在抽象代数中,导出代数是如下标识(signature)的代数结构
- <A, ·, +, ', 0, 1, D>
这里的
- <A, ·, +, ', 0, 1>
- 0D = 0
- xDD ≤ x + xD
- (x + y)D = xD + yD
xD 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。
引用
- Esakia, L., Intuitionistic logic and modality via topology, Annals of Pure and Applied Logic, 127 (2004) 155-170
- McKinsey, J.C.C. and Tarski, A., The Algebra of Topology, Annals of Mathematics, 45 (1944) 141-191
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