Learning Łukasiewicz Logic Fragments by Quadratic Programming

In this paper we provide a framework to embed logical constraints into the classical learning scheme of kernel machines, that gives rise to a learning algorithm based on a quadratic programming problem. In particular, we show that, once the constraints are expressed using a specific fragment from the Łukasiewicz logic, the learning objective turns out to be convex. We formulate the primal and dual forms of a general multi–task learning problem, where the functions to be determined are predicates (of any arity) defined on the feature space. The learning set contains both supervised examples for each predicate and unsupervised examples exploited to enforce the constraints. We give some properties of the solutions constructed by the framework along with promising experimental results.