On the Limitations of Provenance for Queries With Difference

TL;DR

This paper investigates the limitations of provenance semirings in handling database queries with difference, revealing fundamental failures in satisfying expected equivalence axioms across various semirings.

Contribution

It demonstrates that extending provenance semirings to queries with difference inherently fails to meet certain axioms, highlighting fundamental limitations.

Findings

Provenance semirings cannot satisfy key equivalence axioms for queries with difference.

Extensions to support difference are fundamentally limited for certain semirings.

Some semirings can support difference, but not all, indicating inherent constraints.

Abstract

The annotation of the results of database transformations was shown to be very effective for various applications. Until recently, most works in this context focused on positive query languages. The provenance semirings is a particular approach that was proven effective for these languages, and it was shown that when propagating provenance with semirings, the expected equivalence axioms of the corresponding query languages are satisfied. There have been several attempts to extend the framework to account for relational algebra queries with difference. We show here that these suggestions fail to satisfy some expected equivalence axioms (that in particular hold for queries on "standard" set and bag databases). Interestingly, we show that this is not a pitfall of these particular attempts, but rather every such attempt is bound to fail in satisfying these axioms, for some semirings. Finally, we show particular semirings for which an extension for supporting difference is (im)possible.