• Journal of KIISE:Computer Systems and Theory
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• v.26 no.12
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• pp.1485-1492
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• 1999

대규모 시스템 명세의 올바름을 검증하기 위한 유한 상태 LTS에 기반을 둔 CTL논리 적용에 있어 가장 큰 문제점은, 시스템 내부의 병렬 프로세스간의 상호작용으로 인한 상태폭발이다. 그러나 Modal mu-calculus 논리를 시스템 안전성 및 필연성 특성 명세에 사용하면, 행위에 의한 순환적 정의가 가능하므로 상태폭발 문제가 해결 가능하다. 본 논문에서는 LTS로 명세화된 통신 프로토콜 시스템 모델의 안전성 및 필연성 특성을 모형 검사 기법에 의해 검증함에 있어, 시제 논리로 사용된 Modal mu-calculus 안전성 및 필연성 논리식과 CTL 의 안전성 및 필연성 논리식의 극한값이 동일함을 두 논리식을 만족하는 상태 집합이 같다는 것을 보임으로써 증명한다. 증명된 결과는 I/O FSM 모델로 표현된 통신 프로토콜의 안전성 및 필연성 검사를 위해 이론적인 기반으로서, 컴퓨터를 이용한 모형검사 기법에 효과적인 방법으로 응용이 가능하다.Abstract In applying CTL-based model checking approach to correctness verification of large state transition system specifications, the major obstacle is the combinational explosion of the state space arising due to interaction of many loosely coupled parallel processes. If, however, the modal mu-calculus viewed as a CTL-based logic with recursion, is used to specify the safety and liveness property of a given system, it is possible to resolve this problem. In this paper, we discuss the problem of verifying communication protocol system specified in LTS, and prove that a logic expression specifying safety and liveness in modal mu-calculus is semantically identical to the maximum value of the expression in CTL. This relation is verified by the proof that the sets of states satisfying the two logic expressions are equivalent. The proof can be used as a theoretical basis for verifying safety and liveness of communication protocols represented as I/O FSM model.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.6
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• pp.2470-2491
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• 2018

Web-scale open information extraction (Open IE) plays an important role in NLP tasks like acquiring common-sense knowledge, learning selectional preferences and automatic text understanding. A large number of Open IE approaches have been proposed in the last decade, and the majority of these approaches are based on supervised learning or dependency parsing. In this paper, we present a novel method for web scale open information extraction, which employs cosine distance based on Google word vector as the confidence score of the extraction. The proposed method is a purely unsupervised learning algorithm without requiring any hand-labeled training data or dependency parse features. We also present the mathematically rigorous proof for the new method with Bayes Inference and Artificial Neural Network theory. It turns out that the proposed algorithm is equivalent to Maximum Likelihood Estimation of the joint probability distribution over the elements of the candidate extraction. The proof itself also theoretically suggests a typical usage of word vector for other NLP tasks. Experiments show that the distance-based method leads to further improvements over the newly presented Open IE systems on three benchmark datasets, in terms of effectiveness and efficiency.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.45-56
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• 2010

Sequent Calculus is a symmetrical version of the Natural Deduction which Gentzen restructured in 1934, where he presents 'Hauptsatz'. In this thesis, we will examine why the Cut-Elimination Theorem has such an important status in Proof Theory despite of the efficiency of the Cut Rule. Subsequently, the dynamic side of Curry-Howard correspondence which interprets the system of Natural Deduction as 'Simply typed $\lambda$-calculus', so to speak the correspondence of Cut-Elimination and $\beta$-reduction in $\lambda$-calculus, will also be studied. The importance of this correspondence lies in matching the world of program and the world of mathematical proof. Also it guarantees the accuracy of program.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.4
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• pp.132-137
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• 2007

A point-wise car-like robot moving in the plane changes its direction with a constraint on turning curvature. In this paper, we consider the problem of computing a shortest path of bounded curvature between a prescribed initial configuration (position and orientation) and a polygonal goal, and propose a new geometric proof showing that the shortest path is either of type CC or CS (or their substring), where C specifies a non-degenerate circular arc and S specifies a non-degenerate straight line segment. Based on the geometric property of the shortest path, the shortest path from a configuration to a polygonal goal can be computed in linear time.

• Journal of IKEEE
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• v.17 no.4
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• pp.559-563
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• 2013

This paper analytically proves the equivalence between two main oscillator phase noise theories, which are based on the ISF, and Floquet vector, respectively. For this purpose, this study obtains the power spectral density matrix from the ISF-based phase noise theory. As a result, one can prove that the power spectral density matrix obtained from the ISF-based phase noise theory is essentially equivalent to the power spectral density matrix presented by the Floquet vector-based phase noise theory, which manifests the equivalence of the two main theories. This study is intended to provide deeper insight into the relations between the two main theories.

• The Mathematical Education
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• v.50 no.2
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• pp.135-148
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• 2011

We can say that the history of mathematics is the history on the development of the number system. The number starts from Natural number and is constructed to Integer number and Rational number. The Rational number is not the complete number analytically so that Real number is completed by the idea of the nested interval method. Real number is completed analytically, however, is not by algebra, so the algebraically completed type of the rational number, through the way that similar to the process of completing real number, is Complex number. The purpose of this study is to show the most appropriate way for the development of the human being thinking about the teaching and leaning of Complex number. To do this, We have to consider the proof of the existence of Complex number, the background of the introduction of Complex number and the background knowledge that the teachers to teach Complex number should have. Also, this study analyzes the knowledge to be taught of Complex number based on the anthropological theory of didactics and finally presents the teaching method of Complex number based on this theory.

• Journal of the Korean Geotechnical Society
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• v.26 no.7
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• pp.161-170
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• 2010

For the development of load and resistance factor design, reliability analysis is required to calibrate resistance factors in the framework of reliability theory. The distribution of measured-to-predicted pile resistance ratio was obrained based on only the results of load tests conducted to failure for the assessment of uncertainty regarding pile resistance and used in the conventional reliability analysis. In other words, successful pile load test (piles resisted twice their design loads without failure) results were discarded, and therefore, were not reflected in the reliability analysis. In this paper, a new systematic method based on Bayesian theory is used to update reliability indices of driven steel pipe piles by adding more proof pile load test results, even not conducted to failure, to the prior distribution of pile resistance ratio. Fifty seven static pile load tests performed to failure in Korea were compiled for the construction of prior distribution of pile resistance ratio. The empirical method proposed by Meyerhof is used to calculate the predicted pile resistance. Reliability analyses were performed using the updated distribution of pile resistance ratio. The challenge of this study is that the distribution updates of pile resistance ratio are possible using the load test results even not conducted to failure, and that Bayesian updates are most effective when limited data are available for reliability analysis.

• The Journal of Korean Medical History
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• v.17 no.1
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• pp.105-118
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• 2004

The four precious results are beard below after thorough study of Jeoneul(錢乙)'s descended piece and main citation reference from Song(宋) era. 1. Jeoneul(錢乙)'s historical period seems that he finished his life in the age of 82, from Cheonseong(天聖) 10years(Year 1032) to Jeonghwa(政和) 3years(Year 1113) in North Song(北宋) era. However, it also seems that his life terminated Seonhwa(宣和)元年in 1119. The title of "Soayakjeungjikgyeol(小兒藥證直訣)" was reflected in "Sagojeonseo(四庫全書)" as "Soayakjeungjikgyeol(小兒藥證直訣)", however according to various of previous descended references and citations indicate that "Soayakjeungjikgyeol(小兒藥證直訣)" is more appropriate than "Soayakjeungjikgyeol(小兒藥證直訣)". Furthermore, the name, Yeomhyochung(閻孝忠), who edited the reference "Soayakjeungjikgyeol(小兒藥證直訣)" was appeared as Yeomgyechung(閻孝忠) in many different old references. Thus, even though, Sagogoan(四庫館) and Juhakhae(周學海) looked as Yeomgyechung(閻孝忠), but it seems Yeomhyochung(閻孝忠) in "Songsa(宋史)" Yemunji(藝文志) is more authentic than others. 2. When first edition of "Soayakjeungjikgyeol(小兒藥證直訣)" was published, Yeomhyochung(閻孝忠)'s the first book of "Yeomssisoabangnon(閻氏小兒方論)" and the first chapter of Yugi's "Jeonjungyangjeon(錢仲陽傳)" were attached in one book. Not long after of the first edition, Donggeup(董汲)'s first book of "Soabanjinbigeupbangnon(小兒斑疹備急方論)" and Jeoneul(錢乙)'s additional attachment was added in prescription reference. Among these references which were published in Song era, the original copy which Jinsegeol(陳世傑) published in Chung era in Ganghi(康熙) 58years (Year 1719) was remained and the first edition that Yangsugyeong(楊守敬) collected in Japan was published in "(lbonbangseoji(日本訪書志)" called Seonhwabon(宣和本). 3. Ungjonglip(熊宗立)'s "LyujeungjuseokJeonssisoabanggyeol(類證注釋錢氏小兒方訣)", Seolgi(薛己)'s "Gyojeongjeonssisoayakjeungjikgyeol(校正錢氏小兒藥證直訣)" Muyeongjeon-Chuijinbon(武英殿聚珍本) were followed Yangsugyeong(楊守敬)'s called Seonhwabon(宣和本) theory, in addition Yubang(劉昉)'s "Yuyusinseo(幼幼新書)" and "Soayakjeungjikgyeol(小兒藥證直訣)" quoted from Chosun "Euibangyuchui(醫方類聚)" also followed Yangsugyeong(楊守敬)'s called Seonhwabon(宣和本) theory. On the other hand, Jinsegeol(陳世傑)'s Gisudangbon(起秀堂本) and reprinted Juhakhaebon(周學海本) belong to parts of Songbokganbon(宋復刊本). 4. In major references and citation materials descended from "Soayakjeungjikgyeol(小兒藥證直訣)", Yubang(劉昉)'s "Yuyusinseo(幼幼新書)" and "Soauisaengchongaminonbang(小兒衛生總微論方)" were cited in Song era and some related parts in "Yeongnakdaejeon(永樂大典)", "Soayakjeungjikgyeol(小兒藥證直訣)" related sections, Ungjonglip(熊宗立)'s reedited and annotated part of "Lyujeungjuseokjeonssisoabanggyeol(類證注釋錢氏小兒方訣)", Seolgi(薛己)'s proof reading and annotated "Gyojujeonssisoayakjeungjingyeol(校注錢氏小兒藥證直訣)", "Euibangyuchui(醫方類聚)"'s quotation. In Chung(淸)era, Jinsegeol(陳世傑)'s re-published reference, Gisudangbon(起秀堂本), which was simply printed in Song and proof read and republished Juhakhaebon(周學海本), Muyeongjeonchuijinbon(武英殿聚珍本) compiled from "Yeongnakdaejeon(永樂大典)", Yangsugyeong(楊守敬)'s "Jeonssisoayakjeungjikgyeol(錢氏小兒藥證直訣)" mentioned in "Ilbonbangseoji(日本訪書志)", Jangsui's annotation, "Soayakjeungjikgyeoljeonjeong(小兒藥證直訣箋正)" and Simgeumo(沈金鰲)'s "Yuguaseokmi(幼科釋謎)" which was applied Jeoneul(錢乙)'s theory and prescription.

• Journal of the Korean School Mathematics Society
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• v.1 no.1
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• pp.175-184
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• 1998

The purpose of this study is that the Van Hiele theory can be applied to even vocational high school students. Through the comparison of Van Hiele level distribution of middle school students and high school students, it is that the aims of this study is to study the geomatric level of vocational high school students and to analize them, even so it can be to find for them the effective method of Geomatric education The subject of study is three kinds of vocational high school - commercial high school, industrial high school, fisheries high school - boys (240), girls (120) in Boryeong city, Chungchong Nam Do. We referred to Kim Mi-cheong′ thesis(1994) and Cheong Yean-sok′s thesis(1992) and compared my result with them. The method and the process of the study were based on the th method of CDASSG project. And we used Van Hiele Level Test as an instrument of measurement. We got the following conclusion as the result of the study 1. The 86％ of the subject of the study was applied to the theory of Van Hiele - "Any students can reach level n just through level n-1." Even so the propriety of the theory proved to be from this study again. 2. The 88% of the subject of the study is applicable to below level 2. So if the proof is introduced to them in the class, it was very difficult for them to understand it. 3. The geometric level of vocational high school students is the same as the second grade of middle school. But we think to be desirable that a basic concept puts first in importance through recomposed teaching materials, because 68% of the students is seldom changed at level 1.