Axiomatizing approximate inclusion
Matilda Häggblom
TL;DR
This paper addresses approximate variants of inclusion dependencies by defining quantity- and ratio-approximate inclusion atoms within a team-semantic framework. It develops complete axiomatizations for quantity-approximate inclusion under arity limits and for unary ratio-approximate inclusion, and it characterizes their computational complexity (PSPACE-complete in general, PTIME for unary cases). The results enable sound and complete reasoning about approximate dependencies and show how approximations affect decidability, with practical implications for data quality tasks. The work also outlines avenues for future research, including k-anonymity extensions and broader logical formulations.
Abstract
We introduce two approximate variants of inclusion dependencies and examine the axiomatization and computational complexity of their implication problems. The approximate variants allow for some imperfection in the database and differ in how this degree is measured. One considers the error relative to the database size, while the other applies a fixed threshold independent of size. We obtain complete axiomatizations for both under some arity restrictions. In particular, restricted to unary inclusion dependencies, the implication problem for each approximate variant is decidable in PTIME. We formalise the results using team semantics, where a team corresponds to a uni-relational database.