In abstract algebra, a derivative algebra is an algebraic structure of the signature where is a Boolean algebra and is a unary operator, the derivative operator, satisfying the identities: 0 = 0 x ≤ x + x (x + y) = x + y. x is called the derivative of x. Derivative algebras provide an algebraic abstraction of the derived set operator in topology. They also play the same role for the modal logic wK4 = K + p∧□p → □□p that Boolean algebras play for ordinary propositional logic.

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  • In abstract algebra, a derivative algebra is an algebraic structure of the signature where is a Boolean algebra and is a unary operator, the derivative operator, satisfying the identities: 0 = 0 x ≤ x + x (x + y) = x + y. x is called the derivative of x. Derivative algebras provide an algebraic abstraction of the derived set operator in topology. They also play the same role for the modal logic wK4 = K + p∧□p → □□p that Boolean algebras play for ordinary propositional logic.
  • 在抽象代数中，导出代数是如下标识(signature)的代数结构 这里的 是布尔代数而 是一元算子导出算子，它满足如下恒等式: 0 = 0 x ≤ x + x (x + y) = x + y x 叫做 x 的导出(derivative)。导出代数为拓扑学中导集算子提供代数抽象。它还为模态逻辑 wK4 = K + p∧□p → □□p 扮演布尔代数对普通命题逻辑所扮演的角色。
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rdfs:comment
  • In abstract algebra, a derivative algebra is an algebraic structure of the signature where is a Boolean algebra and is a unary operator, the derivative operator, satisfying the identities: 0 = 0 x ≤ x + x (x + y) = x + y. x is called the derivative of x. Derivative algebras provide an algebraic abstraction of the derived set operator in topology. They also play the same role for the modal logic wK4 = K + p∧□p → □□p that Boolean algebras play for ordinary propositional logic.
  • 在抽象代数中，导出代数是如下标识(signature)的代数结构 这里的 是布尔代数而 是一元算子导出算子，它满足如下恒等式: 0 = 0 x ≤ x + x (x + y) = x + y x 叫做 x 的导出(derivative)。导出代数为拓扑学中导集算子提供代数抽象。它还为模态逻辑 wK4 = K + p∧□p → □□p 扮演布尔代数对普通命题逻辑所扮演的角色。
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  • Derivative algebra (abstract algebra)
  • 导出代数
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