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The "semantic integrity" of a data base is said to be violated when the data base ceases to represent a legitimate configuration of the application environment it is intended to model. In the context of the relational data model, it is possible to identify multiple levels of semantic integrity information: (1) the description of the domains of the data base, as abstract sets of atomic data values (domain definition), (2) the specification of the fundamental structure of the relations of the data base (relation structure specification), (3) the definition of the abstract operations which are meaningful in terms of the application environment (structured operations), and (4) the expression of additional semantic information not contained in the structure of the relations nor in the identities of their underlying domains (relation constraints). A high level, nonprocedural domain definition language facilitates the description of domains. Such a language allows the specification of the properties of the values constituting a domain, and the action that is to occur if an attempt is made to update a column entry such that it does not belong to the underlying domain of that column. The specification of relation structure and structured operations can also be accomplished by means of high level integrity (sub)languages. A relation constraint has three components: (1) the assertion predicate on the state of the data base or on transitions between data base states), (2) the validity requirement (the occasion(s) at which the assertion must hold), and (3) the violation -action (the action that is to occur if the assertion does not hold at a time when it should). Relation constraint specification can be related to an expression framework (classification scheme) which is useful for the construction of a relation constraint language and specification methodology. Assertions are more than expressions of some relationships among different values in a data base; an assertion singles out the data that is constrained, the states the properties that this data must possess. A classification is provided of the various predicate types used to identify constrained data and to state the properties that they are to possess. A semantic integrity subsystem (of a generalized relational data base management system) can support the generation and maintenance of integrity specifications, verify that these specifications are met by the data base, and take appropriate action if violations are detected.