Derivative algebra (abstract algebra)
- <A, ·, +, ', 0, 1, D>
- <A, ·, +, ', 0, 1>
- 0D = 0
- xDD ≤ x + xD
- (x + y)D = xD + yD.
xD 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.
- 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