设是一个偏序集，若对于任意的，都有最小上界（并），或者对于任意的，都有最大下界（交），则称构成一个半格。

也可以将半格定义为一个代数结构。一个半格是一个代数结构或，其中和如同在格的定义中所述。

In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset. Dually, a meet-semilattice (or lower semilattice) is a partially ordered set which has a meet (or greatest lower bound) for any nonempty finite subset. Every join-semilattice is a meet-semilattice in the inverse order and vice versa.