Information visualization encounters a wide variety of different data domains. The visualization community has developed representation methods and interactive techniques. As a community, we have realized that the requirements in each domain are often dramatically different. In order to easily apply existing methods, researchers have developed a semiology of graphic representations. We have extended this research into a framework that includes operators and interactions in visualization systems, such as a visualization spreadsheet. We discuss properties of this framework and use it to characterize operations spanning a variety of different visualization techniques. The framework developed in this paper enables a new way of exploring and evaluating the design space of visualization operators, and helps end--users in their analysis tasks.