• Journal for History of Mathematics
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• v.24 no.3
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• pp.37-58
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• 2011

The development of recent Mathematical Logic is mostly originated in Hilbert's Proof Theory. The purpose of the plan so called Hilbert's Program lies in the formalization of mathematics by formal axiomatic method, rescuing classical mathematics by means of verifying completeness and consistency of the formal system and solidifying the foundations of mathematics. In 1931, the completeness encounters crisis by the existence of undecidable proposition through the 1st Theorem of G?del, and the establishment of consistency faces a risk of invalidation by the 2nd Theorem. However, relative of partial realization of Hilbert's Program still exists as a fruitful research program. We have tried to bring into relief through Curry-Howard Correspondence the fact that Hilbert's program serves as source of power for the growth of mathematical constructivism today. That proof in natural deduction is in truth equivalent to computer program has allowed the formalization of mathematics to be seen in new light. In other words, Hilbert's program conforms best to the concept of algorithm, the central idea in computer science.

• Journal for History of Mathematics
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• v.9 no.2
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• pp.30-42
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• 1996

최근 <수학기초론>이란 용어는 Burali-Forti paradox 이후 족(class)과 집합(set) 개념을 이해하려는 시도에서 출발한 20세기적 문제에 적용되고 있다. 이 글에서는 그 해결책으로 제시된 주의ㆍ주장 중 논리적인 모순을 해결하기 위한 Russel의 논리주의적 공리론에 바탕을 두고 살펴보려고 한다. 제 2장에서는 무한의 심연 속에 웅크리고 있는 집합론에서의 역설과 발생 원인에 대하여 살펴보았다. 제 3장에서는 공리론적 집합론 중에서 러셀의 유형론과 그것을 단순화시킨 현대의 유형론을 살펴보고, ZF 집합론과 ZF 집합론의 연장인 처치 집합론의 기본 공리를 살펴보았다.

• Korean Journal of Logic
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• v.8 no.2
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• pp.3-32
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• 2005

Hilbert's rational ambition to establish consistency in Number theory and mathematics in general was frustrated by the fact that the statement itself claiming consistency is undecidable within its formal system by $G\ddot{o}del's$ second theorem. Hilbert's optimism that a mathematician should not say "Ignorabimus" ("We don't know") in any mathematical problem also collapses, due to the presence of a undecidable statement that is neither provable nor refutable. The failure of his program receives more shock, because his system excludes any ambiguity and is based on only mechanical operations concerning signs and strings of signs. Above all, $G\ddot{o}del's$ theorem demonstrates the limits of formalization. Now, the notion of provability in the dimension of syntax comes to have priority over that of semantic truth in mathematics. In spite of his failure, the notion of algorithm(mechanical processe) made a direct contribution to the emergence of programming languages. Consequently, we believe that his program is failure, but a great one.

• The Transactions of the Korea Information Processing Society
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• v.7 no.7
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• pp.2028-2040
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• 2000

A study on workflow as an automated business processing system is done recently. This appear proposes a method to verify commitability and integrity of workflow specifications, which include various dependencies between parallel tasks, using petri nets. For this, firstly, e describe briefly workflow specification method using workflow graphs. Secondly, we propose a method to convert a workflow graph into a petri net to verify workflow specifications. Thirdly, we suggest the commitability verification method using petri nets to check whether workflow specifications can commit or not and the integrity verification method to check whether invalid components exist or not. Lastly, we implement the proposed verification method and propose a defect extraction method.

• The Mathematical Education
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• v.61 no.1
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• pp.29-45
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• 2022

This study tried to analyze the problems by critically examining how the chance is taught in relation to the concept of chance and randomness in the Korean elementary school mathematics curriculum. To this end, the concepts of chance and randomness were first examined, and problems were presented in based on this by the literature analysis on mathematics curriculum material and textbooks for elementary school in Korea. As a result, there was a lack of experience in reasoning based on data, and randomness instruction was not performed properly. In addition, as the teaching of the sample space was omitted, contradictory materials were being used. Moreover, it was pointed out that the teaching of chance is focused on a specific grade level. For the improvement of the teaching of chance, a teaching of the probability experiment and the sample space were mainly suggested, and it was also suggested that the contents of the data area be adjusted for the composition focused on a specific grade.

• The Journal of the Convergence on Culture Technology
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• v.7 no.4
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• pp.325-330
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• 2021

This study set out to investigate the forms, attributes, and escape methods of post-subjects projected on the investigator's works in connection with rhizomatic thinking proposed as a way of social transformation by Deleuze and Guattari and examine their social connotations. Post-subjects projected on the investigator's works are not completed wholes of some sort, but like materials whose constant premise is change and creation. In the investigator's works, post-subjects have conscious and unconscious desire. It is the desire of creation with positive attributes including Deleuze's and Guattari's pursuit of changes in a contradicting society. When desire is deployed in post-subjects, they will carry out an escape. This way of escape is rhizomatic proposed by Deleuze and Guattari. It deconstructs contradicting things and repeats connection, contact, and severance with the outside world, building a new order. Rhizomatic post-subjects appearing in the investigator's works depict the escape process and method in abstract ways through the variable installation of objets combined with a color field of repeating brushes. In this work, the goal of post-subjects is to make a safe landing in a space where beings are recognized for their values and free and creative lives. These post-subjects are nomads creating a new landscape continuously, wandering around vast plains, and also artists and literary figures resisting a contradicting society. That is, they are connected to the concept of a war machine proposed by Deleuze and Guattari as a concept of social transformation and to the concept of Nietzsche's Agon to devise and create new values and politics based on street passion. They seek after a space where they can co-exist with otherness recognized rather than the complete deconstruction of the old order.

• Korean Journal of Logic
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• v.15 no.1
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• pp.155-190
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• 2012

As far as Hilbert's Program is concerned, there seems to be important differences in the development of Wittgenstein's thoughts. Wittgenstein's main claims on this theme in his middle period writings, such as Wittgenstein and the Vienna Circle, Philosophical Remarks and Philosophical Grammar seem to be different from the later writings such as Wittgenstein's Lectures on the Foundations of Mathematics (Cambridge 1939) and Remarks on the Foundations of Mathematics. To show that differences, I will first briefly survey Hilbert's program and his philosophy of mathematics, that is to say, formalism. Next, I will illuminate in what respects Wittgenstein was influenced by and criticized Hilbert's formalism. Surprisingly enough, Wittgenstein claims in his middle period that there is neither metamathematics nor proof of consistency. But later, he withdraws his such radical claims. Furthermore, we cannot find out any evidences, I think, that he maintained his formerly claims. I will illuminate why Wittgenstein does not raise such claims any more.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.32 no.2
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• pp.87-93
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• 2014

Cadastral parcel objects as polygons are fundamental dataset which represent land administration and management of the real world. Thus it is necessary to assure topological seamlessness of cadastral datasets which means no overlaps or gaps between adjacent parcels. However, the problem of overlaps or gaps are frequently found due to non-coinciding edges between adjacent parcels. These erroneous edges are called uncertain edges, and polygons containing at least one uncertain edge are called uncertain polygons. In this paper, we proposed a new algorithm to efficiently search parcels of uncertain polygons between two adjacent cadastral datasets. The algorithm first selects points and polylines around adjacent datasets. Then the Constrained Delaunay Triangulation (CDT) is applied to extract triangles. These triangles are tagged by the number of the original cadastral datasets which intersected with the triangles. If the tagging value is zero, the area of triangles mean gaps, meanwhile, the value is two, the area means overlaps. Merging these triangles with the same tagging values according to adjacency analysis, uncertain edges and uncertain polygons could be found. We have performed experimental application of this automated derivation of partitioned boundary from a real land-cadastral dataset.

• Journal of the Korean School Mathematics Society
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• v.14 no.3
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• pp.355-375
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• 2011

This paper was designed for the purpose of helping the functional comprehension on the concept of a circumcenter and an incenter of triangle and offering the help for teaching-learning process on their definitions. We analysed the characteristic of the definition on a circumcenter and an incenter of triangle and studied the context, mean and purpose on the definition. The definition focusing on the construction is the definition stressed on the consistency of the concept through the fact that it is possible to draw figure of the concept. And this definition is the thing that consider the extend of the concept from triangle to polygon. Meanwhile this definition can be confused because the concept is not connected with the terminology. The definition focusing on the meaning is easy to memorize the concept because the concept is connected with the terminology but is difficult to search for the concept truth. And this definition is the thing that has the grounds on the occurrence but is taught in a made-knowledge. The definition focusing on both the construction and meaning is the definition that the starting point is vague in the logical proof process. We hope that the results are used to improve the understanding the concept of a circumcenter and an incenter of triangle in the field of mathematical education.

• Korean journal of communication and information
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• v.68
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• pp.130-165
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• 2014

By exploring the works of popular culture, our research aims to demonstrate that culture and politics revolve around each other. Culture and politics are not separate but are articulated into cultural politics; the process of articulation reveals various comparable areas, including contradictions and differences. Our research pays specific attention to Japanese modernity in the eight popular manga series by Naoki Urasawa. These works seemingly value peace and brotherhood, placing themselves in opposition to the logics of the conservative right wing. After engaging in a thorough reading and re-reading, however, we found three salient themes in the deep layers of the works: first, no-nationality a-nationality; second, the relationship between Japan and the West, and representation of Asia; and third, nostalgia for Japan of the past, and transnational desire. The manga series contain the ideas of leaving Asia and entering the West and overcoming modernity. Our research findings reveal that the works of popular culture, specifically those by Naoki Urasawa, subtly expose transnational desires of Japan in tandem with the tensions in international politics between Asia and Japan.