• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.321-332
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• 2014

In this article we introduce different types of multiplier I-convergent double sequence spaces. We study their different algebraic and topological properties like solidity, symmetricity, completeness etc. The decomposition theorem is established and some inclusion results are proved.

• Journal for History of Mathematics
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• v.13 no.1
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• pp.125-136
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• 2000

The notion of MV-algebra was introduced by C.C. Chang in 1958 to provide an algebraic proof of the completeness of Lukasiewicz axioms for infinite valued logic. These algebras appear in the literature under different names: Bricks, Wajsberg algebra, CN-algebra, bounded commutative BCK-algebras, etc. The purpose of this paper is to give a topological lattice completion of semisimple MV-algebras. To this end, we characterize the complete atomic center MV-algebras and semisimple algebras as subalgebras of a cube. Then we define the $\delta$-completion of semisimple MV-algebra and construct the $\delta$-completion. We also study some important properties and extension properties of $\delta$-completion.

• Korean Journal of Logic
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• v.16 no.1
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• pp.1-15
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• 2013

Yang [12] investigated weakening-free fuzzy logics expanded by the delta connective $\Delta$, which can be interpreted as Baaz's projection and its generalizations. In this paper, we keep investigating such logics with an alternative delta connective $\Delta$, which can be regarded as a variant of the Baaz projection. The main difference is that although our new $\Delta$ satisfies many properties of Baaz projection, it can nether be interpreted as Baaz's projection itself nor its generalizations. For this, we first introduce several weakening-free fuzzy logics with the alternative connective $\Delta$. The algebraic structures corresponding to the systems are then defined, and their algebraic completeness is proved.

• Korean Journal of Logic
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• v.11 no.1
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• pp.131-156
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• 2008

This paper first investigates several uninorm logics (introduced by Metcalfe and Montagna in [8]) as fuzzy-relevance logics. We first show that the uninorm logic UL and its extensions IUL, UML, and IUML are fuzzy-relevant; fuzzy in Cintula's sense, i.e., the logic L is complete with respect to linearly ordered L-matrices; and relevant in the weak sense that ${\Phi}{\rightarrow}{\Psi}$ is a theorem only if either (i) $\Phi$ and $\Psi$ share a sentential variable or constant, or (ii) both $\sim\Phi$ and $\Psi$ are theorems. We next expand these systems to those with $\triangle$.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.47-56
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• 2012

In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSH-algebras bearing in mind the results indicated by Or lowska and Rewitzky in [E. Orlowska and I. Rewitzky, Discrete Dualities for Heyting Algebras with Operators, Fund. Inform. 81 (2007), no. 1-3, 275-295] for Heyting algebras. In addition, we introduce a propositional calculus and prove this calculus has TSH-algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus.

• Korean Journal of Logic
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• v.22 no.2
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• pp.291-307
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• 2019

This paper deals with set-theoretic Kripke-style semantics for FR, a fuzzy version of R of Relevance. For this, first, we introduce the system FR and its corresponding Kripke-style semantics. Next, we provide set-theoretic completeness results for it.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.3B
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• pp.360-374
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• 2004

The OSPF protocol is the most widely used Interior Gateway Routing Protocol. Therefore, for the reliability of behavior of gigabit swiching routers, it is essential to guarantee the interoperability and the safety of the OSPF protocol. In this paper, we analyze the standard document of the OSPF protocol, so that we provide a formal specification that specifies the protocol behaviors by detailed design level using the algebraic formal method. By referring available source codes of the OSPF protocol, we supplement the formal specification to express more detailed behaviors that is not specified definitely in the standard. We also formally verify the interoperability and the safety of the protocol state machine of the specification. By showing that the formal specification specify all of the states and the transition events that appear in the standard document of the OSPF protocol, we prove that the state machine has the completeness, and prove it has the interoperability. To prove that the specification of the protocol has the safety, we formally verify the reachability, the liveness, the livelock-free property, and the deadlock-free property. As a result, we prove the protocol has the consistency. The specification and the validation are also effective to the OSPF Version 3 that inherit the protocol mechanism of the OSPF Version 2.