... In this article, we characterize, using postulates, whole classes of strategies for conjunction, disjunction, and negation, meaningful from the viewpoint of probability theory. (1) We propose a probabilistic relational data model and a generic probabilistic relational algebra that neatly captures various strategies satisfying the postulates, within a single unified framework. (2) We show that as long as the chosen strategies can be computed in polynomial time, queries in the positive fragment of the probabilistic relational algebra have essentially the same data complexity as classical relational algebra. (3) We establish various containments and equivalences between algebraic expressions, similar in spirit to those in classical algebra. (4) We develop algorithms for maintaining materialized probabilistic views. (5) Based on these ideas, we have developed

This paper describes a generalization of the relational model in order to capture and manipulate a type of probabilistic information. Probabilistic databases are formalized by means of logic theories based on a probabilistic first-order language proposed by Halpern. A sound a complete method is described for evaluating queries in probabilistic theories. The generalization proposed can be incorporated into existing relational systems with the addition of a component for manipulating propositional formulas. 1

Large sensor networks are being widely deployed for measurement, detection, and monitoring applications. Many of these applications involve database systems to store and process data from the physical world. This data has inherent measurement uncertainties that are properly represented by continuous probability distribution functions (pdf's). We introduce a new object-relational data type, the Gaussian ADT GADT, that models physical data as gaussian pdf's, and we show that existing index structures can be used as fast access methods for GADT data. We also present a measure-theoretic model of probabilistic data and evaluate GADT in its light.

... 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...

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

We present a probabilistic data model for complex values. More precisely, we introduce probabilistic complex value relations, which combine the concept of probabilistic relations with the idea of complex values in a uniform framework. We elaborate a modeltheoretic definition of probabilistic combination strategies, which has a rigorous foundation on probability theory. We then define an algebra for querying database instances, which comprises the operations of selection, projection, renaming, join, Cartesian product, union, intersection, and difference. We prove that our data model and algebra for probabilistic complex values generalizes the classical relational data model and algebra. Moreover, we show that under certain assumptions, all our algebraic operations are tractable. We finally show that most of the query equivalences of classical relational algebra carry over to our algebra on probabilistic complex value relations. Hence, query optimization techniques for classical relational algebra can easily be applied to optimize queries on probabilistic complex value relations. Keywords: Complex value databases, probabilistic databases, data model, relational algebra, query languages. AMS Subject classification: Primary 68P15, 68P20; Secondary 68T30, 68T37 1.

Most database systems are designed under assumptions of precision of both the data stored in their databases, and the requests to retrieve data. In reality, however, these assumptions are often invalid, and in recent years considerable attention has been given to issues of imprecision in database systems. In this paper we review the major solutions for accommodating imprecision, and we describe issues that have yet to addressed, offering possible research directions. 1

We present a generalisation of the relational data model based on a 4-valued paraconsistent logic. Our data model is capable of manipulating incomplete as well as inconsistent information. For this model, we define algebraic operators that are generalisations of the usual operators, such as union, selection, join, on ordinary relations. Our data model can underlie any database management system that deals with incomplete or inconsistent information. As another application of our model and its algebra, we present a bottomup method for constructing the weak well-founded model of general deductive databases. This method can be very simply extended to construct the well-founded model.

Databases are models of the real world. Yet, our knowledge of the real world is often imperfect, thus challenging our ability to create databases of integrity. To uphold the integrity of a database in situations where knowledge of the real world is imperfect, one may either (1) restrict the model to that portion of the real world about which perfect information is available, or (2) develop formalisms that allow the representation of imperfect information. This paper surveys some of the better-known database formalisms for capturing imperfect information. Imperfections in the specification and processing of transactions also have important impact on the quality of the information delivered to users, and this survey discusses them as well.