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

TL;DR

This paper demonstrates that world-set algebra, a variable-free query language for uncertain databases, precisely captures second-order logic over finite structures and the polynomial hierarchy, and proves its closure under composition.

Contribution

It establishes the exact expressive power of world-set algebra as equivalent to second-order logic and resolves the open problem of its closure under composition.

Findings

World-set algebra captures second-order logic over finite structures.

It is equivalent to the polynomial hierarchy.

The algebra is closed under composition.

Abstract

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.