Abstract: This study presents a formal solution based on the techniques of description logics to solve the problem of ontology matching process which consists of detecting the semantic mappings between two given ontologies. Composing the relations between their subsumers does the deduction of the relations among the semantic entities of different ontologies. It also, presents some performed experiments to assess the effectiveness of the composition operation and to verify that the proposed solution returns complete and precise results. The results obtained look very promising, comparing with expert mappings.