There is a real promise of achieving technical interoperation of large data sets from many widely dispersed sources. Where such shared access is achieved we find differences in the meanings of the terms used to describe the data (the metadata or schemas) and the terms used in the data themselves: the descriptors, the names, the classifiers, and also in the data structures, i.e., the hierarchies, the scope and the level of detail represented in the data files. We present a means to interoperate when terminologies differ by presenting an algebra over ontologies. Those ontologies cover terms used in the descriptive metadata and within the data files themselves. Use of the concepts in our approach involves two phases: compiling the terminological matches, using expert-mediated tools, and executing interoperation processes, focused on a specific application subsequently.