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Consistent Answers of Conjunctive Queries on Graphs
During the past decade, there has been an extensive investigation of the
computational complexity of the consistent answers of Boolean conjunctive
queries under primary key constraints. Much of this investigation has focused
on self-join-free Boolean conjunctive queries. In this paper, we study the
consistent answers of Boolean conjunctive queries involving a single binary
relation, i.e., we consider arbitrary Boolean conjunctive queries on directed
graphs. In the presence of a single key constraint, we show that for each such
Boolean conjunctive query, either the problem of computing its consistent
answers is expressible in first-order logic, or it is polynomial-time solvable,
but not expressible in first-order logic