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Mathematically, the security level access may also be expressed in terms of the lattice (a [[partial order]] set) where each object and subject have a greatest lower bound (meet) and least upper bound (join) of access rights. For example, if two subjects ''A'' and ''B'' need access to an object, the security level is defined as the meet of the levels of ''A'' and ''B''. In another example, if two objects ''X'' and ''Y'' are combined, they form another object ''Z'', which is assigned the security level formed by the join of the levels of ''X'' and ''Y''.
LBAC is known as a label-based (or rule-based) access control restriction as opposed to [[role-based access control]] (RBAC).
Lattice based access control models were first formally defined by [[Dorothy E. Denning|Denning]] (1976); see also Sandhu (1993).
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