  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.
