The Shapley Value of Inconsistency Measures for Functional Dependencies

Authors Ester Livshits, Benny Kimelfeld

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Ester Livshits
  • Technion - Israel Institute of Technology, Haifa, Israel
Benny Kimelfeld
  • Technion - Israel Institute of Technology, Haifa, Israel

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Ester Livshits and Benny Kimelfeld. The Shapley Value of Inconsistency Measures for Functional Dependencies. In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Quantifying the inconsistency of a database is motivated by various goals including reliability estimation for new datasets and progress indication in data cleaning. Another goal is to attribute to individual tuples a level of responsibility to the overall inconsistency, and thereby prioritize tuples in the explanation or inspection of dirt. Therefore, inconsistency quantification and attribution have been a subject of much research in Knowledge Representation and, more recently, in Databases. As in many other fields, a conventional responsibility sharing mechanism is the Shapley value from cooperative game theory. In this paper, we carry out a systematic investigation of the complexity of the Shapley value in common inconsistency measures for functional-dependency (FD) violations. For several measures we establish a full classification of the FD sets into tractable and intractable classes with respect to Shapley-value computation. We also study the complexity of approximation in intractable cases.

Subject Classification

ACM Subject Classification
  • Theory of computation → Incomplete, inconsistent, and uncertain databases
  • Information systems → Data cleaning
  • Shapley value
  • inconsistent databases
  • functional dependencies
  • database repairs


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