• School Mathematics
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• v.16 no.3
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• pp.491-502
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• 2014

This paper analyzed pre-service teachers' justification of $0.99{\cdots}$=1 from their disproof of $0.99{\cdots}$ <1. Some pre-service teachers thought of the difference between $0.99{\cdots}$ and 1 as an infinitesimal. On the contrary, the others claimed that the difference between $0.99{\cdots}$ and 1 was zero as the standard real, but were content with their intuitive justifications. The pre-service teachers' limitation revealed in the process of disproving $0.99{\cdots}$ <1 can be closely related to the orthodox view: the standard real number system is the only absolutely true number system. The existence of nonstandard real number system in which $0.99{\cdots}$ is less than 1, shows that the plain question of whether or not $0.99{\cdots}$ equals 1, cannot be properly answered by common explanations of textbooks or teachers' intuitive justification.

• Korean Journal of Logic
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• v.20 no.3
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• pp.313-333
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• 2017

In this paper, we deal with standard completeness of some axiomatic extensions of the involutive mianorm logic IMIAL. More precisely, first, seven involutive mianorm-based logics are introduced. Their algebraic structures are then defined, and their corresponding algebraic completeness is established. Next, standard completeness is established for four of them using construction in the style of Jenei-Montagna.

• Korean Journal of Logic
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• v.18 no.2
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• pp.197-215
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• 2015

In this paper, we deal with standard completeness of some axiomatic extensions of the involutive micanorm logic IMICAL. More precisely, first, four involutive micanorm-based logics are introduced. Their algebraic structures are then defined, and their corresponding algebraic completeness is established. Next, standard completeness is established for two of them using construction in the style of Jenei-Montagna.

• Korean Journal of Logic
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• v.20 no.2
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• pp.273-292
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• 2017

In this paper, we deal with some axiomatic extensions of the involutive micanorm logic IMICAL. More precisely, first, the two involutive micanorm-based logics $P_nIMICAL$ and $FP_nIMICAL$ are introduced. Their algebraic structures are then defined, and their corresponding algebraic completeness is established. Next, standard completeness is established for $FP_nIMICAL$ using construction in the style of Jenei-Montagna.

• Korean Journal of Logic
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• v.23 no.1
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• pp.1-23
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• 2020

This paper deals with mianorm-based logics with right and left n-potency axioms and their fixpointed involutive extensions. For this, first, right and left n-potent logic systems based on mianorms, their corresponding algebraic structures, and their algebraic completeness results are discussed. Next, completeness with respect to algebras whose lattice reduct is [0, 1], known as standard completeness, is established for these systems via Yang's construction in the style of Jenei-Montagna. Finally, further standard completeness results are introduced for their fixpointed involutive extensions.

• Korean Journal of Logic
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• v.11 no.2
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• pp.171-197
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• 2008

In this paper we deal with new standard completeness proofs of some systems introduced by Metcalfe and Montagna in [10]. For this, this paper investigates several fuzzy-relevance logics, which can be regarded as neighbors of the R of Relevance with mingle (RM). First, the monoidal uninorm idempotence logic MUIL, which is intended to cope with the tautologies of left-continuous conjunctive idempotent uninorms and their residua, and some schematic extensions of it are introduced as neighbors of RM. The algebraic structures corresponding to them are defined, and standard completeness, completeness on the real unit interval [0, 1], results for them are provided.

• Korean Journal of Logic
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• v.12 no.2
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• pp.115-139
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• 2009

This paper investigates an extension of the uninorm (based) logic UL, which is obtained by adding (t-weakening, $W_t$) (($\phi$ & $\psi$) ${\wedge}$ t) $\rightarrow$ $\phi$ to UL introduced by Metcalfe and Montagna in [8]. First, the t-weakening uninorm logic $UL_{Wt}$ (the UL with $W_t$) is introduced. The algebraic structures corresponding to $UL_{Wt}$ is then defined, and its algebraic completeness is established. Next standard completeness (i.e. completeness on the real unit interval [0, 1]) is established for this logic by using Jenei and Montagna-style approach for proving standard completeness in [3, 6].

• Proceedings of the Korean Society of Medical Physics Conference
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• 2003.09a
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• pp.66-66
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• 2003

목적 : 선량측정의 정확성을 향상시키기 위하여 물 흡수선량 표준에 토대를 두고 있는 표준측정법, AAPM TG-51과 IAEA TRS-398, 이 발표되어 선량측정의 파라다임이 변화하고 있다. 본 연구에서는 이들 대표적인 표준측정법에 대하여 사용자 편의성을 고려하여 웹에 기반한 선량교정 프로그램을 개발하고자 한다. 대상 및 방법 : 미국의학물리학회 AAPM TG-51과 국제원자력기구 IAEA TRS-398 표준측정법에 선량교정 프로그램은 Microsoft IIS 6.0 웹서버와 .NET 플렛폼상에서 Visual Studio. NET 도구를 사용하여 개발하였다. 개발언어로는 C# 언어를 사용하였고 각 표준측정법에 대한 선량교정 작업서는 ASP. NET 페이지로 작성하였다. 웹페이지와 산량 교정 모듈을 분리하여서 개발 후 유지보수가 쉽게 설계하였다. 또한 기준점에서의 선량 계상에 사용하는 모든 물리적인 파라미터와 데이터는 데이터베이스에 저장하였다. 이로써 향후 수식체계의 변화 또는 물리적인 데이터의 변화로 인한 프로그램 수정이 최소화하도록 하였다. 결과 : 이들 표준측정법은 모두 물 흡수선량 교정인수에 토대를 두고 있으나 측정 조건 및 물리적인 자료 에 있어 약간의 차이를 보이고 있다. 그러므로 각 표준측정법간의 유사점 및 차이점을 비교 분석하기가 용이하였다. 그리고 개발된 프로그램을 이용하여 표준측정법에서 제시된 선량교정 작업서에 따라 선량 교정을 수행한 교정 결과 데이터를 XML 파일 형식으로 저장하여 이전의 측정 자료를 관리할 수 있게 하였다. 이 과거 측정 자료를 사용하여 출력 선량 교정의 변화 및 기타 중요한 물리적인 데이터 값의 변화를 분석할 수 있다. 결론 : 두 표준측정법에 대한 선량교정 프로그램은 사용자가 선호하는 표준측정법을 선택할 수 있고, 웹에 토대를 두고 있어 프로그램으로 전국 방사선종양학과의 방사선치료기기의 출력 및 물리적인 변화에 대한 자료를 비교 분석하기 용이하고 수작업으로 인해 발생할 수 있는 실수 및 오차를 줄일 수 있다. 또한 개발된 프로그램의 활용을 통하여 국내 실정에 적합한 물 흡수선량 표준에 기반한 표준측정법 개발에 토대를 마련하는데 있어 기여할 것으로 사료된다.

• Korean Journal of Logic
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• v.17 no.2
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• pp.323-349
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• 2014

In this paper, we show that the standard completeness for the extension of UL with compensation-free reinforcement (cfr) $(({\phi}&{\psi}){\rightarrow}({\phi}{\wedge}{\psi})){\vee}(({\phi}{\vee}{\psi}){\rightarrow}({\phi}&{\psi}))$ can be established. More exactly, first, the compensation-freely reinforced uninorm logic $UL_{cfr}$ (the UL with (cfr)) is introduced. The algebraic structures of $UL_{cfr}$ are then defined, and its algebraic completeness is established. Next, standard completeness (i.e. completeness on [0, 1]) is established for $UL_{cfr}$ by using the method introduced in Yang (2009).

• Radiation Oncology Journal
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• v.20 no.4
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• pp.381-390
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• 2002

Purpose : To develop a dose calibration program for the IAEA TRS-277 and AAPM TG-21, based on the air kerma calibration factor (or the cavity-gas calibration factor), as well as for the IAEA TRS-398 and the AAPM TG-51, based on the absorbed dose to water calibration factor, so as to avoid the unwanted error associated with these calculation procedures. Materials and Methods : Currently, the most widely used dosimetry Protocols of high energy photon beams are the air kerma calibration factor based on the IAEA TRS-277 and the AAPM TG-21. However, this has somewhat complex formalism and limitations for the improvement of the accuracy due to uncertainties of the physical quantities. Recently, the IAEA and the AAPM published the absorbed dose to water calibration factor based, on the IAEA TRS-398 and the AAPM TG-51. The formalism and physical parameters were strictly applied to these four dose calibration programs. The tables and graphs of physical data and the information for ion chambers were numericalized for their incorporation into a database. These programs were developed user to be friendly, with the Visual $C^{++}$ language for their ease of use in a Windows environment according to the recommendation of each protocols. Results : The dose calibration programs for the high energy photon beams, developed for the four protocols, allow the input of informations about a dosimetry system, the characteristics of the beam quality, the measurement conditions and dosimetry results, to enable the minimization of any inter-user variations and errors, during the calculation procedure. Also, it was possible to compare the absorbed dose to water data of the four different protocols at a single reference points. Conclusion : Since this program expressed information in numerical and data-based forms for the physical parameter tables, graphs and of the ion chambers, the error associated with the procedures and different user could be solved. It was possible to analyze and compare the major difference for each dosimetry protocol, since the program was designed to be user friendly and to accurately calculate the correction factors and absorbed dose. It is expected that accurate dose calculations in high energy photon beams can be made by the users for selecting and performing the appropriate dosimetry protocol.