Dealing with Missing Values Meaning Unknown in Probabilistic Approximations

We describe probabilistic approximations dealing with missing values. A relation used by Kryszkiewicz for indiscernibility of missing values is applied to deal with the missing values in previous work, but the relation considers only the indiscernibility of a missing value with another value. There are two possibilities for missing values. A missing value may be indiscernible from a value, or it may be discernible from that value. To deal with the two possibilities, we handle missing values in probabilistic approximations by using possible world semantics, as it is used by Lipski in incomplete databases. As a result, we obtain the lower and the upper bound of the actual probabilistic approximation. We can obtain these bounds without worrying about the number of possible tables.