The basic notions of posets and lattices are introduced with a wide presentation of examples. In particular, distributive and modular lattices are treated. With respect to the distributive behavior, we discuss Boolean algebras with the associated orthocomplementation mapping. General orthoalgebras are also investigated with application to the quantum logic of subspaces of a finite dimensional Hilbert space.
Cattaneo, G., Ciucci, D. (2009). Posets and Lattices. In B.W. Wah (a cura di), Encyclopedia of Computer Science and Engineering (pp. 2190-2208). John Wiley & Sons [10.1002/9780470050118.ecse320].
Posets and Lattices
Ciucci, DE
2009
Abstract
The basic notions of posets and lattices are introduced with a wide presentation of examples. In particular, distributive and modular lattices are treated. With respect to the distributive behavior, we discuss Boolean algebras with the associated orthocomplementation mapping. General orthoalgebras are also investigated with application to the quantum logic of subspaces of a finite dimensional Hilbert space.
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