Many domains of interest today are characterized by both uncertainty and complex relational structure. Therefore probabilistic structure learning is a popular research topic in artificial intelligence and machine learning. The research area of Statistical Relational Learning (SRL) specifically attempts to effectively represent, reason, and learn in domains that are governed by these characteristics. This thesis studies the problem of probabilistic structure learning under the Markov Logic Networks (MLN) framework. In particular, it addresses the issue of exploiting the background knowledge axiomatization to effectively constrain the space of possible structures by learning clauses subject to specific characteristics defined by these axioms. We focus on the domain of symbolic event recognition under uncertainty by using the axiomatization of a probabilistic variant of the Event Calculus (MLN−EC) as background knowledge. We employ an online strategy in order to effectively handle large training sets and incrementally refine the previously learned structure. We demonstrate the effectiveness of our method through experiments in the domain of activity recognition, using a publicly available benchmark dataset for video surveillance.