Least fixpoints as meanings of recursive definitions.

Answering queries approximately has recently been proposed as a way to reduce query response times in on-line decision support systems, when the precise answer is not necessary or early feedback is helpful. Most of the work in this area uses sampling-based techniques and handles aggregate queries, ignoring queries that return relations as answers. In this paper, we extend the scope of approximate query answering to general queries. We propose a novel and intuitive error measure for quantifying the error in an approximate query answer, which can be a multiset in general.

This paper proposes and investigates an approach to deduction in probabilistic logic, using as its medium a language that generalizes the propositional version of Nilsson's probabilistic logic by incorporating conditional probabilities. Unlike many other approaches to deduction in probabilistic logic, this approach is based on inference rules and therefore can produce proofs to explain how conclusions are drawn. We show how these rules can be incorporated into an anytime deduction procedure that proceeds by computing increasingly narrow probability intervals that contain the tightest entailed probability interval. Since the procedure can be stopped at any time to yield partial information concerning the probability range of any entailed sentence, one can make a tradeoff between precision and computation time. The deduction method presented here contrasts with other methods whose ability to perform logical reasoning is either limited or requires finding all truth assignments consistent ...

Modern decision support systems require very quick (interactive) responses from the DBMS, but pose complex queries on large volumes of data. In this paper, we present a novel solution to this problem: we precompute concise histogram statistics on the data to answer the queries quickly, but approximately. Our hypothesis is that many decision support applications can tolerate small errors in query results in return for large reductions in response times. In particular, we propose the use of multiple histograms to approximate the data cube and answer aggregate queries approximately using this summarized data. We enhance histograms to estimate the quality of the approximate answers. We primarily explore the interaction among various histograms on the data cube in order to minimize the space needed when an upper bound on the errors is given. Our main contribution in this paper is an efficient technique for selecting a provably near-optimal set of histograms on the data cube. Extensive ex...

The use of data at different levels of information con-tent is essential to the performance of multimedia, scientific, and other large databases because it can significantly decrease I/O and communication costs.

The variety of power domain constructions proposed in the literature is put into a general algebraic framework. Power constructions are considered algebras on a higher level: for every ground domain, there is a power domain whose algebraic structure is specified by means of axioms concerning the algebraic properties of the basic operations empty set, union, singleton, and extension of functions. A host of derived operations is introduced and investigated algebraically. Every power construction is shown to be equipped with a characteristic semiring such that the resulting power domains become semiring modules. Power homomorphisms are introduced as a means to relate different power constructions. They also allow to define the notion of initial and final constructions for a fixed characteristic semiring. Such initial and final constructions are shown to exist for every semiring, and their basic properties are derived. Finally, the known power constructions are put into the general framewo...

We show the equivalence of several different axiomatizations of the notion of (abstract) probabilistic domain in the category of dcpo's and continuous functions. The axiomatization with the richest set of operations provides probabilistic selection among a finite number of possibilities with arbitrary probabilities, whereas the poorest one has binary choice with equal probabilities as the only operation. The remaining theories lie in between; one of them is the theory of binary choice by Graham [1]. 1 Introduction A probabilistic programming language could contain different kinds of language constructs to express probabilistic choice. In a rather poor language, there might be a construct x \Phi y, whose semantics is a choice between the two possibilities x and y with equal probabilities 1=2. The `possibilities' x and y can be statements in an imperative language or expressions in a functional language. A quite rich language could contain a construct [p 1 : x 1 ; : : : ; p n : x n ],...

Lower, upper, sandwich, mixed, and convex power domains are isomorphic to domains of second order predicates mapping predicates on the ground domain to logical values in a semiring. The various power domains differ in the nature of the underlying semiring logic and in logical constraints on the second order predicates.

In a system based on the imprecise-computation technique, each time-critical task is designed in such a way that it can produce a usable, approximate result in time whenever a failure or overload prevents it from producing the desired, precise result. This section describes ways to use this technique together with traditional fault-tolerance methods to reduce the costs of providing fault tolerance andenhancedavailability. Specifically, an imprecise mechanism for the generation and use of approximate results can be integrated in a natural way with traditional checkpointing and replication mechanisms. Algorithms and process structures for this integration and rules for determining when approximate results can be used in place of the desired results are discussed.

One of the approaches for integrating object-oriented programs with databases is to instantiate objects from relational databases by evaluating view queries. In that approach, it is often necessary to evaluate some joins of the query by left outer joins to prevent information loss caused by the tuples discarded by inner joins. It is also necessary to filter some relations with selection conditions to prevent the retrieval of unwanted nulls. The system should automatically prescribe joins as inner or left outer joins and generate the filters, rather than letting them be specified manually for every view definition. We develop such a mechanism in this paper. We first develop a rigorous system model to facilitate the mapping between an object-oriented model and the relational model. The system model provides a well-defined context for developing a simple mechanism. The mechanism requires only one piece of information from users: null options on an object attribute. The semantics of these ...