A BL-algebra is a structure in which is a non-empty set with four binary operations and two constants 0 and 1 satisfying the following axioms:
BL-1 is a bounded lattice;
BL-2 is an abelian monoid; which means that $\ast $ is commutative and associative with ;
BL-3 iff (residuation);
BL-4 (divisibility);
BL-5 (prelinearity);
A BL-algebra is called a MV-algebra if , or equivalently where .