A relational database may not satisfy certain integrity constraints (ICs) for several reasons. However most likely most of the information in it is still consistent with the ICs. The answers to queries that are consistent with the ICs can be considered sematically correct answers, and are characterized [2] as ordinary answers that can be obtained from every minimally repaired version of the database. In this paper we address the problem of specifying those repaired versions as the minimal models of a theory written in Annotated Predicate Logic [27]. It is also shown how to specify database repairs using disjunctive logic program with annotation arguments and a classical stable model semantics. Those programs are then used to compute consistent answers to general first order queries. Both the annotated logic and the logic programming approaches work for any set of universal and referential integrity constraints. Optimizations of the logic programs are also analyzed.