There is a growing need to define a semantic mapping from a database schema to an ontology. Such a mapping is an integral part of the data integration systems that use an ontology as a unified global view. However, both ontologies and database schemas evolve over time in order to accommodate updated information needs. Once the ontology and the database schema associated with a semantic mapping evolved, it is necessary and important to maintain the validity of the semantic mapping to reflect the new semantics in the ontology and the schema. In this paper, we propose a formulation of the mapping maintenance problem and outline a possible solution using illustrative examples. The main points of this paper are: (1) to differentiate the semantic mapping maintenance problem from the schema mapping adaptation problem which only adapts mappings when schemas change; (2) to develop an approach for specifying the validity of a semantic mapping in terms of two-way legal instances translation b...