FUNCTIONAL DEPENDENCIES AND INCOMPLETE INFORMATION

Functional dependencies play an important role in relational database design. They are defined in the context of a single relation which at all times must contain tuples with non-null entries. In this paper we examine an extension of the functional dependency interpretation to handle null values, that is, entries in tuples that represent incomplete information in a relational database. A complete axiomatization of inference rules for extended functional dependencies is also presented. Only after having such results is it possible to talk about decompositions and normalization theory in a context of incomplete information. Finally, we show that there are several practical advantages in using nulls and a weaker notion of constraint satisfiability.Information Systems Working Papers Serie

Polynomial conjunctive query rewriting under unary inclusion dependencies

Ontology-based data access (OBDA) is widely accepted as an important ingredient of the new generation of information systems. In the OBDA paradigm, potentially incomplete relational data is enriched by means of ontologies, representing intensional knowledge of the application domain. We consider the problem of conjunctive query answering in OBDA. Certain ontology languages have been identified as FO-rewritable (e.g., DL-Lite and sticky-join sets of TGDs), which means that the ontology can be incorporated into the user's query, thus reducing OBDA to standard relational query evaluation. However, all known query rewriting techniques produce queries that are exponentially large in the size of the user's query, which can be a serious issue for standard relational database engines. In this paper, we present a polynomial query rewriting for conjunctive queries under unary inclusion dependencies. On the other hand, we show that binary inclusion dependencies do not admit polynomial query rewriting algorithms

A relational model for incomplete information in temporal databases

In temporal database systems the time varying aspects of data are captured by time-stamping data values. Research in temporal databases has concentrated on developing models in which it is essential that all the information be known;In the present work a relational model for incomplete information is presented. The model allows incomplete temporal information to be stored, and provides a powerful, yet simple, algebra to query the incomplete information;The incomplete information model presented here generalizes a well-known model for temporal databases with complete information. The algebraic expressions in the model produce results that are reliable in the sense that they never report incorrect information. This is shown by introducing the notion of completions of relations and databases. It is also shown that except for certain cases of selection, if the definition of the operators were strengthened to give more information, we could obtain results that are not reliable. This result is obtained by introducing the concepts of extensions of relations and more informative relations;Update operations create, change, and changekey are defined. These operations allow the user to modify the state of the database to reflect changes in the real world, to correct errors in the database, and to increase the information content of incomplete objects as more information becomes available

Fragments of Bag Relational Algebra: Expressiveness and Certain Answers

International audienceWhile all relational database systems are based on the bag data model, much of theoretical research still views relations as sets. Recent attempts to provide theoretical foundations for modern data management problems under the bag semantics concentrated on applications that need to deal with incomplete relations, i.e., relations populated by constants and nulls. Our goal is to provide a complete characterization of the complexity of query answering over such relations in fragments of bag relational algebra. The main challenges that we face are twofold. First, bag relational algebra has more operations than its set analog (e.g., additive union, max-union, min-intersection, duplicate elimination) and the relationship between various fragments is not fully known. Thus we first fill this gap. Second, we look at query answering over incomplete data, which again is more complex than in the set case: rather than certainty and possibility of answers, we now have numerical information about occurrences of tuples. We then fully classify the complexity of finding this information in all the fragments of bag relational algebra

Fragments of bag relational algebra: Expressiveness and certain answers

While all relational database systems are based on the bag data model, much of theoretical research still views relations as sets. Recent attempts to provide theoretical foundations for modern data management problems under the bag semantics concentrated on applications that need to deal with incomplete relations, i.e., relations populated by constants and nulls. Our goal is to provide a complete characterization of the complexity of query answering over such relations in fragments of bag relational algebra. The main challenges that we face are twofold. First, bag relational algebra has more operations than its set analog (e.g., additive union, max-union, min-intersection, duplicate elimination) and the relationship between various fragments is not fully known. Thus we first fill this gap. Second, we look at query answering over incomplete data, which again is more complex than in the set case: rather than certainty and possibility of answers, we now have numerical information about occurrences of tuples. We then fully classify the complexity of finding this information in all the fragments of bag relational algebra

Knowledge-preserving Certain Answers for SQL-like Queries

International audienceAnswering queries over incomplete data is based on finding answers that are certainly true, independently of how missing values are interpreted. This informal description has given rise to several different mathematical definitions of certainty. To unify them, a framework based on "explanations", or extra information about incomplete data, was recently proposed. It partly succeeded in justifying query answering methods for relational databases under set semantics, but had two major limitations. First, it was firmly tied to the set data model, and a fixed way of comparing incomplete databases with respect to their information content. These assumptions fail for reallife database queries in languages such as SQL that use bag semantics instead. Second, it was restricted to queries that only manipulate data, while in practice most analytical SQL queries invent new values, typically via arithmetic operations and aggregation. To leverage our understanding of the notion of certainty for queries in SQL-like languages, we consider incomplete databases whose information content may be enriched by additional knowledge. The knowledge order among them is derived from their semantics, rather than being fixed a priori. The resulting framework allows us to capture and justify existing notions of certainty, and extend these concepts to other data models and query languages. As natural applications, we provide for the first time a well-founded definition of certain answers for the relational bag data model and for valueinventing queries on incomplete databases, addressing the key shortcomings of previous approaches

Imperfect Data In Database Context. How Are They Stored In Extended Relational Databases

Building a more accurate reality model requires taking into account imperfect information present in our knowledge and language. This paper presents several aspects of data imperfection in the database context and the appropriate frameworks for their treatment. It’s concluding that null value, possibility distribution and probability theory are the best solutions to represent incomplete, imprecise and uncertain data. For each of these problems there are some relational model extension proposals, including data representation and relational algebra