An alternative approach to data cleaning, which makes sure that the consistent data can be identified if desired, when queries are answered from the database, is discussed. The set of databases tuples either inserted or deleted into/from the database to restore consistency has to be made minimal under set inclusion. Answers to queries should be obtained by querying the given, inconsistent databases. There are many different semantics for null values and for databases that represent incomplete information. The exchange of data is governed by data mappings, which are mappings derived by transitivity, and a peer's own local constraint that have to be be respected, when data from other peer is received.