Boolean logic - ορισμός. Τι είναι το Boolean logic
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Τι (ποιος) είναι Boolean logic - ορισμός

SET THEORY CONCEPT
Boolean valued model; Boolean-valued logic

Boolean logic         
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  • NOT]] gates.
  • Figure 2. Venn diagrams for conjunction, disjunction, and complement
VARIANT OF ORDINARY ELEMENTARY ALGEBRA
Laws of classical logic; Complement (Boolean algebra); Boolean Algebra; Boolean value; Boolean Logic; Boolean algebra (basic concepts); Boolean algebra (logic); Complete Boolean algebra (computer science); Logic function; Logic operation; Complement (boolean algebra); Boolean problem; Boolean equation; Boolean terms; Elementary Boolean algebra; Boolean logic; Boolean logic (computer science); Boolean logic in computer science; Introduction to Boolean algebra; Boolean searching; AND list; OR list; And List; Or List; And list; Or list; Boolean algebra (introduction); Introduction to boolean algebra; Boolean Connectors; Boolean attribute; Duality principle (Boolean algebra); Duality principle (boolean algebra); BooleanAlgebra; Switching algebra; Applications of boolean algebra; History of Boolean algebra; Logical algebra; Contact algebra; Boolean operator (Boolean algebra); Boolean operation (Boolean algebra); Boolean identity; Boolean identities; Boolian algebra; Boolian Algebra
<mathematics> A logic based on Boolean algebra. (1995-03-25)
Boolean algebra         
  • thumb
  • NOT]] gates.
  • Figure 2. Venn diagrams for conjunction, disjunction, and complement
VARIANT OF ORDINARY ELEMENTARY ALGEBRA
Laws of classical logic; Complement (Boolean algebra); Boolean Algebra; Boolean value; Boolean Logic; Boolean algebra (basic concepts); Boolean algebra (logic); Complete Boolean algebra (computer science); Logic function; Logic operation; Complement (boolean algebra); Boolean problem; Boolean equation; Boolean terms; Elementary Boolean algebra; Boolean logic; Boolean logic (computer science); Boolean logic in computer science; Introduction to Boolean algebra; Boolean searching; AND list; OR list; And List; Or List; And list; Or list; Boolean algebra (introduction); Introduction to boolean algebra; Boolean Connectors; Boolean attribute; Duality principle (Boolean algebra); Duality principle (boolean algebra); BooleanAlgebra; Switching algebra; Applications of boolean algebra; History of Boolean algebra; Logical algebra; Contact algebra; Boolean operator (Boolean algebra); Boolean operation (Boolean algebra); Boolean identity; Boolean identities; Boolian algebra; Boolian Algebra
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0, respectively. Instead of elementary algebra, where the values of the variables are numbers and the prime operations are addition and multiplication, the main operations of Boolean algebra are the conjunction (and) denoted as ∧, the disjunction (or) denoted as ∨, and the negation (not) denoted as ¬.
Boolean algebra         
  • thumb
  • NOT]] gates.
  • Figure 2. Venn diagrams for conjunction, disjunction, and complement
VARIANT OF ORDINARY ELEMENTARY ALGEBRA
Laws of classical logic; Complement (Boolean algebra); Boolean Algebra; Boolean value; Boolean Logic; Boolean algebra (basic concepts); Boolean algebra (logic); Complete Boolean algebra (computer science); Logic function; Logic operation; Complement (boolean algebra); Boolean problem; Boolean equation; Boolean terms; Elementary Boolean algebra; Boolean logic; Boolean logic (computer science); Boolean logic in computer science; Introduction to Boolean algebra; Boolean searching; AND list; OR list; And List; Or List; And list; Or list; Boolean algebra (introduction); Introduction to boolean algebra; Boolean Connectors; Boolean attribute; Duality principle (Boolean algebra); Duality principle (boolean algebra); BooleanAlgebra; Switching algebra; Applications of boolean algebra; History of Boolean algebra; Logical algebra; Contact algebra; Boolean operator (Boolean algebra); Boolean operation (Boolean algebra); Boolean identity; Boolean identities; Boolian algebra; Boolian Algebra
<mathematics, 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 op and ot), 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)

Βικιπαίδεια

Boolean-valued model

In mathematical logic, a Boolean-valued model is a generalization of the ordinary Tarskian notion of structure from model theory. In a Boolean-valued model, the truth values of propositions are not limited to "true" and "false", but instead take values in some fixed complete Boolean algebra.

Boolean-valued models were introduced by Dana Scott, Robert M. Solovay, and Petr Vopěnka in the 1960s in order to help understand Paul Cohen's method of forcing. They are also related to Heyting algebra semantics in intuitionistic logic.