A complete lattice is a lattice for which every subset, possibly infinite, has a least upper bound and a greatest lower bound. In this case, we denote $up-tack equals square-cap upper L$ called bottom and $down-tack equals square-cup upper L$ (called top).

[0] Julien Henry. Static Analysis by Abstract Interpretation and Decision Procedures. Software Engineering [cs.SE]. Université de Grenoble, 2014. English.