Most real databases contain data whose correctness is uncertain. In order to work with such data, there is a need to quantify the integrity of the data. This is achieved by using probabilistic databases.
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A probabilistic database is an uncertain database in which the possible worlds have associated probabilities. Probabilistic database management systems are currently an active area of research. "While there are currently no commercial probabilistic database systems, several research prototypes exist..."
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. In probabilistic databases this is even more crucial since such databases have to represent very large numbers of possible worlds, often exponential in the size of one world (a classical database), succinctly.
Terminology
In a probabilistic database, each data item - relation, tuple and value that an attribute can take - is associated with a probability ∈ (0,1], with 0 representing that the data is certainly incorrect, and 1 representing that it is certainly correct.
Possible Worlds
A probabilistic database could exist in multiple states. For example, if we are uncertain about the existence of a tuple in the database, then the database could be in two different states with respect to that tuple - the first state contains the tuple, while the second one does not. Similarly, if an attribute can take one of the values x, y or z, then the database can be in three different states with respect to that attribute.
Each of these states is called a possible world.
Consider the following database:
(Here {b3,b3′,b3′′} denotes that the attribute can take any of the values b3,b3′ or b3′′)
Then the actual state of the database may or may not contain the first tuple (depending on whether it is correct or not). Similarly, the value of the attribute B may be b3,b3′ or b3′′.
Consequently, the possible worlds corresponding to the database are as follows:
Types of Uncertainties
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, we can represent different possible worlds.