| slovo | definícia |
boolean algebra
(wn) | Boolean algebra
n 1: a system of symbolic logic devised by George Boole; used in
computers [syn: Boolean logic, Boolean algebra] |
boolean algebra
(foldoc) | Boolean algebra
(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 |
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