follow Dictionary.com

Stories We Like: A Guide to the Comma

Boolean algebra

[boo-lee-uh n] /ˈbu li ən/
noun
1.
Logic. a deductive logical system, usually applied to classes, in which, under the operations of intersection and symmetric difference, classes are treated as algebraic quantities.
2.
Mathematics. a ring with a multiplicative identity in which every element is an idempotent.
Origin
1885-1890
1885-90; named after George Boole; see -an
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
Cite This Source
British Dictionary definitions for Boolean algebra

Boolean algebra

/ˈbuːlɪən/
noun
1.
a system of symbolic logic devised by George Boole to codify logical operations. It is used in computers
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
Cite This Source
Boolean algebra in Science
Boolean algebra
  (b'lē-ən)   
A form of symbolic logic, in which variables, which stand for propositions, have only the values "true" (or "1") and "false" (or "0"). Relationships between these values are expressed by the Boolean operators AND, OR, and NOT. For example, "a + b" means "a OR b", and its value is true as long as either a is true or b is true (or both). Boolean logic can be used to solve logical problems, and provides the mathematical tools fundamental to the design of digital computers. It is named after the mathematician George Boole. Also called Boolean logic. See also logic gate.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
Cite This Source
Boolean algebra in Technology
logic
(After the logician George Boole)
1. Commonly, and especially in computer science and digital electronics, this term is used to mean two-valued logic.
2. This is in stark contrast with the definition used by pure mathematicians who in the 1960s introduced "Boolean-valued models" into logic precisely because a "Boolean-valued model" is an interpretation of a theory that allows more than two possible truth values!
Strangely, a Boolean algebra (in the mathematical sense) is not strictly an algebra, but is in fact a lattice. A Boolean algebra is sometimes defined as a "complemented distributive lattice".
Boole's work which inspired the mathematical definition concerned algebras of sets, involving the operations of intersection, union and complement on sets. Such algebras obey the following identities where the operators ^, V, - and constants 1 and 0 can be thought of either as set intersection, union, complement, universal, empty; or as two-valued logic AND, OR, NOT, TRUE, FALSE; or any other conforming system.
a ^ b = b ^ a a V b = b V a (commutative laws) (a ^ b) ^ c = a ^ (b ^ c) (a V b) V c = a V (b V c) (associative laws) a ^ (b V c) = (a ^ b) V (a ^ c) a V (b ^ c) = (a V b) ^ (a V c) (distributive laws) a ^ a = a a V a = a (idempotence laws) --a = a -(a ^ b) = (-a) V (-b) -(a V b) = (-a) ^ (-b) (de Morgan's laws) a ^ -a = 0 a V -a = 1 a ^ 1 = a a V 0 = a a ^ 0 = 0 a V 1 = 1 -1 = 0 -0 = 1
There are several common alternative notations for the "-" or logical complement operator.
If a and b are elements of a Boolean algebra, we define a partial ordering, though it is not necessarily a linear ordering since some Boolean algebras contain incomparable values.
Note that these laws only refer explicitly to the two distinguished constants 1 and 0 (sometimes written as LaTeX \top and \bot), and in two-valued logic there are no others, but according to the more general mathematical definition, in some systems variables a, b and c may take on other values as well.
(1997-02-27)
The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
Cite This Source

Word of The Day

Difficulty index for Boolean algebra

Few English speakers likely know this word

Word Value for Boolean

0
0
Scrabble Words With Friends

Quotes with Boolean algebra