Resolution in general, logic programming in particular, and even more so abductive logic programming and deductive databases are paraconsistent.
Deductive databases are theory systems which change over time.
Because of the goal-orientedness of query answering which focuses on consistent subsets of relevant database clauses, computed answers in deductive databases typically make sense, almost no matter to which degree consistency or integrity is corrupted. 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, i.e., integrity violation, a certain amount of paraconsistency can be tolerated some times, in order to accommodate such requests. We discuss to which extent deduc tive databases can or do tolerate various degrees of paraconsistency. We do not discuss consistency nor integrity in terms of compatibility of replicated or distributed data or in terms of data security.