Detecting Errors in Numeric Attributes

To detect errors in numeric data, this paper proposes numeric functional dependencies (NFDs), a class of dependencies that allow us to specify arithmetic relationships among numeric attributes. We show that NFDs subsume conditional functional dependencies (CFDs); hence, we can catch data inconsistencies, numeric or not, in a uniform logic framework by using NFDs as data quality rules. Better still, NFDs do not increase the complexity of reasoning about data quality rules. We show that the satisfiability and implication problems for NFDs remain NP-complete and coNP-complete, respectively, the same as their counterparts for CFDs. Moreover, NFDs can be implemented in SQL and hence, error detection can be readily supported by DBMS. In addition, we show that NFDs and CFDs can be extended across multiple tables, without increasing the complexity of static analyses and error detection.