• Korean Journal of Logic
• /
• v.18 no.1
• /
• pp.133-153
• /
• 2015

In his paper "Structural Equations Approach to Token Causation: The Active Route Account Revisited" Professor Sungsu Kim defends the active route account. The active route account is the theory of causation which overcomes counterexamples to the counterfactual theories of causation, while maintaining the counterfactual theorist's essential intuition that an effect depends counterfactually on a cause. Unfortunately, there are counterexamples to the active route account itself. Professor Sungsu Kim attempts to defend the active route account by rebutting those counterexamples. In this paper, I argue that his defense of the active route account is not successful.

• Communications of Mathematical Education
• /
• v.30 no.3
• /
• pp.393-418
• /
• 2016

Theory and fundamentals of mathematics consist mostly of proposition form. Activities by research of the proposition which leads to determine the true or false, justify the true propositions and refute with counterexample improve logical reasoning skills of students in emphases on mathematics education. Also, utilizing of counterexamples in school mathematics combines mathematical knowledge through the process of finding a counterexample, help the concept study and increase the critical thinking. These effects have been found through previous research. But many studies say that the learners have difficulty in generating counterexamples for false propositions and materials have not been developed a lot for the counterexample utilizing that can be applied in schools. So, this study analyzed the current textbook and examined the use of counterexamples and developed educational materials for counterexamples that can be applied at schools. That materials consisted of making true & false propositions and students was divided into three groups of academic achievement level. And then this study looked at the change of the students' thinking after counterexample classes. As a study result, in all three groups was showed a positive change in the cognitive domain and affective domain. Especially, in top-level group was mainly showed a positive change in the cognitive domain, in upper-middle group was mainly showed in the cognitive and the affective domain, in the sub-group was mainly found a positive change in the affective domain. Also in this study shows that the class that makes true or false propositions in education of utilizing counterexample, made students understand a given proposition, pay attention to easily overlooked condition, carefully observe symbol sign and change thinking of cognitive domain helping concept learning regardless of academic achievement levels of learners. Also, that class gave positive affect to affective domain that increase interest in the proposition and gain confidence about proposition.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.65-73
• /
• 1996

• Communications for Statistical Applications and Methods
• /
• v.26 no.6
• /
• pp.583-589
• /
• 2019

Counterexamples of a skew-normal distribution are developed to improve our understanding of this distribution. Two examples on bivariate non-skew-normal distribution owning marginal skew-normal distributions are first provided. Sum of dependent skew-normal and normal variables does not follow a skew-normal distribution. Continuous bivariate density with discontinuous marginal density also exists in skew-normal distribution. An example presents that the range of possible correlations for bivariate skew-normal distribution is constrained in a relatively small set. For unified skew-normal variables, an example about converging in law are discussed. Convergence in distribution is involved in two separate examples for skew-normal variables. The point estimation problem, which is not a counterexample, is provided because of its importance in understanding the skew-normal distribution. These materials are useful for undergraduate and/or graduate teaching courses.

• Korean Journal of Logic
• /
• v.16 no.2
• /
• pp.189-231
• /
• 2013

The purpose of this paper is to show that Williamson's counterexamples and Fara's paradox do not conclusively refute supervaluationism. I will achieve this purpose on the basis of local validity. In general, people regard supervaluational validity as global validity. And D-introduction, which is premise of Williamson's counterexamples and Fara's paradox, is justified only if we assume global validity. But it cannot correctly grasp supervaluational semantics, especially semantic character of D-operator. So I will show that validity of supervaluationism is local and define global validity by local validity. Strategy of this paper is to protect supervaluationism against Williamson's counterexamples and Fara's paradox by minimal modification of supervaluationism and to prove that supervaluational logic is not revisionary and weak for solving the sorites paradox.

• Journal of the Korean Statistical Society
• /
• v.20 no.1
• /
• pp.77-83
• /
• 1991

In this article various notions of multivariate negative dependence for random variables are obtained. Various properties and interrelationships are also derived from these notions. Several counterexamples are given to illustrate that other implications may not hold.

• Communications of the Korean Mathematical Society
• /
• v.20 no.3
• /
• pp.457-466
• /
• 2005

We study in this note rings whose prime radicals are completely prime. We obtain equivalent conditions to the complete 2-primal-ness and observe properties of completely 2-primal rings, finding examples and counterexamples to the situations that occur naturally in the process.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.639-648
• /
• 2013

In this paper, we study Finsler metrics of constant S-curvature. First we produce infinitely many Randers metrics with non-zero (constant) S-curvature which have vanishing H-curvature. They are counterexamples to Theorem 1.2 in [20]. Then we show that the existence of (${\alpha}$, ${\beta}$)-metrics with arbitrary constant S-curvature in each dimension which is not Randers type by extending Li-Shen' construction.

• Journal of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1485-1498
• /
• 2018

We disprove a conjecture of Bombieri regarding univalent functions in the unit disk in some previously unknown cases. The key step in the argument is showing that the global minimum of the real function (n sin x - sin(nx))/(m sin x - sin(mx)) is attained at x = 0 for integers m > $n{\geq}2$ when m is odd and n is even, m is sufficiently big and $0.5{\leq}n/m{\leq}0.8194$.

• Proceedings of the Korean Information Science Society Conference
• /
• 2004.04b
• /
• pp.352-354
• /
• 2004

현재의 모델 체커는 모델이 속성을 만족하지 않을 경우 반례를 사용자에게 보여주어서 디버깅을 돕는다. 모델 체커에서 반례는 중요한 장점 중에 하나이지만 대부분의 모델 체커에서 반례로서 하나의 경로만을 보여주게 된다. 하지만 사용자가 원하는 것은 그 이상의 정보를 원할 수 있다. 따라서 반례에서 좀더 많은 정보를 보여줄 필요가 있다. 이런 종류의 연구로서 트리 형식의 반례 생성과 증명 형식의 반례생성이 있었다. 하지만 이 연구들은 시스템이 가질 수 있는 모든 경로를 알아낼 수는 없고 또한 증명 형식의 반례 생성의 경우 상태공간을 다른 형식으로 변경을 해야 한다. 본 논문에서는 반례로서 도달 가능한 모든 경로를 그래프 형식으로 보여줄 수 있는 그래프 형식의 반례를 정의하고 생성방법에 대해서 알아본다