• Journal for History of Mathematics
• /
• v.23 no.1
• /
• pp.79-88
• /
• 2010

G$\ddot{o}$del's proof attempts to establish the existence of God by the definition that God is a being having all positive properties. The proof uses here second order modal logic system $S_5$ with the axiom ${\diamondsuit}{\Box}p{\rightarrow}{\Box}p$. We review the G$\ddot{o}$del's own version and prove his ontological theorems.

• Journal of Korean Philosophical Society
• /
• v.141
• /
• pp.1-42
• /
• 2017

This paper's purpose is to seek to grasp how Descartes demonstrates proofs of God's existence on the basis of his works especially Meditations. To consider these points, I shall explore first, second, third proofs that are present in his works, and contents related to God. Descartes argues that there is idea of God within me, but it is God, which is first proof. On the basis of this fact, Descartes shows only God is the cause of thinking self who has idea of God(second proof), both of them are called Cosmological argument. To investigate this, at first he states that representative reality that is different from formal reality sets a kind of hierarchy, the degree of this reality is equally applied to cause and effect, consequently to the cause of my idea or existence(God). From Meditation V, third proof which is called Ontological argument, Descartes examined a supremely perfect God can't be separated from God's existence(perfection) just as surly as the certainty of any shape or number, for example triangle, namely it is quite evident that God's existence includes his essence. Through these processes I shall examine following points: the way of having Descartes' proofs of God's existence itself is not only exposed, God's existence who guarantees cogito ergo sum which is never doubted, despite doubting all things that is outside, is but also postulated; Proofs for the existence of God are an ultimate source of ensuring the clear and distinct perception of human reason, Descartes uses reason suitable for non-christians instead of faith suitable for Christians for these methods, which are similarities with the traditional views on the one hand, but nevertheless there are some of discontinuities establishing authority or power of the first philosophical principle to which God is subjected, on the other.

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

• Korean Journal of Logic
• /
• v.16 no.3
• /
• pp.407-436
• /
• 2013

I examine the notion of truth in the intuitionistic type theory and provide a better explanation of the objective intuitionistic conception of mathematical truth than that of Dag Prawitz. After a brief explanation of the distinction among proposition, type and judgement in comparison with Frege's theory of judgement, I examine the judgements of the form 'A true' in the intuitionistic type theory and explain how the determinacy of the existence of proofs can be understood intuitionistically. I also examine how the existential judgements of the form 'Pf(A) exists' should be understood. In particular, I diagnose the reason why such existential judgements do not have propositional contents. I criticize an understanding of the existential judgements as elliptical judgements. I argue that, at least in two respects, the notion of truth explained in this paper is a more advanced version of the objective intuitionistic conception of mathematical truth than that provided by Prawitz. I briefly consider a subjectivist's objection to the conception of truth explained in this paper and provide an answer to it.

• YAKHAK HOEJI
• /
• v.1 no.1
• /
• pp.19-22
• /
• 1948

Yucca schotti, Samuela carnerosana, Agave strita 각부분에 있어 결실전후의 steroidal sapogenin 분포상태를 연구하여 결실후에는 monohydroxy steroid는 존재치 않고 단지복합 polyhydroxy steroid만이 존재함을 증명하였다.

• Journal of Industrial Technology
• /
• v.18
• /
• pp.61-67
• /
• 1998

이 논문에서는 Diruchlet 경계 조건을 갖는 비선형 타원형 방정식 $-{\Delta}u+g(u)=f(x)$의 해의 존재에 대한 연구를 하였다. 존재하는 해의 다중성을 증명하기 위하여 임계점 이론과 롤의 정리를 사용하였으며, 대응되는 범함수에 따라서 방정식의 해와 임계점이 동시에 나타난다는 정리를 이용하였다. 이 때 $g(u)=bu^+-au^-$으로 나타날 때 외력항 (방정식의 우변)의 상수로 주어지는 경우 적어도 두 개의 해가 존재한다는 것을 증명하였다. 만약 우변(외력항)의 상수가 음수이거나 0인 경우이 방정식의 해가 존재하지 않거나 자명한 해만 존재하기 때문에 상수는 양수인 것으로 가정하였다.

• Journal of Industrial Technology
• /
• v.17
• /
• pp.131-135
• /
• 1997

이 논문에서는 이동하는 파를 해로 갖는 편미분 방정식의 해를 찾는 방법에 대하여 연구하였다. 특히 이 해가 움직이는 근원을 가질 경우에 앞쪽으로 이동하는 해가 존재하는지의 여부를 파악하는데 어떻게 증명할 것인지를 보였다. 앞쪽으로 이동하는 해를 갖는 경우는 반응-확산 방정식에서 그 해를 찾아 볼 수 있으며, 움직이는 근원을 가진 경우에 앞쪽으로 진행되는 해를 갖는 경우는 화학 공정의 모델등에서 그 해를 찾아 볼 수 있는데 이 문제를 중심으로 어떻게 해의 존재 여부를 증명할 수 있는지를 보였다.

• Journal of Educational Research in Mathematics
• /
• v.25 no.3
• /
• pp.367-379
• /
• 2015

The existence of mathematical objects was considered through diorism which was used in ancient Greece as conditions for the existence of the solution of the problem. Proposition I-22 of Euclid Elements has diorism for the existence of triangle. By discussing the diorism in Elements, ancient Greek mathematician proved the existence of defined object by postulates or theorems. Therefore, the existence of mathematical object is verifiability in the axiom system. From this perspective, construction is the main method to guarantee the existence in the Elements. Furthermore, we suggest some implications about the existence of mathematical objects in school mathematics.

• Journal of Korean Philosophical Society
• /
• no.122
• /
• pp.1-23
• /
• 2018

In the final argument for the immortality of the soul in the Phaedo, Socrates establishes a new type of cause which he describes as 'more sophisticated' and on the basis of it attempts to show that the soul is immortal. In the process, he introduces three examples for the cause, i.e. three, fire, and snow. But there has been considerable controversy over the ontological status of the three and the soul. Some scholars think that they are all forms; others believe that neither of them is. In this paper I argue that in fact one of them is a form, while the others are not. I also argue that the fact that they do not have the same ontological status and the uncertainty in the nature of the soul itself weaken the cogency of the final argument as a whole.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2004.11a
• /
• pp.327-330
• /
• 2004

테스팅이 오류의 존재를 증명할 수 있는데 반해서, 정형 검증 기술은 시스템에 오류가 존재하지 않음을 증명할 수 있다. 모델 체킹은 이런 정형 검증 기술 중의 하나이다. 최근에 모델 체킹을 이용하여 코드를 자동으로 검증하려는 연구들이 많다. 하지만 이런 연구는 일반적인 환경에서의 검사만을 할 수 있다. 반면에 임베디드 소프트웨어는 실시간성, 외부 환경, 다중 스레드 등의 다양한 특성이 존재한다. 따라서 임베디드 소프트웨어와 같이 안전한 소프트웨어 시스템을 필요로 하는 환경을 위한 모델 체킹을 수행하기는 힘들다. 본 논문에서는 임베디드 소프트웨어에 대한 모델체킹 도구가 검증할 수 있어야 하는 실시간 시스템의 검증, 외부 환경에 대한 고려, 다중 스레드 시스템의 검증 등을 설명하고, 기존 도구들이 얼마나 만족하고 있는지 조사해본다.