## lattice

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.

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## lattice

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

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## lattice

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.

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## lattice

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’.

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## lattice

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

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## lattice

latticeAttis, gratis, lattice •malpractice, practice, practise •Atlantis, mantis •pastis •Lettice, lettuce, Thetis •apprentice, compos mentis, in loco parentis, prentice •Alcestis, testis •poetess • armistice •appendicitis, arthritis, bronchitis, cellulitis, colitis, conjunctivitis, cystitis, dermatitis, encephalitis, gastroenteritis, gingivitis, hepatitis, laryngitis, lymphangitis, meningitis, nephritis, neuritis, osteoarthritis, pericarditis, peritonitis, pharyngitis, sinusitis, tonsillitis •epiglottis, glottis •solstice •mortise, rigor mortis •countess • viscountess •myosotis, notice, Otis •poultice • justice • giantess • clematis •Curtis • interstice • Tethys •Glenrothes • Travis •Jarvis, parvis •clevis, crevice, Nevis •Elvis, pelvis •Avis, Davies, mavis •Leavis • Divis • novice • Clovis •Jervis, service •marquess, marquis