A BL-algebra is a structure in which X is a non empty set with four binary operations and two constants 0 and 1 satisfying the following axioms:
BL-1 (X,∧,∨,0,1) is a bounded lattice;
BL-2 (X,∗,1) is an abelian monoid, i. e., ∗ is commutative and associative with x∗1=x;
BL-3 x∗y≤z iff (Residuation);
BL-4 (Divisibility);
BL-5 (Prelinearity).