A characterization of residual implications derived from left-continuous uninorms

In this paper, a set of axioms is given that characterizes those functions I:[0, 1]2 → [0, 1] for which a left-continuous uninorm U exists in such a way that I is the residual implication derived from U. A characterization for the particular cases when U is representable, when U is continuous in image and when U is idempotent are also given.