In many practical applications of fuzzy logic it seems clear that one needs more flexibility
in the choice of the conjunction: in particular, the associativity and the commutativity of
a conjunction may be removed. Motivated by these considerations, we present several classes
of conjunctors, i.e. binary operations on [0,1] that are used to extend the boolean conjunction
from {0,1} to [0,1], and characterize their respective residual implicators. We establish
hence a one-to-one correspondence between construction methods for conjunctors and construction
methods for residual implicators. Moreover, we introduce some construction methods directly in the class
of residual implicators, and, by using a deresiduation procedure, we obtain new conjunctors