• Journal for History of Mathematics
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• v.23 no.2
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• pp.23-56
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• 2010

본 논문의 목적은 집합론이 메타논리학에 필수불가결하다는 주장, 즉 필수불가결성 논제에 반대하는 것이다. 만일 집합론이 메타논리학에 필수불가결하다면, 집합론을 포함하게 되는 논리적 탐구는 논리학의 가장 근본적인 특성들인 주제중립성과 보편적 적용가능성을 결여하게 되기 때문이다. 논리학의 주제중립성은 논리학의 명제들이 개별 과학과 같은 특정한 지식 분야에 국한되지 않는다는 것을 말하며, 논리학의 보편적 적용가능성은 논리학의 명제들과 추론 규칙들이 모든 과학 분야들과 합리적 담론들에서 사용될 수 있다는 것을 말한다. 나아가 주제중립성과 보편적 적용가능성을 지니기 위해서는, 논리학을 기술하는 메타논리적 용어들과 개념들 역시 이러한 특성들을 지녀야만 한다. 하지만 필수불가결성 논제를 받아들이게 되면, 우리는 논리학이 적용되는 모든 분야에서 집합론의 용어들과 집합론적 개념들이 필수불가결하다는 것을 받아들여야만 한다. 그리고 이는 분명 불합리한 일이다. 필수불가결성 논제가 그럴듯하지 않다는 것을 보이기 위해서 나는 집합과 관련된 존재론적 문제를 살펴볼 것이다. 이러한 탐구는 집합이 어떤 식으로 이해되든지 간에 존재론적으로 보수적인 "논리적 존재자" 로 간주되기 어렵다는 것을 보여줄 것이다.

• Journal of Digital Convergence
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• v.14 no.6
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• pp.253-261
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• 2016

As many people use internet through the various programs of PC and mobile devices, the possibility of private data leak is increasing. A program should be used after checking security of information flow. Security analysis of information flow is a method that analyzes security of information flow in program. If the information flow is secure, there is no leakage of personal information. If the information flow not secure, there may be a leakage of personal information. This paper proposes a method of analyzing information flow that facilitates SAT solver. The method translates a program that includes variables where security level is set into propositional formula representing control and information flow. The satisfiability of the formula translated is determined by using SAT solver. The security of program is represented through the result. Counter-example is generated if the program is not secure.

• Proceedings of the Korean Information Science Society Conference
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• 2003.04c
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• pp.37-39
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• 2003

본 연구에서는 만족성 검사기를 이용하여 두 유한 상태 기계의 행위가 동치인지를 검사한다. 기존의 동치 검사는 대부분 BDD를 기반으로 했었기 때문에 변수 순서 배열 및 내부 BDD노드 폭발 문제에 시달렸었다. 하지만 여기서는 BDD대신 명제 논리를 이용하기 때문에 위와 같은 문제점을 피할 수 있다. 하지만 논리식을 만족성 검사기의 입력 형태인 논리곱 정규형으로 변환하는 과정에서 절의 3기는 식의 크기에 지수적으로 증가하였다.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.123-135
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• 2008

This study analysed the schemata which are requisite to understand and prove examples of mathematical induction, and examined students' construction of the schemata. We verified that the construction of implication-valued function schema and modus ponens schema needs function schema and proposition-valued function schema, and needs synthetic coordination for successive mathematical induction schema. Given this background, we establish $1{\sim}4$ levels for students' understanding of the mathematical induction. Further, we analysed cognitive difficulties of students who studying mathematical induction in connection with these understanding levels.

• Journal of KIISE:Software and Applications
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• v.37 no.2
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• pp.148-154
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• 2010

In the study of the formal semantics of uncertain databases, we typically take an algebraic approach by mapping an uncertain database to possible worlds which are a set of relational databases. In this paper, we present a new semantics for uncertain databases which takes a logical approach by translating uncertain databases into logical theories. A characteristic feature of our semantics is that it uses linear logic, instead of propositional logic, as its logical foundation. Linear logic is suitable for a logical interpretation of uncertain information because unlike propositional logic, it treats logical formulae not as persistent facts but as consumable resources. As the main result, we show that our semantics is faithful to the operational account of uncertain databases in the algebraic approach.

• Korean Journal of Logic
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• v.14 no.2
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• pp.105-121
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• 2011

The late professor Young-Jung Kim advanced a view that Existential Specification Rule (ES Rule) can be understood as a kind of polylemma. In arguing for this view, he also claimed that all propositions containing free variables are universal propositions. In this paper, I argue that his view on free variables incur numerous problems. Moreover, I introduce a new rule of inference called 'Universalized Conditionalization Rule' (UC Rule), so that I can show that his insight about ES Rule can be substantialized without an appeal to his problematic view on free variables. Finally, I show that ES Rule can be directly derived from UC Rule.

• Environmental and Resource Economics Review
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• v.23 no.2
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• pp.187-224
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• 2014

We present key issues to consider in estimating damages from price-fixing cases and then apply the procedure addressing those issues to a transportation fuel market. Among the five methods of overcharge calculation, the regression analysis incorporating the yardstick method is the best. If the price equation relates the domestic price to the foreign price and the exchange rate as in the transportation fuel market, the functional form satisfying both logical consistency and modeling flexibility is the log-log functional form. If the data under analysis is of time series in nature, then the ARDL model should be the base model for each market and the regression analysis incorporating the yardstick method combines these ARDL equations to account for inter-market correlation and arrange constant terms and collusion-period dummies across component equations appropriately so as to identify the overcharge parameter. We propose a two-step test for the benchmarked market: (a) conduct market-by-market Spearman or Kendall test for randomness of the individual market price series first and (b) then conduct across-market Friedman test for homogeneity of the market price series. Statistical significance is the minimal requirement to establish the alleged proposition in the world of uncertainty. Between the sensitivity analysis and the model selection process for the best fitting model, the latter is far more important in the economic analysis of damage in price-fixing litigation. We applied our framework to a transportation fuel market and could not reject the null hypothesis of no overcharge.