• Korean Journal of Cognitive Science
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• v.10 no.4
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• pp.71-83
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• 1999

Conventional symbolic inference systems lack flexibility because they do not well reflect flexible semantic structure of knowledge and use symbolic logic for their basic inference mechanism. For solving this problem. we have recently proposed the 'Connectionist Semantic Network(CSN)' as a model for flexible knowledge representation and inference based on neural networks. The CSN is capable of carrying out both approximate reasoning and commonsense reasoning based on similarity and association. However. we have difficulties in representing general and structured high-level knowledge and variable binding using the connectionist framework of the CSN. In this paper. we propose a hybrid system called SymCSN(Symbolic CSN) that combines a symbolic module for representing general and structured high-level knowledge and a connectionist module for representing and learning low-level semantic structure Simulation results show that the SymCSN is a plausible model for human-like flexible knowledge representation and inference.

• Research in Mathematical Education
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• v.8 no.1
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• pp.1-18
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• 2004

Current interest in mathematics learning that focuses on understanding, mathematical reasoning and meaning making underscores the need to develop ways of analyzing classrooms that foster these types of learning. In this paper, the author show that the constructs of social and socio-mathematical norms, which grew out of taking a symbolic interactionist perspective, and Toulmins scheme for argumentation, as elaborated for mathematics education by Krummheuer [The ethnology of argumentation. In: The emergence of mathematical meaning: Interaction in classroom cultures (1995, pp. 229-269). Hillsdale, NJ: Erlbaum], provide us with means to analyze aspects of explanation, justification and argumentation in mathematics classrooms, including means through which they can be fostered. Examples from a variety of classrooms are used to clarify how these notions can inform instruction at all levels, from the elementary grades through university-level mathematics.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.887-890
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• 1993

By introducing the notion of constraint-oriented fuzzy inference, we will show that it provides us ways of fuzzy control methods that has abilities of adaptation, learning and self-organization. The basic supporting techniques behind these abilities are“hard”processing by Artificial Intelligence or traditional computational framework and“soft”processing by Neural Network or Genetic Algorithm techniques. The reason that these techniques can be incorporated to fuzzy control systems is that the notion of“constraint”itself has two fundamental properties, that is, the“modularity”property due to its declarativeness and the“logicality”property due to its two-valuedness. From the former property, the modularity property, decomposing and integrating constraints can be done easily and efficiently, which enables us to carry out the above“soft”processing. From the latter property, the logicality property, Qualitative Reasoning and Instance Generalization by Symbolic Reasoning an be carried out, thus enabling the“hard”processing.

• Communications of Mathematical Education
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• v.18 no.1 s.18
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• pp.1-18
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• 2004

Current interest in mathematics learning that focuses on understanding, mathematical reasoning and meaning making underscores the need to develop ways of analyzing classrooms that foster these types of learning. In this paper, I show that the constructs of social and sociomathematical norms, which grew out of taking a symbolic interactionist perspective, and Toulmins scheme for argumentation as elaborated for mathematics education by Krummheuer, provide us with means to analyze aspects of explanation justification and argumentation in mathematics classrooms, including means through which they can be fostered. Examples from a variety of classrooms are used to clarify how these notions can inform instruction at all levels, from the elementary grades through university-level mathematics.

• The Mathematical Education
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• v.43 no.1
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• pp.97-107
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• 2004

Current interest in mathematics learning that focuses on understanding, mathematical reasoning and meaning making underscores the need to develop ways of analyzing classrooms that foster these types of learning. In this paper, I show that the constructs of social and sociomathematical norms, which grew out of taking a symbolic interactionist perspective, and Toulmin's scheme for argumentation, as elaborated for mathematics education by Kummheuer, provide us with means to analyze aspects of explanation, justification and argumentation in mathematics classrooms, including means through which they can be fostered. Examples from a variety of classrooms are used to clarify how these notions can inform instruction at all levels, from the elementary grades through university-level mathematics.

• Proceedings of the Korea Society for Simulation Conference
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• 1994.10a
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• pp.12-12
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• 1994

Simulation output knowledge analysis is one of problem-solving and/or knowledge adquistion process by investgating the system behavior under study through simulation . This paper describes an approach to simulation outputknowldege analysis using fuzzy neural network model. A fuzzy neral network model is designed with fuzzy setsand membership functions for variables of simulation model. The relationship between input parameters and output performances of simulation model is captured as system behavior knowlege in a fuzzy neural networkmodel by training examples form simulation exepreiments. Backpropagation learning algorithms is used to encode the knowledge. The knowledge is utilized to solve problem through simulation such as system performance prodiction and goal-directed analysis. For explicit knowledge acquisition, production rules are extracted from the implicit neural network knowledge. These rules may assit in explaining the simulation results and providing knowledge base for an expert system. This approach thus enablesboth symbolic and numeric reasoning to solve problem througth simulation . We applied this approach to the design problem of broadband communication network.

• Journal of KIISE
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• v.45 no.1
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• pp.22-29
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• 2018

Over the decades, neural networks have been successfully used in numerous applications from speech recognition to image classification. However, these neural networks cannot explain their results and one needs to know how and why a specific conclusion was drawn. Most studies focus on extracting binary rules from neural networks, which is often impractical to do, since data sets used for machine learning applications contain continuous values. To fill the gap, this paper presents an algorithm to extract logic rules from a trained neural network for data with continuous attributes. It uses hyperplane-based linear classifiers to extract rules with numeric values from trained weights between input and hidden layers and then combines these classifiers with binary rules learned from hidden and output layers to form non-linear classification rules. Experiments with different datasets show that the proposed approach can accurately extract logical rules for data with nonlinear continuous attributes.

• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.453-475
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• 2007

School algebra starts with introducing algebraic expressions which have been one of the cognitive obstacles to the students in the transfer from arithmetic to algebra. In the recent studies on the teaching school algebra, algebraic thinking is getting much more attention together with algebraic expressions. In this paper, we examined the processes of the transfer from arithmetic to algebra and ways for teaching early algebra through algebraic thinking factors. Issues about algebraic thinking have continued since 1980's. But the theoretic foundations for algebraic thinking have not been founded in the previous studies. In this paper, we analyzed the algebraic thinking in school algebra from historico-genetic, epistemological, and symbolic-linguistic points of view, and identified algebraic thinking factors, i.e. the principle of permanence of formal laws, the concept of variable, quantitative reasoning, algebraic interpretation - constructing algebraic expressions, trans formational reasoning - changing algebraic expressions, operational senses - operating algebraic expressions, substitution, etc. We also identified these algebraic thinking factors through analyzing mathematics textbooks of elementary and middle school, and showed the middle school students' low achievement relating to these factors through the algebraic thinking ability test. Based upon these analyses, we argued that the readiness for algebra learning should be made through the processes including algebraic thinking factors in the elementary school and that the transfer from arithmetic to algebra should be accomplished naturally through the pre-algebra course. And we searched for alternative ways to improve algebra curriculums, emphasizing algebraic thinking factors. In summary, we identified the problems of school algebra relating to the transfer from arithmetic to algebra with the problem of teaching algebraic thinking and analyzed the algebraic thinking factors of school algebra, and searched for alternative ways for improving the transfer from arithmetic to algebra and the teaching of early algebra.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.611-626
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• 2010

The purpose of this study is to explore the composite properties of linear functions using CAS calculators. The meaning and processes in which technological tools such as CAS calculators generated to instrument are reviewed. Other theoretical topic is the design of an exploring model of observing-conjecturing-reasoning and proving using CAS on experimental mathematics. Based on these background, the researchers analyzed the properties of the family of composite functions of linear functions. From analysis, instrumental capacity of CAS such as graphing, table generation and symbolic manipulation is a meaningful tool for this exploration. The result of this study identified that CAS as a mediator of mathematical activity takes part of major role of changing new ways of teaching and learning school mathematics.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.18 no.11
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• pp.94-103
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• 2017

As automatic hacking tools and techniques have been improved, the number of new vulnerabilities has increased. The CVE registered from 2010 to 2015 numbered about 80,000, and it is expected that more vulnerabilities will be reported. In most cases, patching a vulnerability depends on the developers' capability, and most patching techniques are based on manual analysis, which requires nine months, on average. The techniques are composed of finding the vulnerability, conducting the analysis based on the source code, and writing new code for the patch. Zero-day is critical because the time gap between the first discovery and taking action is too long, as mentioned. To solve the problem, techniques for automatically detecting and analyzing software (SW) vulnerabilities have been proposed recently. Cyber Grand Challenge (CGC) held in 2016 was the first competition to create automatic defensive systems capable of reasoning over flaws in binary and formulating patches without experts' direct analysis. Darktrace and Cylance are similar projects for managing SW automatically with artificial intelligence and machine learning. Though many foreign commercial institutions and academies run their projects for automatic binary analysis, the domestic level of technology is much lower. This paper is to study developing automatic detection of SW vulnerabilities and defenses against them. We analyzed and compared relative works and tools as additional elements, and optimal techniques for automatic analysis are suggested.