The May 2011 edition of the CACM has interesting article that claims noSQL databases are are merely a variant of SQL databases. The authors describe how noSQL can be seen as a mathematical dual of SQL, replacing sets with monads.
A mathematical model underlying noSQL systems would have several benefits:

- An answer for those who consider SQL more powerful/appropriate/cooler since it has a sound theoretical basis.
- Allow for possibility of standardization across the current multitude of largely incompatible systems
- Guide further improvements in functionality.

Sets are quite familiar and covered in high school mathematics. Monads are famously opaque, with many conflicting metaphors being used to describe them. The usefulness of the CACM article is thus limited by the lack of a good explanation of monads!
A set of slides on coSQL by the CACM authors are

available.