Although a database view embodies partial information about the state of the main schema, the state of the view schema is a quotient (and not a subset) of the state of the main schema. It is the information content of the view state, the set of sentences which are true for that state, and not the state itself which is a subset of the information content of the state of the main schema. There are thus two dual approaches to modelling this partiality, one based upon structures, with a consequent quotient relationship, and another based upon logical theories, with a consequent subset relationship. In this work, a representation for database views is developed which combines these two approaches. The state-based representation is expanded so that the information content embodied in a wide class of views, including those defined by SPJ queries, is fully representable, thus permitting the view state to be modelled internally as a subset of the main database state. The utility of this framework is demonstrated with a simple solution to the uniqueness problem for view updates via constant complement.