On Representation and Querying Incomplete Information in Databases with Multisets

We extend the approach to representation of partial information based on orderings on objects from sets to multisets. We characterize orderings arising under the closed-and the open-world assumptions and analyze their complexity. We prove that, in contrast to the set case, where orderings are rst-order deenable and are thus expressible in standard database query languages, the orderings on bags are not expressible in standard bag languages. As a corollary of this result, we give an example of a query on nested relations whose inexpressibility in the extension of relational algebra to nested objects cannot be proved by reduction to the rst-order case.