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While tags in collaborative tagging systems serve primarily an indexing purpose, facilitating search and navigation of resources, the use of the same tags by more than one individual can yield a collective classification schema. We present an approach for making explicit the semantics behind the tag space in social tagging systems, so that this collaborative organization can emerge in the form of groups of concepts and partial ontologies. This is achieved by using a combination of shallow pre-processing strategies and statistical techniques together with knowledge provided by ontologies available on the semantic web. Preliminary results on the del.icio.us and Flickr tag sets show that the approach is very promising: it generates clusters with highly related tags corresponding to concepts in ontologies and meaningful relationships among subsets of these tags can be identified.