Ontology matching is the process of identifying alignment between ontologies with the objective to facilitate interoperability and knowledge integration. A limitation of state of the art ontology matching systems is that the produced alignments usually only contain equivalence relations, while other relations, such as subsumption relations, are often neglected. Furthermore, an ontology matching system is normally composed of a set of differently tuned matching algorithms, but their appropriateness and order of execution typically require human judgement. The COMPOSE framework identifies subsumption relations automatically using a three-stage matcher composition process. These three processes are ontology analysis, matcher selection, and matcher combination. Within this framework we integrate existing techniques for all three processes with novel ones and evaluate the feasibility of the framework in an experiment involving six acknowledged ontologies.