Unifying Causality, Diagnosis, Repairs and View-Updates in Databases

In this work we establish and point out connections between the notion of query-answer causality in databases and database repairs, model-based diagnosis in its consistency-based and abductive versions, and database updates through views. The mutual relationships among these areas of data management and knowledge representation shed light on each of them and help to share notions and results they have in common. In one way or another, these are all approaches to uncertainty management, which becomes even more relevant in the context of big data that have to be made sense of.

💡 Research Summary

This paper establishes a comprehensive bridge among four major topics in data management: query‑answer causality, database repairs, model‑based diagnosis (both consistency‑based and abductive), and view‑based updates. By treating each of these as a form of inconsistency resolution, the authors show how results and techniques from one area can be systematically transferred to the others.

The causality framework starts with a relational instance D split into endogenous tuples Dⁿ (potential causes) and exogenous tuples Dˣ (outside the analyst’s control). For a Boolean conjunctive query Q, a tuple t∈Dⁿ is an actual cause if there exists a minimal contingency set Γ⊆Dⁿ such that removing Γ∪{t} makes Q false while removing only Γ leaves Q true. The responsibility of t is defined as ρ(t)=1/(|Γ|+1), providing a quantitative ranking of causes.

The authors then map this notion onto database repair theory. When Q is unexpectedly true, its negation can be expressed as a denial constraint κ(Q). An S‑repair (subset‑minimal) or C‑repair (cardinality‑minimal) of D with respect to κ(Q) corresponds to a minimal way of restoring consistency. Crucially, t is an actual cause iff there exists an S‑repair that does not contain t; the size of the smallest set of deleted endogenous tuples gives the responsibility. Conversely, given all actual causes and their minimal contingency sets, one can reconstruct all S‑repairs of D. This two‑way correspondence allows the rich algorithmic toolbox of repair computation (e.g., hitting‑set based methods) to be reused for causality detection, and vice‑versa.

Next, the paper embeds causality into consistency‑based diagnosis. The database is encoded as a first‑order theory SD, the denial constraint κ(Q) is rewritten as κ(Q)ₑₓₜ that assumes all tuples are normal, and the observation is the fact that Q holds. The resulting theory is inconsistent. A diagnosis is a minimal set Δ⊆Dⁿ of tuples to be marked abnormal (ab) such that SD∪{ab(P(c))|P(c)∈Δ}∪{¬ab(P(c))|P(c)∈Dⁿ\Δ}∪{Q} becomes consistent. The paper proves that t is an actual cause iff it belongs to some minimal diagnosis, and that responsibility equals 1 divided by the size of a minimum‑cardinality diagnosis containing t. This equivalence brings the extensive complexity results from diagnosis (e.g., hitting‑set duality) to the responsibility problem, showing that deciding whether a tuple is a most responsible cause is as hard as finding a minimum diagnosis.

The abductive perspective is then explored using Datalog. A Datalog program Π together with a database D defines a Datalog abductive problem (AP) where the goal predicate ans is true. The task is to find minimal subsets Δ of abducible facts (hypotheses) that, together with Π and D, entail ans. The authors show that such minimal abductive explanations correspond exactly to actual causes for ans, and that responsibility can again be measured by the cardinality of a smallest explanation. This connection extends causality beyond conjunctive queries to recursive Datalog queries, opening the way to apply abductive reasoning tools (e.g., Prolog‑based abductive solvers) to causal analysis.

Finally, the paper discusses view‑updates. A view definition can be seen as a denial constraint; updating the view induces a set of violations that must be repaired. By choosing preferred repairs—e.g., those that modify only endogenous tuples or that minimize changes to exogenous data—one obtains a principled semantics for view‑updates that aligns with the causality‑responsibility framework. The authors suggest annotating tuples with an “endogenous/exogenous” flag to enforce such preferences, and they point out that many existing repair notions (subset‑minimal, cardinality‑minimal, preferred) can be directly interpreted as different causality models.

Overall, the paper demonstrates that causality, repairs, diagnosis, and view‑updates are different manifestations of the same underlying problem: restoring consistency between a database and a set of logical constraints. By formalizing the translations among them, the authors enable cross‑fertilization of algorithms, complexity results, and practical techniques, and they provide a unified theoretical foundation for future work on uncertainty management in large‑scale data systems.