# lattice

views updated Jun 08 2018

lattice An algebraic structure, such as a Boolean algebra, in which there are two dyadic operations that are both commutative and associative and satisfy the absorption and idempotent laws. The two dyadic operators, denoted by ∧ and ∨, are called the meet and the join respectively.

An alternative but equivalent view of a lattice is as a set L on which there is a partial ordering defined. Further, every pair of elements has both a greatest lower bound and a least upper bound. The least upper bound of {x,y} can be denoted by x y and is referred to as the join of x and y. The greatest lower bound can be denoted by x y and is called the meet of x and y. It can then be shown that these operations satisfy the properties mentioned in the earlier definition, since a partial ordering ← can be introduced by defining ab iff ab = a

Lattices in the form of Boolean algebras play a very important role in much of the theory and mathematical ideas underlying computer science. Lattices are also basic to much of the approximation theory underlying the ideas of denotational semantics.

# lattice

views updated May 11 2018

lat·tice / ˈlatis/ • n. a structure consisting of strips of wood or metal crossed and fastened together with square or diamond-shaped spaces left between, used typically as a screen or fence or as a support for climbing plants. ∎  an interlaced structure or pattern resembling this: the lattice of branches above her. ∎  Physics a regular repeated three-dimensional arrangement of atoms, ions, or molecules in a metal or other crystalline solid.

lattice

# lattice

views updated May 18 2018

lattice.
1. A came.

2. System of small, light bars crossing each other at intervals, often made of laths, or light slips of wood forming regular square- or lozenge-shaped openings. Lattices formed of square-sectioned wood arranged in square, rectangular, and diagonal patterns were a common feature of C18 and C19 Chinoiserie.

3. Undivided part of a C18 theatre auditorium between the boxes and the pit.

# lattice

views updated May 08 2018

lattice A regular, three-dimensional framework which indicates the ordered arrangement of atoms in crystals. The smallest complete lattice is known as the ‘unit cell’ and it may be repeated many times to form a complete crystal. The shape of the unit cell varies according to the arrangement of the points of the lattice in space, i.e. a ‘space lattice’.

# lattice

views updated May 14 2018

lattice XIV —OF. lattis, f. latte LATH (- Gmc.).