The CIDOC-CRM ontology is a standard for cultural heritage data modeling. Despite its large exploitation, the ontology is primarily maintained in a semi-formal notation, which makes it difficult to homogeneously exploit it in digital environments. In addition, the ontology consists of several classes and relations, whereas one sometimes wishes to reuse it but only partially. The purpose of the paper is to contribute to the use of CIDOC by strengthening its foundations. On the basis of formal ontology theories, we propose a first analysis of the ontology to enhance its conceptual structure. We also present a preliminary modularization of CIDOC aimed at enhancing both its formalization and usage.