the LMU München, where this paper was written. A preliminary version was

Deductive databases are paraconsistent theory systems which change over time. They do not support the inference of arbitrary consequences from inconsistent components, such as contradictory definitions of database relations (predicates) or violated integrity constraints. Moreover, computed answers in deductive databases typically make sense, almost no matter to which degree consistency or integrity is corrupted. Integrity of the knowledge embodied by a database is expressed by an associated set of database constraints which, taken on its own, may also vary in its degree of (in-)consistency. Deductive databases evolve via sequences of state changes, effected by updates that can be seen as belief revision steps. Instead of rejecting update requests because of inconsistency or integrity violation, a certain amount of paraconsistency can be tolerated sometimes, in order to accommodate such requests. We recapitulate various forms of inconsistency and integrity violation in deductive databases. We investigate to which extent deductive databases can or do tolerate various degrees of paraconsistency. We do not discuss consistency in terms of compatibility of replicated or distributed data, nor do we discuss integrity in terms of security. Paraconsistency in the semantics of databases The field of deductive databases ("pure logic programming") provides a solid semantic foundation which is unparalleled by other programming paradigms. In particular, the semantics of the definite case (pure Horn clause theories), described denotationally as the least fixpoint of the immediate consequence operator [vK], is unanimously agreed upon. For the non-monotonic inference of negative information from a definite database, there are two competing semantics: The closed world assumption (cwa) [R1] and the database completion (comp) [Cl]. For the semantics of normal deductive databases (which generalize definite databases by admitting clauses with negative literals as premises), a model-oriented and a proof-procedure-oriented line of development can be distinguished. In a sense, they generalize cwa and comp, respectively. The model-oriented line has brought