Matching dependencies (MDs) were introduced to specify the identification or matching of certain attribute values in pairs of database tuples when some similarity conditions are satisfied. Their enforcement can be seen as a natural generalization of entity resolution. In what we call the "pure case" of MDs, any value from the underlying data domain can be used for the value in common that does the matching. We investigate the semantics and properties of data cleaning through the enforcement of matching dependencies for the pure case. We characterize the intended clean instances and also the "clean answers" to queries as those that are invariant under the cleaning process. The complexity of computing clean instances and clean answers to queries is investigated. Tractable and intractable cases depending on the MDs and queries are identified. Finally, we establish connections with database "repairs" under integrity constraints.