Orthocomplemented lattice
From Wikipedia, the free encyclopedia
An orthocomplemented lattice is an algebraic structure consisting of a bounded lattice 
along with a unary function 
called an orthocomplementation. This function must satisfy for any 
- Complement law:
and 
- Involution law:
- Order-reversing law: if
then 
For a given element a the element 
is called the orthocomplement of a. From the axioms it can be shown that this element is unique.
Orthocomplemented lattices satisfy de Morgan's laws:
Boolean algebras are a special case of orthocomplemented lattices, which in turn are special cases of complemented lattices. These structures are most often used in quantum logic, where the closed subspaces of a separable Hilbert space represent quantum propositions and behave as an orthocomplemented lattice.
[edit] External link
- Orthocomplemented lattice at PlanetMath
