Probabilistic database management systems are currently an active area of research.
"While there are currently no commercial probabilistic database systems, several research prototypes exist..."[1] Probabilistic databases distinguish between the logical data model and the physical representation of the data much like relational databases do in the ANSI-SPARC Architecture.
Consequently, the possible worlds corresponding to the database are as follows: There are essentially two kinds of uncertainties that could exist in a probabilistic database, as described in the table below: By assigning values to random variables associated with the data items, different possible worlds can be represented.
The first published use of the term "probabilistic database" was probably in the 1987 VLDB conference paper "The theory of probabilistic databases", by Cavallo and Pittarelli.
[4] The title (of the 11 page paper) was intended as a bit of a joke, since David Maier's 600 page monograph, The Theory of Relational Databases, would have been familiar at that time to many of the conference participants and readers of the conference proceedings.