We characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe. We also show that even without the ordering one application of fixed point suffices to express any query expressible with several alternations of fixed point and negation. This proves that the fixed point query hierarchy suggested by Chandra and Harel collapses at the first fixed point level. It is also a general result showing that in finite model theory one application of fixed point suffices. Introduction and Summary Query languages for relational databases have received considerable attention. In 1972 Codd showed that two natural languages for queries -- one algebraic and the other a version of first order predicate calculus -- have identical powers of expressibility, [Cod72]. Query languages which are as expressive as Codd's Relational Calculus are sometimes called complete. This term is misleading however becau...

Nowadays computer science is surpassing mathematics as the primary field of logic applications, but logic is not tuned properly to the new role. In particular, classical logic is preoccupied mostly with infinite static structures whereas many objects of interest in computer science are dynamic objects with bounded resources. This chapter consists of two independent parts. The first part is devoted to finite model theory; it is mostly a survey of logics tailored for computational complexity. The second part is devoted to dynamic structures with bounded resources. In particular, we use dynamic structures with bounded resources to model Pascal.

The purpose of this paper is to show that logic provides a convenient formalism for studying classical database problems. There are two main parts to the paper, devoted respectively to conventional databases and deductive databases. In the first part, we focus on query languages, integrity modeling and maintenance, query optimization, and data

. We propose a new approach to temporal extensions of SQL. Unlike the current proposals, e.g., SQL/Temporal, we use point-based references to time as the basis of our approach. The proposed language--- SQL/TP---extends the syntax and semantics of SQL/92 in a very natural way: by adding a single data type to represent a linearly ordered universe of individual time instants. Such an extension allows the users to write temporal queries in customary fashion and vastly simplifies the semantics of the proposed language: we merely use the familiar SQL semantics. In this way SQL/TP also fixes many problems present in the semantics of the temporal query languages based on explicit interval-valued temporal attributes. In addition, we propose an efficient query evaluation procedure over a compact interval-based encoding of temporal relations. The algorithm is based on a sophisticated compilation technique that translates SQL/TP queries to SQL/92. In this way existing database systems can be used...

this paper,

We investigate the expressive power of the typed -calculus when expressing computations over finite structures, i.e., databases. We show that the simply typed -calculus can express various database query languages such as the relational algebra, fixpoint logic, and the complex object algebra. In our embeddings, inputs and outputs are -terms encoding databases, and a program expressing a query is a -term which types when applied to an input and reduces to an output.

A Functional Database Phil Trinder D.Phil. Thesis Wolfson College Michaelmas Term, 1989 This thesis explores the use of functional languages to implement, manipulate and query databases. Implementing databases. A functional language is used to construct a database manager that allows efficient and concurrent access to shared data. In contrast to the locking mechanism found in conventional databases, the functional database uses data dependency to provide exclusion. Results obtained from a prototype database demonstrate that data dependency permits an unusual degree of concurrency between operations on the data. The prototype database is used to exhibit some problems that seriously restrict concurrency and also to demonstrate the resolution of these problems using a new primitive. The design of a more realistic database is outlined. Some restrictions on the data structures that can be used in a functional database are also uncovered. Manipulating databases. Functions over the database a...

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. This chapter introduces a new approach to temporal extensions of SQL. The main difference from most of the current proposals is the use single time points, rather than intervals or various other complexvalues for references to time, while still achieving efficient query evaluation. The proposed language, SQL/TP, extends the syntax of SQL/92 to handle temporal data in a natural way: it adds a single data type to represent a linearly ordered universe of time instants. The semantics of the new language naturally extends the standard SQL semantics and eliminates or fixes many of the problems connected with defining a precise semantics to temporal query languages based on explicit interval-valued temporal attributes. The efficient query evaluation procedure is based on a compilation technique that translates SQL/TP queries to SQL/92. Therefore existing off-shelf database systems can be used as back-ends for implementations based on this approach to manage temporal data. 1 Why another temp...

During the last years our research efforts were inspired by two different needs. On one side the number of non-expert users accessing databases is largely growing. On the other side, information systems will be no longer composed by a single centralised architecture, but rather by several heterogeneous component systems. In order to address such needs we have designed a new query system, having both user-oriented and multidatabase features. The system main components are an adaptive visual interface, providing the user with different and interchangeable interaction modalities, and a "translation layer", which creates and offers to the user the illusion of a single homogeneous schema out of several heterogeneous components. Both components are founded on a common ground, i.e. a formally defined and semantically rich data model, the Graph Model, and a minimal set of Graphical Primitives, in terms of which general query operations may be visually expressed. The Graph Model has...