  In this paper we introduce the convex fragment of {\L}ukasiewicz Logic and
discuss its possible applications in different learning schemes. Indeed, the
provided theoretical results are highly general, because they can be exploited
in any learning framework involving logical constraints. The method is of
particular interest since the fragment guarantees to deal with convex
constraints, which are shown to be equivalent to a set of linear constraints.
Within this framework, we are able to formulate learning with kernel machines
as well as collective classification as a quadratic programming problem.
