 고정적이거나 문맥에 따라, 임의로 정해지는 무질서한 것이 아니라, 함께 쓰인 배분적 양화사나 술어의 의미 특성에 따라 합성적으로(compositionally) 실현되는 것임을 보이고자 하였다.

• Language and Information
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• v.12 no.2
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• pp.115-137
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• 2008

We examine the meanings of two plural forms in Korean. Kwak (2003) and Jun (2004) claimed that unmarked (i.e. zero) plural forms denote groups and 'deul' plural forms denote sums, and Kang (2007) indicated problems in such claims. Soon after, Jun (2007) raised an objection to Kang's view by slightly modifying his former analysis, and now this paper is a reply to Jun (2007). Jun's revision of his former view is one step forward but still it is faced with many authentic counter examples. In the mean time, Noh (2008) raised an objection to Kang (2007) from a totally different direction, claiming that unmarked forms are not plural but only singular. This position is not sound, either. We have so many cases where unmarked forms are used with plural interpretation. All in all, our view that unmarked forms denote singular as well plural individuals(sums, groups) and 'deul' forms denote only plural individuals(sums, groups) is to be maintained.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.1-27
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• 2016

We introduce a notion of ternary distributive algebraic structure, give examples, and relate it to the notion of a quandle. Classification is given for low order structures of this type. Constructions of such structures from 3-Lie algebras are provided. We also describe ternary distributive algebraic structures coming from groups and give examples from vector spaces whose bases are elements of a finite ternary distributive set. We introduce a cohomology theory that is analogous to Hochschild cohomology and relate it to a formal deformation theory of these structures.