Approximating Certain and Possible Answers Beyond Sets

Explore a 35-minute lecture by Boris Glavic from the Illinois Institute of Technology, presented at the Simons Institute, on approximating certain and possible answers beyond sets in database systems. Delve into the challenges of handling uncertainty in data across various domains and learn about incomplete and probabilistic databases as principled techniques for modeling this uncertainty. Examine the concepts of certain answers and possible answers semantics in querying incomplete databases, and understand the limitations of these approaches for specific classes of data models, instances, and queries. Discover a novel approach that generalizes incomplete and probabilistic databases using semiring-annotated relations (K-relations) to support diverse data types such as incomplete bag semantics, provenance, and temporal data. Investigate how algebraic properties of semirings provide efficient approximations for certain and possible answers. Learn about attribute-annotated uncertain databases (AU-DBs) and their ability to handle full relational algebra with aggregation and sorting-based operations, enabling efficient approximation of certain answers for complex queries.