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An inconsistent database is a database that violates one or more integrity constraints. A typical approach for answering a query over an inconsistent database is to first clean the inconsistent database by transforming it to a consistent one and then apply the query to the consistent database. An alternative and more principled approach, known as consistent query answering, derives the answers to a query over an inconsistent database without changing the database, but by taking into account all possible repairs of the database.In this paper, we study the problem of consistent query answering over inconsistent databases for the class for conjunctive queries under primary key constraints. We develop a system, called EQUIP, that represents a fundamental departure from existing approaches for computing the consistent answers to queries in this class. At the heart of EQUIP is a technique, based on Binary Integer Programming (BIP), that repeatedly searches for repairs to eliminate candidate consistent answers until no further such candidates can be eliminated. We establish rigorously the correctness of the algorithms behind EQUIP and carry out an extensive experimental investigation that validates the effectiveness of our approach. Specifically, EQUIP exhibits good and stable performance on conjunctive queries under primary key constraints, it significantly outperforms existing systems for computing the consistent answers of such queries in the case in which the consistent answers are not first-order rewritable, and it scales well.

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