An lattice is complemented if every element has a complement. It is orthocomplemented if it is equipped with an involution that sends each element to a complement.
These are both orthocomplemented:
any Boolean algebra, as in classical logic
the subspaces of a Hilbert space, as in Birkhoff–von Neumann quantum logic/Hilbert lattice
Wikipedia, Complemented lattice
P. Pták and S. Pulmannová, Orthomodular structures as quantum logics, ser. Fundamental theories of physics. Kluwer Academic Publishers, 1991.
Last revised on December 26, 2014 at 15:41:01. See the history of this page for a list of all contributions to it.