Theory of Computing Systems

, Volume 52, Issue 3, pp 441–482 | Cite as

Data Cleaning and Query Answering with Matching Dependencies and Matching Functions

  • Leopoldo BertossiEmail author
  • Solmaz Kolahi
  • Laks V. S. Lakshmanan


Matching dependencies were recently introduced as declarative rules for data cleaning and entity resolution. Enforcing a matching dependency on a database instance identifies the values of some attributes for two tuples, provided that the values of some other attributes are sufficiently similar. Assuming the existence of matching functions for making two attribute values equal, we formally introduce the process of cleaning an instance using matching dependencies, as a chase-like procedure. We show that matching functions naturally introduce a lattice structure on attribute domains, and a partial order of semantic domination between instances. Using the latter, we define the semantics of clean query answering in terms of certain/possible answers as the greatest lower bound/least upper bound of all possible answers obtained from the clean instances. We show that clean query answering is intractable in general. Then we study queries that behave monotonically w.r.t. semantic domination order, and show that we can provide an under/over approximation for clean answers to monotone queries. Moreover, non-monotone positive queries can be relaxed into monotone queries.


Databases Data cleaning Matching dependency Entity resolution Matching function Semantic domination Lattice Certain answer Possible answer Query relaxation 



This work was supported by NSERC Strategic Network on Business Intelligence (BIN ADC01, Years 1 and 2) and (BIN ADC05, Year 3); and NSERC/IBM CRDPJ/371084-2008, which is gratefully acknowledged. L. Bertossi is a Faculty Fellow of the IBM Center for Advanced Studies.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Leopoldo Bertossi
    • 1
    Email author
  • Solmaz Kolahi
    • 2
  • Laks V. S. Lakshmanan
    • 2
  1. 1.Carleton UniversityOttawaCanada
  2. 2.University of British ColumbiaVancouverCanada

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