• Korean Journal of Cognitive Science
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• v.1 no.2
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• pp.347-360
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• 1989

Retearches on epistemology for artificial intelligence have started quite recently.Recently,Konolige made a contribution to epistemology by proposing a deduction model based on an efficieit modal logic for a proof mechanism for belief.In this thesis,a unified and generalized proof mechanism for the epistemic logic using a formal system called a View is pesented.In addition,the algorithm to adapt the theorem prover according to the given rule schema,which charncterizes the deduction model of the epistemic logic,is constructed. With this algorlthm,multiple agents having different rule schemas can co-exist in the proposed system. The soundness and completeness of the proposed proof mechanism is proved and a simple theorem prover is implemented to demonstrate the usefulness and practilcality.

• 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 of Educational Research in Mathematics
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• v.16 no.2
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• pp.95-113
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• 2006

The study tries to differentiate the levels of mathematical reasoning from inductive reasoning to formal reasoning for teaching gradually. Because the formal point of view without the relation to objects has limitations in the creation of a new knowledge, our mathematics education needs consider the such characteristics. We propose an intuitive level of proof related in concrete operations and perceptual experiences as an intermediating step between inductive and formal reasoning. The key activity of the intuitive level is having insight on the generality of reasoning. The details of the process should pursuit the direction for going away from objects and near to formal reasoning. We need teach the mathematical reasoning gradually according to the appropriate level of reasoning more differentiated.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.131-148
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• 2016

Mathematical formal justification may be seen as a bridge towards the proof. By requiring the mathematically gifted students to prove the generalized patterned task rather than the implementation of deductive justification, may present challenges for the students. So the research questions are as follow: (1) What are the difficulties the mathematically gifted elementary students may encounter when formal justification were to be shifted into a generalized form from the given patterned challenges? (2) How should the teacher guide the mathematically gifted elementary students' process of transition to formal justification? The conclusions are as follow: (1) In order to implement a formal justification, the recognition of and attitude to justifying took an imperative role. (2) The students will be able to recall previously learned deductive experiment and the procedural steps of that experiment, if the mathematically gifted students possess adequate amount of attitude previously mentioned as the 'mathematical attitude to justify'. In addition, we developed the process of questioning to guide the elementary gifted students to formal justification.

• Journal of the Korean Society of Costume
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• v.67 no.3
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• pp.15-30
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• 2017

The purpose of this study is to analyze the formative characteristics of Hanbok among youngsters based on SNS proof shots, identify new characteristics of Hanbok as part of play and travel rather than as formal Hanbok, and provide information for the Hanbok market. As research methodology, our search was carried out by using '#Hanbok Travel' as the search word in Instagram, where the Hanbok proof shot phenomenon is actively under way. A total of 535 posts from March 21, 2016 to April 1, 2016 were selected as objects of this study, excluding posts containing Hanbok with indiscernible shape, Korean traditional costume manufacturers' promotional posts, and repetitive posts by one person. First, the 535 posts were analyzed by season, region, number of people, and gender, and after men's data were excluded, 644 Hanboks were left for analysis. Their formative characteristics were analyzed by using SPSS 21.0. The results showed that the formative characteristics of Hanbok shown in SNS proof shots included diversification of length in jeogori(Korean traditional jacket), skirt, and sleeve, use of pragmatic material and achromatic color, and reduced use of decorative technique. Hanboks shown in the Hanbok proof shots should be considered as significant data because each shots show clothes selected and worn directly by user's side, unlike the existing studies centering on Hanbok designers' works.

• Journal of KIISE:Software and Applications
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• v.37 no.1
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• pp.54-59
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• 2010

Special-purpose microcontrollers PLCs have been widely used in the area of industrial automation. For the research of analysis and verification for PLC programs, first of all we have to specify formal sematics of PLC programming languages. This paper defines formally the operational semantics of LD language. After we transform the graphical language LD into its textual representation Symbolic LD, we give semantics of Symbolic LD since LD language is a graphical language. This paper defines the natural sematics of Symbolic LD and formalizes it in Coq proof assistant.

• Journal of KIISE:Software and Applications
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• v.35 no.12
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• pp.800-807
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• 2008

We introduce some well-known approaches to formalization and automatization of the meta-theory of a programming language with binders. They represent the trends in POPLmark Challenge. We demonstrate some characteristics of each approach by showing how to formalize some basic notations and concepts of Lambda-calculus using the proof assistant Coq.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.585-596
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• 1998

Some new problems of the theory of the finite automata are considered. Applying the finite automata in various tasks of the formal languages theory is observed. Special proof of Kleene's theorem is obtained. This proof is used for the defining the star-height of the finite automaton. The proper-ties of the last object are considered. The star-height of the finite automaton is used for reformulating the star-height problem of regular expression for finite automata. The method of the reduction of the star-height problem to the task of making special finite automaton is obtained. This reformulating can help to solve the star-height problem by new way.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1521-1536
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• 2017

This paper introduces a representation style of variable binding using dependent types when formalizing meta-theoretic properties. The style we present is a variation of the Coquand-McKinna-Pollack's locally-named representation. The main characteristic is the use of dependent families in defining expressions such as terms and formulas. In this manner, we can handle many syntactic elements, among which wellformedness, provability, soundness, and completeness are critical, in a compact manner. Another point of our paper is to investigate the roles of free variables and constants. Our idea is that fresh constants can entirely play the role of free variables in formalizing meta-theories of first-order predicate logic. In order to show the feasibility of our idea, we formalized the soundness and completeness of LJT with respect to Kripke semantics using the proof assistant Coq, where LJT is the intuitionistic first-order predicate calculus. The proof assistant Coq supports all the functionalities we need: intentional type theory, dependent types, inductive families, and simultaneous substitution.

• Education of Primary School Mathematics
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• v.16 no.2
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• pp.123-145
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• 2013

This study was expected to yield the meaningful conclusions from the experimental group who took lessons based on inductive activities using GeoGebra at the beginning of proof learning and the comparison one who took traditional expository lessons based on deductive activities. The purpose of this study is to give some helpful suggestions for teaching proof to mathematically gifted elementary students. To attain the purpose, two research questions are established as follows. 1. Is there a significant difference in proof abilities between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? 2. Is there a significant difference in proof attitudes between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? To solve the above two research questions, they were divided into two groups, an experimental group of 10 students and a comparison group of 10 students, considering the results of gift and aptitude test, and the computer literacy among 20 elementary students that took lessons at some education institute for the gifted students located in K province after being selected in the mathematics. Special lesson based on the researcher's own lesson plan was treated to the experimental group while explanation-centered class based on the usual 8th grader's textbook was put into the comparison one. Four kinds of tests were used such as previous proof ability test, previous proof attitude test, subsequent proof ability test, and subsequent proof attitude test. One questionnaire survey was used only for experimental group. In the case of attitude toward proof test, the score of questions was calculated by 5-point Likert scale, and in the case of proof ability test was calculated by proper rating standard. The analysis of materials were performed with t-test using the SPSS V.18 statistical program. The following results have been drawn. First, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in proof ability than the comparison group who took traditional proof lessons. Second, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in the belief and attitude toward proof than the comparison group who took traditional proof lessons. Third, the survey about 'the effect of inductive activities using GeoGebra on the proof' shows that 100% of the students said that the activities were helpful for proof learning and that 60% of the reasons were 'because GeoGebra can help verify processes visually'. That means it gives positive effects on proof learning that students research constant character and make proposition by themselves justifying assumption and conclusion by changing figures through the function of estimation and drag in investigative software GeoGebra. In conclusion, this study may provide helpful suggestions in improving geometry education, through leading students to learn positive and active proof, connecting the learning processes such as induction based on activity using GeoGebra, simple deduction from induction(i.e. creating a proposition to distinguish between assumptions and conclusions), and formal deduction(i.e. proving).