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The word “ontology” is used with different senses in different communities. The most radical difference is perhaps between the philosophical sense, which has of course a well-established tradition, and the computational sense, which emerged in the recent years in the knowledge engineering community, starting from an early informal definition of (computational) ontologies as “explicit specifications of conceptualizations”. In this paper we shall revisit the previous attempts to clarify and formalize such original definition, providing a detailed account of the notions of conceptualization and explicit specification, while discussing at the same time the importance of shared explicit specifications.