We present a probabilistic relational algebra (PRA) which is a generalization of standard relational algebra. Here tuples are assigned probabilistic weights giving the probability that a tuple belongs to a relation. Based on intensional semantics, the tuple weights of the result of a PRA expression always confirm to the underlying probabilistic model. We also show for which expressions extensional semantics yields the same results. Furthermore, we discuss complexity issues and indicate possibilities for optimization. With regard to databases, the approach allows for representing imprecise attribute values, whereas for information retrieval, probabilistic document indexing and probabilistic search term weighting can be modelled. As an important extension, we introduce the concept of vague predicates which yields a probabilistic weight instead of a Boolean value, thus allowing for queries with vague selection conditions. So PRA implements uncertainty and vagueness in combination with the...

A specific query establishes a rigid qualification and is concerned only with data that match it precisely. A vague query establishes a target qualification and is concerned also with data that are close to this target. Most conventional database systems cannot handle vague queries directly, forcing their users to retry specific queries repeatedly with minor modifications until they match data that are satisfactory. This article describes a system called VAGUE that can handle vague queries directly. The principal concept behind VAGUE is its extension to the relational data model with data metrics, which are definitions of distances between values of the same domain. A problem with implementing data distances is that different users may have different interpretations for the notion of distance. VAGUE incorporates several features that enable it to adapt itself to the individual views and priorities of its users.

Probabilistic databases have received considerable attention recently due to the need for storing uncertain data produced by many real world applications. The widespread use of probabilistic databases is hampered by two limitations: (1) current probabilistic databases make simplistic assumptions about the data (e.g., complete independence among tuples) that make it difficult to use them in applications that naturally produce correlated data, and (2) most probabilistic databases can only answer a restricted subset of the queries that can be expressed using traditional query languages. We address both these limitations by proposing a framework that can represent not only probabilistic tuples, but also correlations that may be present among them. Our proposed framework naturally lends itself to the possible world semantics thus preserving the precise query semantics extant in current probabilistic databases. We develop an efficient strategy for query evaluation over such probabilistic databases by casting the query processing problem as an inference problem in an appropriately constructed probabilistic graphical model. We present several optimizations specific to probabilistic databases that enable efficient query evaluation. We validate our approach by presenting an experimental evaluation that illustrates the effectiveness of our techniques at answering various queries using real and synthetic datasets. 1

This paper deals with the application of fuzzy logic in a relational database environment with the objective of capturing more meaning of the data. It is shown that with suitable interpretations for the fuzzy membership functions, a fuzzy relational data model can be used to represent ambiguities in data values as well as impreciseness in the association among them. Relational operators for fuzzy relations have been studied, and applicability of fuzzy logic in capturing integrity constraints has been investigated. By introducing a fuzzy resemblance measure EQUAL for comparing domain values, the definition of classical functional dependency has been generalized to fuzzy functional dependency (ffd). The implication problem of ffds has been examined and a set of sound and complete inference axioms has been proposed. Next, the problem of lossless join decomposition of fuzzy relations for a given set of fuzzy functional dependencies is investigated. It is proved that with a suitable restriction on EQUAL, the design theory of a classical relational database with functional dependencies can be extended to fuzzy relations satisfying fuzzy functional dependencies.

A probabilistic learning model for vague queries and missing or imprecise information in databases is described. Instead of retrieving only a set of answers, our approach yields a ranking of objects from the database in response to a query. By using relevance judgements from the user about the objects retrieved, the ranking for the actual query as well as the overall retrieval quality of the system can be further improved. For specifying different kinds of conditions in vague queries, the notion of vague pred-icates is introduced. Based on the underlying probabilistic model, also imprecise or missing attribute values can be treated easily. In addition, the corresponding formulas can be applied in combination with standard predicates (from two-valued logic), thus extending standard database systems for coping with missing or imprecise data.

This paper surveys methods for representing and reasoning with imperfect information. It opens with an attempt to classify the different types of imperfection that may pervade data, and a discussion of the sources of such imperfections. The classification is then used as a framework for considering work that explicitly concerns the representation of imperfect information, and related work on how imperfect information may be used as a basis for reasoning. The work that is surveyed is drawn from both the field of databases and the field of artificial intelligence. Both of these areas have long been concerned with the problems caused by imperfect information, and this paper stresses the relationships between the approaches developed in each.

... In this paper, we first introduce the syntax of Temporal-Probabilistic (TP) relations and then show how they can be converted to an explicit, significantly more space-consuming form called Annotated Relations. We then present a Theoretical Annotated Temporal Algebra (TATA). Being explicit, TATA is convenient for specifying how the algebraic operations should behave, but is impractical to use because annotated relations are overwhelmingly large. Next, we

In this paper, it is shown that fuzzy sets and possibility theory provide an homogeneous framework for the representation of both imprecise/uncertain information and soft queries with a flexible interpretation. Incompletely known information as well as flexible query handling capabilities are expected to extend the range of applications for future database management systems. The term fuzzy databases which is extensively used in the specialized literature covers several different meanings which are reviewed. A special emphasis is put on flexible queries addressed to regular databases. Such queries enables the user to easily express preferences among more or less admissible attribute values. Several approaches for introducing flexibility, including fuzzy sets, are compared. A query language based on SQL is outlined and some issues related to query processing are discussed. In addition, possibility theory proves to be useful for representing imperfectly known data and soft constraints. P...

In this paper, a probabilistic relational model is presented which combines relational algebra with probabilistic retrieval. Based on certain independence assumptions, the operators of the relational algebra are redefined such that the probabilistic algebra is a generalization of the standard relational algebra. Furthermore, a special join operator implementing probabilistic retrieval is proposed. When applied to typical document databases, queries can not only ask for documents, but for any kind of object in the database. In addition, an implicit ranking of these objects is provided in case the query relates to probabilistic indexing or uses the probabilistic join operator. The proposed algebra is intended as a standard interface to combined database and IR systems, as a basis for implementing user-friendly interfaces. 1 Introduction The fields of databases (DB) and information retrieval (IR) have been coexisting for a very long time, but with little influence on each other. IR peop...

The need to incorporate and treat information given in fuzzy terms in Relational Databases has concentrated a great effort in the last years. This paper focuses on the treatment of functional dependencies (f.d.) between attributes of a relation scheme. We review other approaches to this problem and present some of its missfunctions concerning intuitive properties a fuzzy extension of f.d. should verify. Then we introduce a fuzzy extension of this concept to overcome the previous anomalous behaviors and study its properties. Of primary interest is the completeness of our fuzzy version of Armstrong axioms in order to derive all the fuzzy functional dependencies logically implied by a set of f.f.d. just using these axioms. 1 1 The Crisp Relational Model Relational Databases ([Codd 70]) constitute the main approach to the treatment of databases. It is considered a set of Attributes fA h g h=1:::n and an instance r of a relation scheme R(A 1 ; : : : ; A n ). The database contain several