A Compositional Query Algebra for Second-Order Logic and Uncertain Databases

World-set algebra is a variable-free query language for uncertain databases. It constitutes the core of the query language implemented in MayBMS, an uncertain database system. This paper shows that world-set algebra captures exactly second-order logic over finite structures, or equivalently, the polynomial hierarchy. The proofs also imply that world-set algebra is closed under composition, a previously open problem.

💡 Research Summary

The paper investigates World‑Set Algebra (WSA), a variable‑free query language designed for uncertain databases, and establishes its exact expressive power and compositional properties. WSA extends the classical relational algebra (selection, projection, rename, product, union, difference) with two additional operators: repair‑key and possible A. The repair‑key operator nondeterministically selects a maximal subset of a relation that satisfies a functional dependency on a given attribute set A, effectively “repairing” the relation to make A a key. The possible A operator aggregates tuples that appear in the results of a sub‑query across all possible worlds that agree on the projection of A, thereby providing a mechanism to reason about “possible” and “certain” tuples across worlds.

The authors first formalize the semantics of WSA using a translation function