Towards a Logical Reconstruction of a Theory for Locally Complete Databases

A relational database stores information about the world. In order to describe how reliable the content of a database is with respect to a certain domain, two cardinal concepts are generally used: correctness and completeness. Correctness refers to whether the database stores only true facts about its intended domain or if it possibly contains false data. Completeness refers to whether the database stores all the information that is true in the world under consideration or not. In this work we study databases that store correct but possibly incomplete information about the world. In particular, we investigate what we call locally complete databases. These are databases that may be complete about certain parts of the world, while being incomplete in general. Such databases consist of a standard relational database supplemented with a number of specifications, called local closed world assumptions, of the areas in the real world where the database contains all true tuples. Our study of locally complete databases is divided into three parts. In the first part we investigate how to represent the fact that a relational database is locally complete. For this purpose we extend the idea of a window of expertise of a database predicate to the first-order case. At the reasoning level, we study two important reasoning tasks: computing answers to queries and determining whether a database has complete knowledge on a query. In the second part of the thesis we study methods to perform efficient computation of the reasoning tasks described above. In particular, we present approximate methods for query answering. We prove that for a useful class of queries and locally complete databases these methods are tractable and complete. The third and last part of the thesis deals with extending the query language from standard SQL to queries with modalities. This extension will allow us to retrieve useful information about the knowledge endorsed by a locally complete database. In this part, we also present a prototype of this extension, based on the model expansion system IDP.