• 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.13 no.1
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• pp.1-20
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• 2010

This paper investigates a new proof of standard completeness (i.e. completeness on the real unit interval [0, 1]) for the uninorm (based) logic UL introduced by Metcalfe and Montagna in [15]. More exactly, standard completeness is established for UL by using nuclear completions method introduced in [8, 9].

• Korean Journal of Logic
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• v.16 no.3
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• pp.437-452
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• 2013

This paper verifies the following two: First, I verify the standard completeness proof for the system $ULw_t$ is not correct in the sense that t-weakening uninorms are t-norms, but not weakening-free uninorms. Second, I verify that the proof for $ULw_t$ can be used for the system MTL. That is, I provide a new standard completeness proof for it.

• 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.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).

• Korean Journal of Logic
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• v.14 no.1
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• pp.55-76
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• 2011

Fixed-point conjunctive left-continuous idempotent uninorms have been introduced (see e.g. [2, 3]). This paper studies a system for such uninorms. More exactly, one system obtainable from IUML (Involutive uninorm mingle logic) by dropping involution (INV), called here WUML (Weak Uninorm Mingle Logic), is first introduced. This is the system of fixed-point conjunctive left-continuous idempotent uninorms and their residua with weak negation. Algebraic structures corresponding to the system, i.e., WUML-algebras, are then defined, and algebraic completeness is provided for the system. Standard completeness is further established for WUML and IUML in an analogy to that of WNM (Weak nilpotent minimum logic) and NM (Nilpotent minimum logic) in [4].

• 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.

• Information and Communications Magazine
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• v.24 no.11
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• pp.5-13
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• 2007

광대역 무선 접속 표준을 관장하는 IEEE 802.16 워킹 그룹은 IEEE 802.16 표준을 2004년에 발표하였으며 이 IEEE 802.16 표준안에는 현재 WiMAX(Worldwide Interoperability for Microwave Access)라 불리는 고정 및 저속 이동 접속에 대한 광대역 무선 통신 지원 기술이 포함되어 있다. 특히 여러 기술 중 보안 관점에서 IEEE 802.16 표준은 MAC 계층 안에 PKM(Privacy Key Management)라고 불리는 Security Sub-layer를 가지고 있다. PKM은 PKMv1과 PKMv2로 구분되며, 먼저 PKMv1은 기본적인 인증 및 기밀성 기능을 제공하고 IEEE 802.16 표준에 기본적으로 적용되어있다. 하지만, IEEE 802.16 표준 이후 많은 연구들이 PKMv1의 보안성에 대하여 의문을 제기하였고 이에 따라 IEEE 802.16 표준안의 확장 개선안으로서 완전한 이동성을 바탕으로 하는 2005년 발표된 IEEE 802.16e 표준안에서는 향상된 보안 기능을 제공하는 PKMv2를 제공하며 기존 표준안의 부족한 점을 보완하기 위하여 시도하였다. 이러한 PKMv2는 EAP(Extensible Authentication Protocol) 인증, AES(Advanced Encryption Standard) 기반 기밀성 제공 알고리즘, CMAC/HMAC(Cipher/Hashed Message Authentication Code)을 사용한 메시지 인증 기능 제공 등 보다 다양한 보안 기능을 제공하였다. 그러나 IEEE 802.16e 표준안의 보안 기능은 SS(Subscriber Station)과 BS(Base Station)간의 통신구간 보안에 초점을 맞추어서 네트워크 도메인간의 보안 문제나 핸드오버시 보안과 같은 네트워크 구조적 보안 취약성을 여전히 가지고 있다. 하지만 표준안에서 정의하고 있는 SS와 BS 구간 보안 역시 완전한 솔루션을 제시하고 있지는 않다. 본 논문에서는 이러한 취약성을 고찰하고 그에 따른 대응방안을 제시하였다.

• 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].