• Proceedings of the Korean Society for Cognitive Science Conference
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• 2000.05a
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• pp.322-328
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• 2000

This study discusses cognition as a computable mapping in cognitive system and relates G del's Incompleteness Theorems to the computability of cognition from a metamathematical perspective. Understanding cognition as a from of computation requires not only Turing machine models but also neural network models. In previous studies of computation by cognitive systems, it is remarkable to note how little serious attention has been given to the issue of computation by neural networks with respect to G del's Incompleteness Theorems. To address this problem, first, we introduce a definition of cognition and cognitive science. Second, we deal with G del's view of computability, incompleteness and speed-up theorems, and then we interpret G del's disjunction on the mind and the machine. Third, we discuss cognition as a Turing computable function and its relation to G del's incompleteness. Finally, we investigate cognition as a neural computable function and its relation to G del's incompleteness. The results show that a second-order representing system can be implemented by a finite recurrent neural network. Hence one cannot prove the consistency of such neural networks in terms of first-order theories. Neural computability, theoretically, is beyond the computational incompleteness of Turing machines. If cognition is a neural computable function, then G del's incompleteness result does not limit the compytational capability of cognition in humans or in artifacts.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1998.10a
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• pp.413-420
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• 1998

In this paper, two methods, Stepp's and EQHAZARD, are introduced and applied to a recent earthquake catalog for the entire Korean Peninsula that can estimate the seismicity by incorporating the incompleteness of the earthquake catalog. EQHAZARD method, different from Stepp's method in that it used priori information besides the assumption of stationary Poisson process of the earthquakes, produces the higher seismicity rate for the smaller earthquakes. EQHAZARD method are also used to estimated the incompleteness of the recent earthquake catalog for the southern part of the Korean Peninsula in terms of the Probability of Activity for the specified earthquke magnitude classes and time periods. It is believed that the Probability of Activity thus obtained can be used as a strong priori information in estimating the seismicity for a seismic source within the region where there are not enough earthquakes detected. Finally, it is demonstrated that the arbitrary selection of the methods. of incompleteness analysis brings quite different seismic hazard results, which suggests the need to employ a rigid quantitative method for incompleteness analysis in estimating the seismicity parameters in order to reduce the uncertainty in the Seismic Hazard Results with the EQHAZARD method being one of the competent practical alternatives.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.75-82
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• 2002

G$\ddot{o}$del's metamathematical program from Incompleteness to Speed-up theorems shows the necessity of ever higher systems beyond the fixed formal system and devises the relative consistency.

• Annual Conference on Human and Language Technology
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• 1995.10a
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• pp.258-263
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• 1995

마음과 기계의 관계에 대한 $G{\ddot{o}}del's$의 선언결론(disjunctive conclusion)은 마음과 정보처리형식체계의 논리적 동치성을 함의하고 있다. 그리고 $G{\ddot{o}}del's$의 불완전성 정리(Incompleteness Theorems)에 따르면 마음과 정보처리형식체계의 논리적 동치성은 무모순이며, 동치성 반증의 이론은 그 모델을 가질 수 없다.

• Journal of the Korean Data and Information Science Society
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• v.15 no.3
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• pp.555-563
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• 2004

In classification and discrimination, we often face with incomplete group variable arising typically from many missing values and/or incredible cases. This paper suggests the use of K-means clustering for pre-adjusting incompleteness and in turn classification based on generalized statistical distance is performed. For illustrating the proposed procedure, simulation study is conducted comparatively with CART in data mining and traditional techniques which are ignoring incompleteness of group variable. Simulation study manifests that our methodology out-performs.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.47-58
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• 2006

This paper aims to introduce $G\ddot{o}del's$ life and thought, and insists that implication of the incompleteness theorem is saving blank space. The space has epistemological and ethical meaning, and I argue that the implication supports philosophy of blank space.

• The Journal of the Korea institute of electronic communication sciences
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• v.19 no.1
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• pp.295-300
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• 2024

This paper discusses the incompleteness of the SNOMED CT and proposes a noble metric which evaluates similarity among sibling nodes as a method to address this incompleteness. SNOMED CT encompasses an extensive range of medical terms, but it faces issues of ontology incompleteness, such as missing concepts in the hierarchy. We propose a noble metric for evaluating similarity among nodes within a node group, composed of multiple sibling nodes, to identify missing concepts, and identify groups with low similarity. Analyzing the similarity of sibling node groups in the March 2023 international release of SNOMED CT, the average similarity of 29,199 sibling node groups, which are sub-concepts of the clinical finding concept and are consist of two or more sibling nodes, was found to be 0.81. The group with the lowest similarity was associated with child concepts of poisoning, with a similarity of 0.0036.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.4
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• pp.302-309
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• 2002

A FRF-based substructuring method attempts to predict the dynamic characteristics of a complex structure from predetermined FRFs of the comprising uncoupled substructures. Although this method has the advantage of being able to incorporate experimental component FRFs directly, it is prone to errors : measurement errors, coordinate incompleteness, modal incompleteness, etc. Among the various sources of errors, this paper deals with the problem of modal incompleteness (or residual problem) of which importance is underestimated compared to others. It is a well-known rule of thumb that such a problem can be overcome by including modes up to 2 or 3 times the upper frequency of interest. Using a simulated case study, it is demonstrated that even including modes up to 20 times the upper frequency of interest does not guarantee a satisfactory result. A method to compensate the residual errors is introduced. This method requires the whole FRF matrices of substructures which is practically impossible for a complex structure. An applicable alternative is suggested and applied successfully to the case study. Finally, the effects of measurement errors on the residual compensation are also discussed.

• Journal for History of Mathematics
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• v.13 no.1
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• pp.137-141
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• 2000

This paper discusses Godel's Disjunctive Conclusion in terms of cognitive science and his Incompleteness Theorems from a metamathematical perspective.

• Journal for History of Mathematics
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• v.29 no.1
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• pp.31-44
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• 2016

This essay aims to suggest roughly the "philosophy of limits." The limits mainly refer to those of human experiences and rational thoughts. The philosophy of limits consist of three theses and two consequences(L, M). (1) The limits are necessarily supervenient in the course of searching knowledge. (2) The limits cannot be dissipated ultimately. (3) To recognize the limits is not only an intellectual recognition but also a beginning of whole personality's reaction. (L) It is a rational decision to accept the limits and leave the margins (yeoback/yeoheuck) rather than to try to remove them. (M) To leave the margins (yeoback/yeoheuck) is characteristic of being human, and enables one to harmoniously communicate with others. To justify the philosophy of limits, this essay examine the limits discussed in mathematics and philosophy: set theory, Godel's Incompleteness Theorem, Galois Theorem in mathematics; and Hume, Kant, Kierkegaard, and Wittgenstein in philosophy. I try to interpret consciousness of limits in various cultures. I claim that consciousness of the limits contribute to lucidity of human identity, communication between persons, stimulation of creative thinking.