MV-algebra

Summary

An MV-algebra is an algebraic structure with a truncated addition $\oplus$, a negation $\neg$ and a constant $0$. It is modelled on the unit interval $[0, 1]$ with $x \oplus y = \min(1, x + y)$ and $\neg x = 1 - x$. Chen Chung Chang introduced MV-algebras in 1958 to give an algebraic proof of the completeness of Łukasiewicz infinite-valued logic, a many-valued logic. Every Boolean algebra is an MV-algebra, and MV-algebras play for Łukasiewicz logic the role that Boolean algebras play for classical logic. Daniele Mundici showed that MV-algebras correspond to lattice-ordered abelian groups with a strong unit.