An MV-algebra is an algebraic structure consisting of
- a non-empty set
- a binary operation on
- a unary operation on and
- a constant denoting a fixed element of
which satisfies the following identities:
- and
By virtue of the first three axioms, is a commutative monoid. Being defined by identities, MV-algebras form a variety of algebras. The variety of MV-algebras is a subvariety of the variety of BL-algebras and contains all Boolean algebras.
An MV-algebra can equivalently be defined (Hájek 1998) as a prelinear commutative bounded integral residuated lattice satisfying the additional identity
Read more about MV-algebra: Examples of MV-algebras, Relation To Łukasiewicz Logic, Relation To Functional Analysis, In Software