• Korean Journal of Logic
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• v.5 no.2
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• pp.39-66
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• 2002

일반적으로 엄밀한 방법을 통하여 증명되었다고 말해지는 괴델의 불완전성 정리는 일련의 전제와 배경지식이 요구된다고 하겠다. 이들 중에서 무엇보다도 중요한 것은 정리의 증명에 사용되는 메타언어상의 수학적 참에 대한 개념이다. 일단 확인할 수 있는 것은 "증명도, 반증도 되지 않지만 참인 산수문장의 존재"라는 불완전성 정리의 내용에서 괴델이 가정하고 있는 수학적 참의 개념이 구문론적인 증명개념으로부터 완전히 독립되어야 한다는 점이다. 문제는 그가 가정하고 있는 수학적 참의 개념이 도대체 무엇이어야만 하겠는가라는 점이다. 이 논문은 이 질문과 관련하여 내용적으로 3부분으로 나누어 질 수 있다. I. 괴델의 정리의 증명에 필요한 전제들 및 표의 도움을 얻어 자세히 제시되는 증명과정의 개략도를 통해 문제의 지형도를 조감하였다. II, III. 비트겐슈타인의 괴델비판을 중심으로, "일련의 글자꼴이 산수문장이다"라는 주장의 의미에 대한 상식적 비판 및 해석에 바탕을 둔 모형이론에 대한 대안제시를 통하여 괴델의 정리를 증명하기 위해 필요한 산수적 참에 관한 전제가 결코 "확보된 것이 아니다"라는 점을 밝혔다. IV. 괴델의 정리에 대한 앞의 비판이 초수학적 전제에 대한 것이라면, 3번째 부분에서는 공리체계에서 생성 가능한 표현의 증명여부와 관련된 쌍조건문이 그 도입에 필수적인 괴델화가 갖는 임의성으로 인해 양쪽의 문장의 참, 거짓 여부가 서로 독립적으로 판단 가능하여야만 한다는 점에(외재적 관계!) 착안하여 궁극적으로 자기 자신의 증명여부를 판단하게 되는 한계상황에 도달할 경우(대각화와 관련된 표 참조) 그 독립성이 상실됨으로 인해 사실상 기능이 정지되어야만 한다는 점, 그럼에도 불구하고 이 한계상황을 간파할 경우(내재적 관계로 바뀜!)항상 순환논법을 피할 수 없다는 점을 밝혔다. 비유적으로 거울이 모든 것을 비출 수 있어도 자기 스스로를 비출 수 없다는 점과 같으며, 공리체계 내 표현의 증명여부를 그 체계내의 표현으로 판별하는 괴델의 거울 역시 스스로를 비출 수는 없다는 점을 밝혔다. 따라서 괴델문장이 산수문장에 속한다는 믿음은, 그 문장의 증명, 반증 여부도 아니고 또 그 문장의 사용에서 오는 것도 아니고, 플라톤적 수의 세계에 대한 그 어떤 직관에서 나오는 것도 아니다. 사실상 구문론적 측면을 제외하고는 그 어떤 것으로부터도 괴델문장이 산수문장이라는 근거는 없다. 그럼에도 불구하고 괴델문장을 산수문장으로 볼 경우(괴델의 정리의 증명과정이라는 마술을 통해!), 그것은 확보된 구성요소로부터 조합된 문장이 아니라 전체가 서로 분리불가능한 하나의 그림이라고 보아야한다. 이것은 비트겐슈타인이 공리를 그림이라고 본 것과 완전히 일치하는 맥락이다. 바론 그런 점에서 괴델문장은 새로운 공리로 도입된 것과 사실은 다름이 없다.

• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.379-398
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• 2011

In learning environment at mathematics education, prove and refute are essential abilities to demonstrate whether and why a statement is true or false. Learning proofs and counter examples within the domain of limit of sequence is important because preservice teacher encounter limit of sequence in many mathematics courses. Recently, a number of studies have showed evidence that pre service and students have problem with mathematical proofs but many research studies have focused on abilities to produce proofs and counter examples in domain of limit of sequence. The aim of this study is to contribute to research on preservice teachers' productions of proofs and counter examples, as participants showed difficulty in writing these proposition. More importantly, the analysis provides insight and understanding into the design of curriculum and instruction that may improve preservice teachers' learning in mathematics courses.

• Communications of Mathematical Education
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• v.30 no.3
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• pp.393-418
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• 2016

Theory and fundamentals of mathematics consist mostly of proposition form. Activities by research of the proposition which leads to determine the true or false, justify the true propositions and refute with counterexample improve logical reasoning skills of students in emphases on mathematics education. Also, utilizing of counterexamples in school mathematics combines mathematical knowledge through the process of finding a counterexample, help the concept study and increase the critical thinking. These effects have been found through previous research. But many studies say that the learners have difficulty in generating counterexamples for false propositions and materials have not been developed a lot for the counterexample utilizing that can be applied in schools. So, this study analyzed the current textbook and examined the use of counterexamples and developed educational materials for counterexamples that can be applied at schools. That materials consisted of making true & false propositions and students was divided into three groups of academic achievement level. And then this study looked at the change of the students' thinking after counterexample classes. As a study result, in all three groups was showed a positive change in the cognitive domain and affective domain. Especially, in top-level group was mainly showed a positive change in the cognitive domain, in upper-middle group was mainly showed in the cognitive and the affective domain, in the sub-group was mainly found a positive change in the affective domain. Also in this study shows that the class that makes true or false propositions in education of utilizing counterexample, made students understand a given proposition, pay attention to easily overlooked condition, carefully observe symbol sign and change thinking of cognitive domain helping concept learning regardless of academic achievement levels of learners. Also, that class gave positive affect to affective domain that increase interest in the proposition and gain confidence about proposition.

• Journal of Korean Philosophical Society
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• v.141
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• pp.187-202
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• 2017

The aim of this paper is to clarify the difference between the concept of deduction-induction and Aristotle's concept of syllogismos-epagoge. First, Aristotle does not use the expression 'invalid syllogismos'. But a valid deduction is distinguished from a invalid deduction in modern logic. Second, from Aristotle's point of view syllogismos is paralleled by epagoge. Because syllogismos is equivalent to epagoge in logical form. But a disturbing lack of parallelism exists between deduction and induction by which the standards for establishing inductive conclusions are more demanding than those for deductive ones. Third, instructors in introductory logic courses ordinarily stress the need to evaluate arguments first in terms of the strength of the conclusion relative to the premises. Accordingly, students may be told to assume that premises are true. But Aristotle does not assume that premises are true. A syllogismos start from the conceptually true premise and a epagoge start from the empirically true premise.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.7B
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• pp.1361-1369
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• 1999

A hit-miss transform(HMT) using modified synthetic structuring elements(SEs) for distortion-invariant recognition of multiple objects is proposed. A fundamental problem in an HMT is the determination of the optimal SE needed to improve the false alarm rate, and detect distorted objects with various shapes. The proposed synthetic methods of SE provide good solutions against this problem. One is the multistage synthesis of each true class SE using only set theory, and the other is the multistage synthesis of each true class and false class SE using set theory and SDF(synthetic discriminant function) synthesis method. Simulation results show the proposed methods can be used for the recognition of distorted intraclass objects and the discrimination of similar interclass objects.

• Neonatal Medicine
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• v.17 no.2
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• pp.245-249
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• 2010

Purpose: Numerous false alarms by pulse oximetry, which is widely used in neonatal intensive care unit, can delay response to true alarms. Masimo $SET^{(R)}$ was introduced lately, to overcome false alarms by motion. We compared the clinical performance of two devices (Nellcor $N-595^{(R)}$ and Masimo $SET^{(R)}$) for the evaluation of the false alarm frequency during usual motion artifacts and stable state. Methods: A total of 20 preterm infants weighing 1,000-2,500 g were enrolled in the study. The sensors of two devices were placed on the different feet on the same infants, and both devices were programmed to emit an alarm for episode of hypoxemia (SpO2$\leq$85%). The false alarms were defined as episodes of poor correlation with ECG heart rate, poor waveforms, and the absence of obvious signs of hypoxia. We compared the frequency of false alarms between the two devices. Results: The mean chronological age was 20.8 days and the mean body weight was 1,668 g on the study day. The frequency of total false alarm was significantly fewer for Masimo $SET^{(R)}$ pulse oximetry (48 in Nellcor $N-595^{(R)}$, 27 in Masimo $SET^{(R)}$) although the false alarm during usual motion artifacts was not significantly between two devices (32 in Nellcor $N-595^{(R)}$, 19 in Masimo $SET^{(R)}$). Conclusion: The Masimo $SET^{(R)}$ pulse oximetry has fewer false alarm rates and identified more true hypoxic events than Nellcor $N-595^{(R)}$ pulse oximetry. Therefore, it is useful for adequate oxygen therapy and helps to decrease unnecessary handling by clinicians and nurses.

• Proceedings of the Korean Information Science Society Conference
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• 2012.06b
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• pp.153-154
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• 2012

바디 센서 시스템 환경이란 사용자가 서기, 걷기, 뛰기 등의 행위를 통해 주기적으로 상황이 변하는 동적 환경이다. 이와 같은 시스템에서는 크기가 작고 저전력을 요구하는 센서가 탑재되기 때문에 효율적인 알고리즘을 적용하는 것은 매우 중요한 일이다. 모델체커는 최근 소프트웨어 모델 (Model)을 검증하는 도구로써 주어진 모델과 속성값을 통해 해당 모델의 검증 (Verification) 결과가 참인지 거짓인지 판별해 준다. 본 논문에서는 효율적인 바디 센서 시스템 구축을 위해 서기, 걷기, 뛰기라는 환경에서 개별적으로 동작되는 알고리즘을 모델링 하고 LTL(Linear Temporal Logic) 로 속성을 명세하여 NuSMV 모델 체커를 통해 해당 모델의 Safety와 Liveness를 검증한다.

• Proceedings of the IEEK Conference
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• 2006.06a
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• pp.789-790
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• 2006

본 논문은 요즘 유행하는 웰빙(Well Being)에 대한 관심과 점점 고조되는 사람의 체질구분에 대해 퍼지이론(Fuzzy Theory)를 통해 연구하였다. 또한 각 체질구분에 따른 음식궁합을 따져서 보다 개인적 웰빙음식이 무엇이 있나에 대해 연구하였다. 사람마다 각각에 체질을 가지고 있다. 또한 자신의 체질이 아니더라도, 다른 체질에 대한 특성을 가질 수 있다. 이런 점에서 퍼지이론을 사용하여 체질을 구분할 수 있다. 퍼지이론의 큰 장점이 문제점 해결시 참<1>, 거짓<0>으로 해결하지 않기 때문에 여러 가지 문제 해결점을 가진다는 것이다. 공통적으로 해당하는 체질문항일 경우 퍼지 소속함수 값을 각각 다르게 주어서 최종 포인트에 대한 Fuzzy set 의 크기를 따져 체질구분을 하고, 그에 따른 음식궁합을 규정한다.

• Journal of Digital Convergence
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• v.14 no.2
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• pp.437-447
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• 2016

This study is intended to analyze the conflict between the mother and the daughter revealed in the film, 'Daughter' and tries to suggest the therapeutic counseling techniques in the integrated perspective. It used a convergence in-depth psychological method. After deriving the unconscious conflicts of main characters through several film reviews, it was found that at the unconscious level true self and the false self, the ego ideal and the super ego, the individuation and the dependency are in mutual struggle. For Therapeutic counselling, the most important thing in the initial stage of the counselling is the experience of authenticity. The counsellor himself or herself should establish the right life values and stimulate the ego-ideal and strengthen the drive of true self. Also the counsellor should be aware of the dangers of the religious behavior as the transitional phenomenon. In the final stage, the counselor expects the client to continue to make efforts to change with the hope for the well-being.

• The Journal of the Acoustical Society of Korea
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• v.39 no.4
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• pp.292-302
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• 2020

Machine learning algorithms have made immense contributions in various fields including sonar and radar applications. Recently developed Cycle-Consistency Generative Adversarial Network (CycleGAN), a variant of GAN has been successfully used for unpaired image-to-image translation. We present a modified CycleGAN for translation of underwater ship engine sounds with high perceptual quality. The proposed network is composed of an improved generator model trained to translate underwater audio from one vessel type to other, an improved discriminator to identify the data as real or fake and a modified cycle-consistency loss function. The quantitative and qualitative analysis of the proposed CycleGAN are performed on publicly available underwater dataset ShipsEar by evaluating and comparing Mel-cepstral distortion, pitch contour matching, nearest neighbor comparison and mean opinion score with existing algorithms. The analysis results of the proposed network demonstrate the effectiveness of the proposed network.