Independence Under Incomplete Information
Miika Hannula, Minna Hirvonen, Juha Kontinen, Sebastian Link
TL;DR
This work extends the classical notion of independence to relational databases with incomplete information by introducing possible independence ($X \bot_p Y$) and certain independence ($X \bot_c Y$) atoms. It develops axiomatic systems to capture implication (axiomatisations) and analyzes the computational complexity of implication and model checking across these notions, revealing that CIAs align with complete-information results (via grounding) and admit Armstrong relations, while PIAs exhibit richer and more challenging behavior, with a restricted axiomatisation sufficing in some cases. The paper provides tight data- and combined-complexity results, showing polynomial-time consequences for CIAs and certain unary PIAs, while general PIAs are NP-hard, and demonstrates how these foundations enable more efficient updates and query processing under incomplete data. Overall, the results establish a principled framework for handling independence constraints under incomplete information and outline key directions for broader fragments and Armstrong-relations in this setting.
Abstract
We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and first results regarding the axiomatisability and computational complexity of implication problems associated with these concepts are established. In addition, several results for the data and the combined complexity of model checking are presented. The findings help reduce computational overheads associated with the processing of updates and answering of queries.