[математика] булева алгебра, алгебра логики
булева алгебра, алгебра логики набор операций над двузначными логическими переменными, широко используемый в современных компьютерах. Названа в честь её создателя математика Джорджа Буля (George Boole, 1815 - 1864). Как правило, используются операции логического умножения, логического сложения и отрицания, так как из них можно построить любую другую булеву операцию. Все нынешние компьютеры построены на двузначной логике. Примером машин с трёхзначной логикой были ЭВМ "Сетунь" и "Сетунь-70" (Н.П. Брусенцов, МГУ) Смотри также: logic operation, logical operator Синоним(ы): symbolic logic
булева алгебра, алгебра логики
noun an algebraic system that consists of a set closed under two binary operations and that can be described by any of various systems of postulates all of which can be deduced from the postulates that each operation is commutative, that each operation is distributive over the other, that an identity element exists for each operation, and that for every element in the set there exists another element which when combined with the first under either one of the operations yields the identity element of the other operation
(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.