Abstract
The paper Structure and Complexity of Bag Consistency by Albert Atserias and Phokion Kolaitis [1] studies fundamental structural and algorithmic questions on the global consistency of databases in the context of bag semantics. A collection D of relations is called globally consistent if there is a (so-called "universal") relation over all the attributes that appear in all the relations of D whose projections yield the relations in D. The basic algorithmic problem for consistency is: given a database D, determine whether D is globally consistent. An obvious necessary condition for global consistency is local (or pairwise) consistency: every pair of relations in D must be consistent. This condition is not sufficient however: It is possible that every pair is consistent, but there is no single global relation over all the attributes whose projections yield the relations in D. A natural structural question is: Which database schemas have the property that every locally consistent database over the schema is also globally consistent?
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