• Title/Summary/Keyword: 수리논리

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Intermediate Verification Languages for Program Verification-Why3 and Boogie (프로그램 증명을 위한 중간 증명 언어-Why3와 Boogie)

  • Kim, I.S.
    • Electronics and Telecommunications Trends
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    • v.30 no.4
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    • pp.54-58
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    • 2015
  • 수리 논리 기반의 프로그램 증명방법은 매우 유용한 프로그램 분석방법이지만, 수리 논리식에 대한 증명을 사람이 직접 수행하는 것은 매우 힘들고 고된 작업이다. 본고에서는 이러한 수리 논리 기반의 프로그램 증명을 자동화하기 위하여 개발된 중간 증명 언어(Intermediate Verification Language)에 대하여 살펴보고자 한다.

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A Historical Background of Mathematical Logic and $G{\ddot{o}}del$ (수리논리학의 역사적 배경과 괴델)

  • Park, Chang-Kyun
    • Journal for History of Mathematics
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    • v.21 no.1
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    • pp.17-28
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    • 2008
  • This Paper introduces a historical background of mathematical logic. Logic and mathematics were not developed dependently until the mid of the nineteenth century, when two streams of logic and mathematics came to form a river so that brought forth synergy effects. Since the mid-nineteenth century mathematization of logic were proceeded while attempts to reduce mathematics to logic were made. Against this background $G{\ddot{o}}del's$ proof shows the limitation of formalism by proving that there are true arithmetical propositions that are not provable.

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Constraint Satisfaction and Uncertain Knowledge (제약 조건 만족과 불확실한 지식의 처리)

  • Shin, Yang-Kyu
    • Journal of the Korean Data and Information Science Society
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    • v.6 no.2
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    • pp.17-27
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    • 1995
  • We propose a framework for representing and processing uncertain knowledge on the basis of constraint satisfaction. A system of equations and/or inequalities can be considered as a set of constraints that should be solved, and each constraint in the set is transformed into a corresponding logical formula which can be solved through a constraint solving program. Most of rule-based systems, for instance, use a simple probabilistic theory in order to maintain uncertain knowledge, therefore uncertain knowledge can be represented and processed in the constraint satisfaction program quite efficiently.

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A Study on the Students' Cognition of Chemistry in Science High School by Factor Analysis of Mathematics and Science Achievement (수학·과학 성취도의 요인 분석으로 본 과학고등학교 학생들의 화학 교과에 대한 인식 연구)

  • Shin, Dong-Seon;Choi, Hojun;Kim, Bong Gon
    • Journal of the Korean Chemical Society
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    • v.64 no.2
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    • pp.119-129
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    • 2020
  • For effective teaching-learning activities for students with diverse talents in science high schools, it is important for teachers to understand students' individual differences in perceiving and processing information in the natural world, depending on the students' various talents and subject characteristics. The purpose of this study is to examine the students' cognition of chemistry in science high school through correlations and factor analysis of mathematics/science achievement. In addition, this study attempted to examine the cognition of chemistry subject according to R&E classes. The main participants of the study were freshmen of G science high school (296 students) who entered after three times of curriculum reforms and new admission processes and the students in two other science high schools in Gyeongnam and Ulsan were included. The correlation and factor analysis were conducted by exploratory factor analysis by IBM SPSS Statistics 25 programs. The results of this study were as follows: First, in the correlation analysis between mathematics and science achievement, it was confirmed that the Pearson's coefficient of chemistry showed higher positive correlation coefficient than that of other science subjects. Second, in the factor analysis of mathematics and science achievements, it was found that the factor indicators were divided into two factors as logical-mathematical (mathematics and physics) and naturalistic (life science and earth science). Third, in the factor analysis, it was confirmed that the chemistry is recognized as the subject that requires both logical-mathematical and naturalistic intelligence. Finally, it was confirmed that students' cognitions of chemistry subject were found to differ according to the R&E classes. In other words, the participants of R&E chemistry class, unlike other students, were found to recognize chemistry as the subject that logical-mathematical intelligence is needed.

교사양성대학 수학교육과 '해석학' 강좌 운영 -교육과정 및 교수학습 방법개발과 관련한-

  • Lee, Byeong-Su
    • Communications of Mathematical Education
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    • v.15
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    • pp.23-28
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    • 2003
  • 실수계와 n-차원 벡터 공간을 대수적 특성, 순서적 특성 그리고 위상적 특성을 중심으로 전개하고, 실변수 실가 함수와 n-차원 벡터 공간을 정의역으로 하는 실가함수를 연속성 (미분가능성), 단조성 그리고 볼록성을 중심으로 내용을 다룬다. 특히 실생활과 관련하여 이론을 전개하여 학습을 지도할 수 있는 교육과정을 개발하고, 직관적인 사고와 수리 논리적인 사고의 적절한 배합을 통해 학습자들이 적극적으로 학습에 임할 수 있는 교수 학습 방법을 개발하는 것을 목적으로 한다.

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Turing's Cognitive Science: A Metamathematical Essay for His Centennial (튜링의 인지과학: 튜링 탄생 백주년을 기념하는 메타수학 에세이)

  • Hyun, Woo-Sik
    • Korean Journal of Cognitive Science
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    • v.23 no.3
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    • pp.367-388
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    • 2012
  • The centennial of Alan Mathison Turing(23 June 1912 - 7 June 1954) is an appropriate occasion on which to assess his profound influence on the development of cognitive science. His contributions to and attitudes toward that field are discussed from the metamathematical perspective. This essay addresses (i)Turing's mathematical analysis of cognition, (ii)universal Turing machines, (iii)the limitations of universal Turing machines, (iv)oracle Turing machine beyond universal Turing machine, and (v)Turing test for cognitive science. Turing was a ground-breaker, eager to move on to new fields. He actually opened wider the scientific windows to the mind. The results show that first, by means of mathematical logic Turing discovered a new bridge between the mind and the physical world. Second, Turing gave a new formal analysis of operations of the mind. Third, Turing investigated oracle Turing machines and connectionist network machines as new models of minds beyond the limitations of his own universal machines. This paper explores why the cognitive scientist would be ever expecting a new Turing Test on the shoulder of Alan Turing.

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A Study on the Russian National Curriculum for Training of Mathematics Teachers at Universities (러시아의 수학교사 양성을 위한 국가 수준 교육과정에 대한 연구)

  • 한인기;신현용
    • The Mathematical Education
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    • v.42 no.5
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    • pp.595-606
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    • 2003
  • In this paper we analyze the Russian national curriculum for training of mathematics teachers at universities published by Russian Ministry of Education. From the document we are able to know the structure of the curriculum, compulsory subjects, and minimum mathematical contents for training mathematics teachers at universities.

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A Computational Model for Discussion Activities on Electronic BBS (전자게시판의 토의 활동에 대한 계산 모델)

  • Moon, Gyo-Sik
    • Journal of the Korea Computer Industry Society
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    • v.6 no.2
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    • pp.373-378
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    • 2005
  • Computer-Mediated Communication (CMC) based on electronic bulletin board system (e-BBS) has been widely used for various educational purposes since the advent of the Internet. Instructors can achieve pedagogical goals by analyzing the contents of postings. They can be benefited technically from analytic information on discussion activities. Studies on content analysis and social presence in communication have been traditionally done by social studies. However, researches on computational and logical analysis of the phenomenon are rare. To do that we propose a formal model to represent and analyze communication activities logically. The model consists of interactivity vector providing a formal representation of discussion activities and interactivity chart providing a graphical representation of interactivity vector. The formal approach can be used as a useful technical assistance to analyze and compare discussion groups computationally.

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A Study on Reasoning for Medical Expert Systems (의료용 전문가 시스템에서 추론에 관한 연구)

  • Kim, Jin-Sang;Shin, Yang-Kyu
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.2
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    • pp.359-367
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    • 1999
  • We investigate a logical approach to represent medical knowledge, reason deductively and diagnostically. It is suggested that medical knowledge-bases can be formulated as a set of sentences stated in classical logic where each sentence reflects a doctor's knowledge about the human anatomy or his/her view of patient's symptoms. It is also suggested that a form of temporal reasoning can be captured within the same framework because each sentence can have a different truth value based on time. We apply our logical framework to formalize diagnostic reasoning, where the primary cause of illness is chosen among the set of minimal causation on the basis of abductive hypotheses. Most of our examples are given in the context of medical expert systems.

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The Ontological Conservativeness of Logic and Mereology (논리학의 존재론적 보수성과 부분전체론)

  • Kang, Soo-Whee
    • Korean Journal of Logic
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    • v.13 no.2
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    • pp.167-201
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    • 2010
  • This paper aims to scrutinize the possibility of mereology as philosophically satisfiable metalogic. Motivation for this is straightforward. As I see, a traditional approach to metalogic presented in the name of mathematical logic posits the existence of mathematical entities such as sets, functions, models, etc. to give definitions of logical concepts like logical consequence. As a result, whenever logic is used in any individual sciences, this set-theoretical metalogic cannot but add these mathematical entities to the domain of them. This fact makes this approach contradict to the ontological conservativeness of logic. Mereology, however, has been alleged to be ontologically innocent, while it is a formal system very similar to set theory. So it may well be that some people thought of mereology as a good substitute for set theoretic metalanguage and concepts for ontologically neutral metalogic. Unfortunately, when we look into argument for the ontological innocence of mereology, we can find that mereological entities such as mereological sums or fusions are not ontologically neutral. Thus we can conclude that mereological approach to metalogic is not promising at all.

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