My research is concerned with the problem of Ontology Matching. Ontology Matching (sometimes also refered to as Ontology Alignment) is about finding correspondences between elements (e.g. concepts or roles) of two ontologies covering the same or a similar domain. The matching process can be divided into two steps: First, a set of matching hypotheses is generated. Then, a subset of these hypotheses is chosen as final alignment. In my work I focus on several problems related to the second step. In particular, I suggest the use of logical reasoning to ensure the consistency of the final alignment.