There is a growing need to combine information from multiple existing knowledge bases for unanticipated uses, and to maintain such information when the underlying knowledge bases change. The autonomy of diverse knowledge sources is an obstacle to integrating all pertinent knowledge within a single knowledge base. The cost of maintaining integrated knowledge within a single knowledge base grows both with the volatility and the number of the sources from which the information originates. Establishing and maintaining application specific portions of knowledge sources are therefore major challenges to ontology management. Rather than materializing all of the information from the sources into a single knowledge base, we are developing an algebra that enables the construction of virtual knowledge bases geared towards a specific application. This algebra consists of composable operators that transform contexts into contexts. Operators express the relevant parts of a source and the conditions for combining sources using a rule language. The rules define what is necessary to achieve a valid transformation from the source information to the application context. Rules which expose the relevant parts of a source determine what we call a congruity measure between the source and its target application. The rules which articulate knowledge from diverse sources establish a similarity measure between them. We focus on one example to show how the use of our algebra is an important framework for establishing new applications using existing knowledge, and for maintaining up to date knowledge in the face of changes to the underlying sources. We have used an on-line dictionary that is autonomously maintained to develop a novel thesaurus application. With over 112,000 entries, two million words in the definitions, and semi-annual updates, this dictionary has provided us with a test bed to examine the issues of creation and maintenance of knowledge contexts using an algebraic methodology.