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-algebraExamples of MV-algebras, Relation To Łukasiewicz Logic, Relation To Functional Analysis, In Software

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