This paper explores the algebraic essence of universal logic functions(ULFs)from an algebraic perspective.Under the framework of semi-tensor product of matrices,the“sequential nature”of ULFs is revealed.Utilizing th...This paper explores the algebraic essence of universal logic functions(ULFs)from an algebraic perspective.Under the framework of semi-tensor product of matrices,the“sequential nature”of ULFs is revealed.Utilizing the nature,a technique called universal transformation method is proposed,by which any ULF can be transformed into an equivalent expression with desired features that facilitate achieving specific objectives,such as modeling,analyzing and synthesizing universal logical systems.Furthermore,several useful logical operators are constructed in a mixed-dimensional situation,including power-raising operator,power-descending operator,erasure operator,and appending operator.Finally,these results are applied to model and analyze finite state machines and their networks,which demonstrate the practical value of the method and operators.展开更多
MTL(Monoidal T-norm based logic)代数是基于左连续三角模的模糊逻辑系统的语义代数,而理想理论是研究MTL代数性质的重要工具。利用加法运算给出了MTL代数理想的等价刻画和生成理想的具体结构。通过定义交、并、蕴涵与补运算,证明了全...MTL(Monoidal T-norm based logic)代数是基于左连续三角模的模糊逻辑系统的语义代数,而理想理论是研究MTL代数性质的重要工具。利用加法运算给出了MTL代数理想的等价刻画和生成理想的具体结构。通过定义交、并、蕴涵与补运算,证明了全体理想之集在集合的包含序下是一个代数格。同时,给出了由全体理想之集构成MTL代数和对合MTL代数的充分且必要条件。展开更多
基金supported in part by the National Natural Science Foundation of China under Grants 62073124 and U1804150.
文摘This paper explores the algebraic essence of universal logic functions(ULFs)from an algebraic perspective.Under the framework of semi-tensor product of matrices,the“sequential nature”of ULFs is revealed.Utilizing the nature,a technique called universal transformation method is proposed,by which any ULF can be transformed into an equivalent expression with desired features that facilitate achieving specific objectives,such as modeling,analyzing and synthesizing universal logical systems.Furthermore,several useful logical operators are constructed in a mixed-dimensional situation,including power-raising operator,power-descending operator,erasure operator,and appending operator.Finally,these results are applied to model and analyze finite state machines and their networks,which demonstrate the practical value of the method and operators.
文摘MTL(Monoidal T-norm based logic)代数是基于左连续三角模的模糊逻辑系统的语义代数,而理想理论是研究MTL代数性质的重要工具。利用加法运算给出了MTL代数理想的等价刻画和生成理想的具体结构。通过定义交、并、蕴涵与补运算,证明了全体理想之集在集合的包含序下是一个代数格。同时,给出了由全体理想之集构成MTL代数和对合MTL代数的充分且必要条件。
