Response to “Differential Dependencies Revisited”

A recent article [Vincent et al. 2015] concerns the correctness of several results in reasoning about differential dependencies (dds), originally reported in Song and Chen [2011]. The major concern by Vincent et al. [2015] roots from assuming a type of infeasible differential functions in the given dds for consistency and implication analysis, which are not allowed in Song and Chen [2011]. A differential function is said to be infeasible if there is no tuple pair with values that can satisfy the specified distance constraints. For example, [price(<2, > 4)] requires the difference of two price values to be < 2 and > 4 at the same time, which is clearly impossible. Although dds involving infeasible differential functions may be syntactically interesting, they are semantically meaningless and would neither be specified by domain experts nor discovered from data. For these reasons, infeasible differential functions are not considered [Song and Chen 2011] and the results in Song and Chen [2011] are correct, in contrast to what is claimed in Vincent et al. [2015].