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Dictionary:

Boolean algebra


n.

An algebra in which elements have one of two values and the algebraic operations defined on the set are logical OR, a type of addition, and logical AND, a type of multiplication.


 
 
Accounting Dictionary: Boolean Algebra

The algebra of logic. It is sometimes called symbolic logic. Boolean algebra is a method of expressing logic in a mathematical context. It is primarily concerned with binary operations and based on the cumulative, associative, and distributive laws of binary operations. Boolean algebra provides the theoretical concepts for computer design. It is not used to solve managerial problems directly.

 
Britannica Concise Encyclopedia: Boolean algebra

Symbolic system used for designing logic circuits and networks for digital computers. Its chief utility is in representing the truth value of statements, rather than the numeric quantities handled by ordinary algebra. It lends itself to use in the binary system employed by digital computers, since the only possible truth values, true and false, can be represented by the binary digits 1 and 0. A circuit in computer memory can be open or closed, depending on the value assigned to it, and it is the integrated work of such circuits that give computers their computing ability. The fundamental operations of Boolean logic, often called Boolean operators, are "and," "or," and "not"; combinations of these make up 13 other Boolean operators.

For more information on Boolean algebra, visit Britannica.com.

 
Philosophy Dictionary: Boolean algebra

A Boolean algebra is a system consisting of a set S and two operations, ∩ and ∪ (cap and cup), subject to the following axioms. For all sets a,b,c, that are members of S:

1 a ∩ (b ∩ c) = (a ∩ b) ∩ c.

Also a ∪ (b ∪ c) = (a ∪ b) ∪ c

(associativity)

2 a ∩ b = b ∩ a.

Also a ∪ b = b ∪ a (commutativity)

3 a ∩ (b ∪ c) = (a ∩ b) ∪ (a ∩ c).

Also a ∪ (b ∩ c) = (a ∪ b) ∩ (a ∪ c)

(distributivity)

4 There belong to S two elements, 0 and 1, with the properties

a ∪ 0 = a; a ∩ 1 = a (identity)

5 For each set a in S there exists a set a′ with the properties that a ∪ aprime; = 1, a ∩ aprime; = 0 (complementation).

The propositional calculus can be represented as a Boolean algebra, with ∩ representing &, ∪ representing ∨, and 1 = T, 0 = F. The Boolean operators are then the truth functors, such as &, ∨, and ¬. A Boolean search is a search for things meeting a condition defined with these operators.

 
Columbia Encyclopedia: Boolean algebra
(bū'lēən) , an abstract mathematical system primarily used in computer science and in expressing the relationships between sets (groups of objects or concepts). The notational system was developed by the English mathematician George Boole c.1850 to permit an algebraic manipulation of logical statements. Such manipulation can demonstrate whether or not a statement is true and show how a complicated statement can be rephrased in a simpler, more convenient form without changing its meaning. In his 1881 treatise, Symbolic Logic, the English logician and mathematician John Venn interpreted Boole's work and introduced a new method of diagramming Boole's notation; this was later refined by the English mathematician Charles Dodgson (better known as Lewis Carroll—this method is now know as the Venn diagram. When used in set theory, Boolean notation can demonstrate the relationship between groups, indicating what is in each set alone, what is jointly contained in both, and what is contained in neither. Boolean algebra is of significance in the study of information theory, the theory of probability, and the geometry of sets. The expression of electrical networks in Boolean notation has aided the development of switching theory and the design of computers.

 
Wikipedia: Boolean algebra (disambiguation)

Boolean algebra may mean:

  • Boolean algebra (logic), a logical calculus applying to truth values or sets, used for describing logic circuits and formulating conditional expressions
  • Boolean algebra (structure), a type of algebraic structure modeling the aforementioned logical calculus

For an alternative perspective, see Boolean algebras canonically defined.


This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

 
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Math
mathworld.wolfram.com
 
 
 

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Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved.  Read more
Accounting Dictionary. Dictionary of Accounting Terms. Copyright © 2005 by Barron's Educational Series, Inc. All rights reserved.  Read more
Britannica Concise Encyclopedia. Britannica Concise Encyclopedia. © 2006 Encyclopædia Britannica, Inc. All rights reserved.  Read more
Philosophy Dictionary. The Oxford Dictionary of Philosophy. Copyright © 1994, 1996, 2005 by Oxford University Press. All rights reserved.  Read more
Columbia Encyclopedia. The Columbia Electronic Encyclopedia, Sixth Edition Copyright © 2003, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/  Read more
Wikipedia. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Boolean algebra".  Read more

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