Many people could benefit from collecting and analyzing their own personal digital data, but most do not possess the necessary expertise to do so. Remote collaboration with knowledge discovery experts who do possess this expertise is a possible solution to this conundrum but raises a number of issues of its own, one of which is preserving the data owner's privacy. It is up to the data owner to decide how much data to share with a data analyst, but withholding too much will make the analyst unable to help the data owner effectively, so it is necessary to find a trade-off between these two conflicting interests. We propose a solution whereby the data requirements imposed by analysis tasks and the access restrictions imposed by privacy constraints are encoded formally using an ontology, enabling automatic detection of conflicts. Once a conflict has been identified, the data owner and the data analyst can negotiate a resolution, possibly by transforming the data using a method that makes it no longer sensitive from the data owner's perspective while sufficiently preserving its utility from the data analyst's perspective. Using such an ontology, data owners and data analysts tap into a knowledge base of privacy-preserving data transformations, each with known effects on the utility of the transformed data for analysis. This makes it easier to find an acceptable trade-off between privacy and utility in future collaborations.