Boolean algebra

Meaning

Noun

• An algebraic structure $(\backslash Sigma,\; \backslash vee,\; \backslash wedge,\; \backslash sim,\; 0,\; 1)$ where $\backslash vee$ and $\backslash wedge$ are idempotent binary operators, $\backslash sim$ is a unary involutory operator (called "complement"), and 0 and 1 are nullary operators (i.e., constants), such that $(\backslash Sigma,\; \backslash vee,\; 0)$ is a commutative monoid, $(\backslash Sigma,\; \backslash wedge,\; 1)$ is a commutative monoid, $\backslash wedge$ and $\backslash vee$ distribute with respect to each other, and such that combining two complementary elements through one binary operator yields the identity of the other binary operator. (See Boolean algebra (structure)#Axiomatics.)
• Specifically, an algebra in which all elements can take only one of two values (typically 0 and 1, or "true" and "false") and are subject to operations based on AND, OR and NOT
• The study of such algebras; Boolean logic, classical logic.

Related

Similar words

• switching algebra

Narrower meaning words

• complete Boolean algebra

Broader meaning words

• Kleene algebra
• Heyting algebra
• MV-algebra

Origin

• Named after George Boole (1815–1864), an English mathematician, educator, philosopher and logician.