boolean algebra

Bool·e·an al·gebra

B b

Transcription

- US Pronunciation
- US IPA
- [boo-lee-uh n al-juh-bruh]
- /ˈbu li ən ˈæl dʒə brə/

- US Pronunciation
- US IPA
- [boo-lee-uh n al-juh-bruh]
- /ˈbu li ən ˈæl dʒə brə/

Definitions of boolean algebra words

noun boolean algebra a system of symbolic logic devised by George Boole to codify logical operations. It is used in computers 3
noun boolean algebra Boolean algebra is a branch of symbolic logic used in computers. 3
noun boolean algebra 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. 1
noun boolean algebra Mathematics. a ring with a multiplicative identity in which every element is an idempotent. 1
noun Technical meaning of boolean algebra (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 <= b to mean that a ^ b = a, or equivalently a V b = b. Thus, for example, if ^, V and - denote set intersection, union and complement then <= is the inclusive subset relation. The relation <= is 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. 1
noun boolean algebra (algebra) A De Morgan algebra which also satisfies the law of excluded middle and the law of noncontradiction. 0

See all 8 definitions of boolean algebra

Information block about the term

Origin of boolean algebra

First appearance:

before 1885

One of the 21% newest English words

1885-90; named after George Boole; see -an

Historical Comparancy

Parts of speech for Boolean algebra

noun

adjective

verb

adverb

pronoun

preposition

conjunction

determiner

exclamation

Full grammatical hierarchy of Boolean algebra

boolean algebra popularity

This term is known only to a narrow circle of people with rare knowledge. Only 3% of English native speakers know the meaning of this word.

According to our data most of word are more popular. This word is almost not used. It has a much more popular synonym.

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