The management of privacy and personal information within multi-cultural domain such as clouds and other universal collaborative systems requires intrinsic compliance-checking and assurance modules in order to increase social trust and acceptance. Focusing mainly on medical domains, this issue is particularly important due to the sensitivity of health related data in international data protection law. The use of ontologies and semantic technologies can provide relatively easy interpretation of legislation at run time, and can allow the logging of data access events to serve for future audits. However, the enforcement of semantic web rules (SWRL rules) on complex and heterogeneous architectures is expensive and might present runtime overheads. We believe a mapping of our semantic web privacy policies to a standard access control language such as XACML would be a useful alternative. A translation to XACML, would allow the integration of these policies with existing security and privacy policies being adopted on clouds environments. This paper describes a mathematical formalism for mapping SWRL (Semantic Web Rule Language) privacy rules to XACML policies and also explains the underline implementation requirements of this formalism.