Capturing Missing Tuples and Missing Values

Databases in real life are often neither entirely closed-world nor entirely open-world. Indeed, databases in an enterprise are typically partially closed, in which a part of the data is constrained by master data that contains complete information about the enter prise in certain aspects 121]. It has been shown that despite missing tuples, such a database may turn out to have complete information for answering a query [9].

This paper studies partially closed databases from which both tuples and mikes may be missing. We specify such a database in terms of conditional tables constrained by master data, referred tc as c-instances. We first propose three models to characterize whether a c-instance 7 is complete for a query Q relative to master data. That is, depending on how missing values in 7 are instantiated, the answer to Q in 7 remains unchanged when new tuples are added. We then investigate four. problems, to determine (a) whether a given c-instance is complete for a query Q, (b) whether there exists a c-instance that is complete for Q relative to master data available, (c) whether a c-instance is a minimal-size database that is complete for Q, and (d) whether there exists a c-instance of a bounded size that is complete for Q. We establish matching lower and upper bounds on these problems for queries expressed in a variety of languages, in each of the three models for specifying relative completeness.