🤖 AI Summary
Existing theoretical foundations for database repair—particularly concerning consistency modeling and consistent query answering (CQA)—remain underdeveloped. Method: We propose the first unified repair framework grounded in formal logic (first-order and constraint logic), which rigorously distinguishes integrity constraints from query constraints, supports both hard and soft query semantics, guarantees answer preservation, and enables semantic distance measurement between database instances. It fully logicizes the notion of repair, unifies set- and cardinality-based repairs, and extends naturally to semiring-annotated databases. Contribution/Results: Theoretically, we establish a systematic complexity-theoretic analysis of repair existence and CQA, precisely characterizing multiple classical repair semantics and determining tight computational complexity bounds for key problems under varying constraint classes. This yields a general, decidable foundation for consistent query answering.
📝 Abstract
We introduce a general abstract framework for database repairs, where the repair notions are defined using formal logic. We distinguish between integrity constraints and so-called query constraints. The former are used to model consistency and desirable properties of the data (such as functional dependencies and independencies), while the latter relate two database instances according to their answers to the query constraints. The framework allows for a distinction between hard and soft queries, allowing the answers to a core set of queries to be preserved, as well as defining a distance between instances based on query answers. We illustrate how different notions of repairs from the literature can be modelled within our unifying framework. The framework generalises both set-based and cardinality based repairs to semiring annotated databases. Furthermore, we initiate a complexity-theoretic analysis of consistent query answering and checking existence of a repair within the framework.
