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- 2015
MTL代数的Wajsberg形式及其应用
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Abstract:
摘要： MTL代数是一种重要的基础逻辑代数.本文采用Wajsberg方法,根据逻辑系统MTL中公理的形式,建立了NMTL代数的经典代数表示形式,进而证明了NMTL代数与MTL代数是同一代数结构,证明了满足条件 ？x,y∈L, x→y=(y→0)→(x→0)的NMTL代数L是BR0代数.在此基础上证明了IMTL代数和BR0代数是同一代数结构,并给出BR0代数和BL代数的Wajsberg形式.
Abstract: MTL algebra is an important basic logic algebra. Firstly, the classical algebras forms of NMTL algebra is given by taking Wajsberg's method and some parts of axioms of MTL logic system, and it is proved that NMTL algebra and MTL algebra have identical structure. Secondly, it is proved that an NMTL algebras L satisfying the condition: ？x,y∈L, x→y=(y→0)→(x→0) is BR0 algebra. Finally, it is proved that IMTL algebra and BR0 algebra have identical structure and the Wajsberg forms of BR0 algebra and BL algebra are given
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