Semantic matching determines the mappings between the nodes of two graphs (e.g., ontologies) by computing logical relations (e.g., subsumption) holding among the nodes that correspond semantically to each other. We present an approach to deal with the lack of background knowledge in matching tasks by using semantic matching iteratively. Unlike previous approaches, where the missing axioms are manually declared before the matching starts, we propose a fully automated solution. The benefits of our approach are: (i) saving some of the pre-match efforts, (ii) improving the quality of match via iterations, and (iii) enabling the future reuse of the newly discovered knowledge. We evaluate the implemented system on large real-world test cases, thus, proving empirically the benefits of our approach.