The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce t...The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group.展开更多
在逻辑系统MTL(Monoidal t-norm based Logic)中引入一元逻辑连接词▽,并在原有公理模式的基础上添加若干新公理,构建了一种新的MTL的扩张MTL▽逻辑系统。为了进行相应的语义研究,在MTL代数的基础上,引入一元算子▽,提出MTL▽代数的概念...在逻辑系统MTL(Monoidal t-norm based Logic)中引入一元逻辑连接词▽,并在原有公理模式的基础上添加若干新公理,构建了一种新的MTL的扩张MTL▽逻辑系统。为了进行相应的语义研究,在MTL代数的基础上,引入一元算子▽,提出MTL▽代数的概念,并证明了MTL▽代数的同构定理。基于线性MTL▽代数证明了逻辑系统MTL▽的完备性。展开更多
基金National Natural Science Foundation of China(12161013)Research Projects of Guizhou University of Commerce in 2024。
文摘The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group.
文摘在逻辑系统MTL(Monoidal t-norm based Logic)中引入一元逻辑连接词▽,并在原有公理模式的基础上添加若干新公理,构建了一种新的MTL的扩张MTL▽逻辑系统。为了进行相应的语义研究,在MTL代数的基础上,引入一元算子▽,提出MTL▽代数的概念,并证明了MTL▽代数的同构定理。基于线性MTL▽代数证明了逻辑系统MTL▽的完备性。
