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.

@article{paperbot1690,
  title = {The Shapley Value of Inconsistency Measures for Functional Dependencies},
  author = {Ester Livshits and Benny Kimelfeld},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 18, Issue 2},
  year = {2022},
  doi = {10.46298/lmcs-18(2:20)2022}
}