Efficient recursive aggregation and negation in deductive databases

We present an efficient evaluation technique for modularly stratified deductive database programs for which the local strata level mappings are known at compile time. We present an important subclass of these programs (called EMS-programs) in which one can easily express problems, such as shortest distance, company ownership, bill of materials, and preferential vote counting. Programs written in this style have an easy-to-understand semantics and can be efficiently computed. Another important virtue of these programs is that their modular-stratification properties are independent of the extensional database     

Chain-split evaluation in deductive databases

Many popularly studied recursions in deductive databases can be compiled into one or a set of highly regular chain generating paths, each of which consists of one or a set of connected predicates. Previous studies on chain-based query evaluation in deductive databases take a chain generating path as an inseparable unit in the evaluation. However, some recursions, especially many functional recursions whose compiled chain consists of infinitely evaluable function(s), should be evaluated by chain-split evaluation, which splits a chain generating path into two portions in the evaluation: an immediately evaluable portion and a delayed-evaluation portion. The necessity of chain-split evaluation is examined from the points of view of both efficiency and finite evaluation, and three chain-split evaluation techniques: magic sets, buffered evaluation, and partial evaluation are developed. Our study shows that chain-split evaluation is a primitive recursive query evaluation technique for different kinds of recursions, and it can be implemented efficiently in deductive databases by extensions to the existing recursive query evaluation methods     

Constraint-based query evaluation in deductive databases

Constraints play an important role in the efficient query evaluation in deductive databases. Constraint-based query evaluation in deductive databases is investigated, with emphasis on linear recursions with function symbols. Constraints are grouped into three classes: rule constraints, integrity constraints, and query constraints. Techniques are developed for the maximal use of different kinds of constraints in rule compilation and query evaluation. The study on the roles of different classes of constraints in set-oriented evaluation of linear recursions shows the following: rule constraints should be integrated with their corresponding deduction rules in the compilation of recursions; integrity constraints, including finiteness constraints and monotonicity constraints, should be used in the analysis of finite evaluability and termination for specific queries; and query constraints, which are often useful in search space reduction and termination, should be transformed, when necessary, and should be pushed into the compiled chains as deeply as possible for efficient evaluation. The constraint-based query-processing technique integrates query-independent compilation and chain-based query evaluation methods and demonstrates its great promise in deductive query evaluation     

Partial evaluation of queries in deductive databases

This paper presents some applications of partial evaluation method to a query optimization in deductive database. A Horn clause transformation is used for the partial evaluation of a query in an intensional database, and its application to multiple query processing is discussed. Three strategies are presented for the compatible case, ordered case and crossed case. In each case, partial evaluation is used to preprocess the intensional database in order to obtain subqueries which direct access to an extensional database.     

Perspectives in deductive databases

I discuss my experiences, some of the work that I have done, and related work that influenced me, concerning deductive databases, over the last 30 years. I divide this time period into three roughly equal parts: 1957–1968, 1969–1978, 1979–present. For the first I describe how my interest started in deductive databases in 1957, at a time when the field of databases did not even exist. I describe work in the beginning years, leading to the start of deductive databases about 1968 with the work of Cordell Green and Bertram Raphael. The second period saw a great deal of work in theorem providing as well as the introduction of logic programming. The existence and importance of deductive databases as a formal and viable discipline received its impetus at a workshop held in Toulouse, France, in 1977, which culminated in the book Logic and Data Bases. The relationship of deductive databases and logic programming was recognized at that time. During the third period we have seen formal theories of databases come about as an outgrowth of that work, and the recognition that artificial intelligence and deductive databases are closely related, at least through the so-called expert database systems. I expect that the relationships between techniques from formal logic, databases, logic programming, and artificial intelligence will continue to be explored and the field of deductive databases will become a more prominent area of computer science in coming years.     

Inductive learning in deductive databases

Most current applications of inductive learning in databases take place in the context of a single extensional relation. The authors place inductive learning in the context of a set of relations defined either extensionally or intentionally in the framework of deductive databases. LINUS, an inductive logic programming system that induces virtual relations from example positive and negative tuples and already defined relations in a deductive database, is presented. Based on the idea of transforming the problem of learning relations to attribute-value form, several attribute-value learning systems are incorporated. As the latter handle noisy data successfully, LINUS is able to learn relations from real-life noisy databases. The use of LINUS for learning virtual relations is illustrated, and a study of its performance on noisy data is presented     

Preference queries in deductive databases

Traditional database query languages such as datalog and SQL allow the user to specify only mandatory requirements on the data to be retrieved from a database. In many applications, it may be natural to express not only mandatory requirements but also preferences on the data to be retrieved. Lacroix and Lavency¹⁰⁾ extended SQL with a notion of preference and showed how the resulting query language could still be translated into the domain relational calculus. We explore the use of preference in databases in the setting of datalog. We introduce the formalism of preference datalog programs (PDPs) as preference logic programs without uninterpreted function symbols for this purpose. PDPs extend datalog not only with constructs to specify which predicate is to be optimized and the criterion for optimization but also with constructs to specify which predicate to be relaxed and the criterion to be used for relaxation. We can show that all of the soft requirements in Reference¹⁰) can be directly encoded in PDP. We first develop anaively-pruned bottom-up evaluation procedure that is sound and complete for computing answers to normal and relaxation queries when the PDPs are stratified, we then show how the evaluation scheme can be extended to the case when the programs are not necessarily stratified, and finally we develop an extension of themagic templates method for datalog¹⁴) that constructs an equivalent but more efficient program for bottom-up evaluation. Kannan Govindarajan, Ph.D.: He obtained his bachelors degree in Computer Science and Engineering from the Indian Institute of Technology, Madras, and he completed his Ph.D. degree in Computer Science from the State University of New York at Buffalo. His dissertation research was on optimization and relaxation techniques for logic languages. His interests lie in the areas of programming languages, databases, and distributed systems. He currently leads the trading community effort in the E-speak Operation in Hewlett Packard Company. Prior to that, he was a member of the Java Products Group in Oracle Corporation. Bharat Jayaraman, Ph.D.: He is a Professor in the Department of Computer Science at the State University of New York at Buffalo. He obtained his bachelors degree in Electronics from the Indian Institute of Technology, Madras (1975), and his Ph.D. from the University of Utah (1981). His research interests are in programming languages and declarative modeling of complex systems. Dr. Jayaraman has published over 50 papers in refereed conferences and journals. He has served on the program committees of several conferences in the area of programming languages, and he is presently on the Editorial Board of the Journal of Functional and Logic Programming. Surya Mantha, Ph.D.: He is a manager in the Communications and Software Services Group of Pittiglio Rabin Todd & McGrath (PRTM), a management consulting firm serving high technology industries. He obtained a bachelors degree in Computer Science and Engineering from the Indian Institute of Technology, Kanpur, an MBA in Finance and Competitive Strategy from the University of Rochester, and a Ph.D. in Computer Science from the University of Utah (1991). His research interests are in the modeling of complex business processes, inter-enterprise application integration, and business strategy. Dr. Mantha has two US patents, and has published over 10 research papers. Prior to joining PRTM, he was a researcher and manager in the Architecture and Document Services Technology Center at Xerox Corporation in Rochester, New York.     

Foundations of secure deductive databases

We develop a formal logical foundation for secure deductive databases. This logical foundation is based on an extended logic involving several modal operators. We develop two models of interaction between the user and the database called “yes-no” dialogs, and “yes-no-don't know” dialogs. Both dialog frameworks allow the database to lie to the user. We develop an algorithm for answering queries using yes-no dialogs and prove that secure query processing using yes-no dialogs is NP-complete. Consequently, the degree of computational intractability of query processing with yes-no dialogs is no worse than for ordinary databases. Furthermore, the algorithm is maximally cooperative to user in the sense that lying is resorted to only when absolutely necessary. For Horn databases, we show that secure query processing can be achieved in linear time-hence, this is no more intractable than the situation in ordinary databases. Finally, we identify necessary and sufficient conditions for the database to be able to preserve security. Similar results are also obtained for yes-no-don't know dialogs     

Inference by generating in deductive databases

A method, APEX, for query evaluation in deductive databases presented in this work is based on discovering of axioms and facts relevant to a given query. The notion of relevancy and migration of facts is derived from an analysis of data flow in the system. APEX is complete, and incorporates efficient query evaluation heuristics. Operation of APEX is illustrated by sample databases involving non-linear recursive axioms and cyclic relations. Main virtues of the method are its generality and adaptivity: it imposes no restrictions on the structure of axioms or the contents of relations, and it employs the knowledge of the actual data acquired at each step of a query evaluation.     

Transactions and updates in deductive databases

In this paper, we develop a new approach that provides a smooth integration of extensional updates and declarative query languages for deductive databases. The approach is based on a declarative specification of updates in rule bodies. Updates are not executed as soon as evaluated. Instead, they are collected and then applied to the database when the query evaluation is completed. We call this approach nonimmediate update semantics. We provide a top-down and equivalent bottom-up semantics which reflect the corresponding computation models. We also package set of updates into transactions and we provide a formal semantics for transactions. Then, in order to handle complex transactions, we extend the transaction language with control constructors still preserving formal semantics and semantics equivalence     

Fast query processing in deductive databases

A special-purpose algorithm, that analyzes the structure of a recursion and exploits its properties in query processing in a deductive database is presented. This method is applied to linear rules, a large and common class of recursion. The structural approach to rule processing (SARP) prototype system that implements the algorithm is described     

Programming with non-determinism in deductive databases

While non-determinism has long been established as a key concept in logic pro-gramming, its importance in the context of deductive databases was recognized only recently. This paper provides an overview of recent results on this topic with the aim of providing an introduction to the theory and practice of non-determinism in deductive databases. In particular we (i) recall the main results linking non-deterministic constructs in database languages to the theory of data complexity and the expressibility hierarchy of query languages; (ii) provide a reasoned introduction to effective programming with non-deterministic constructs; (iii) compare the usage of non-deterministic constructs in languages such as LDL++ to that of traditional logic programming languages; (iv) discuss the link between the semantics of logic programs with non-deterministic constructs and the stable-model semantics of logic programs with negation.     

Query evaluation in recursive databases: bottom-up and top-down reconciled

It is desirable to answer queries posed to deductive databases by computing fixpoints because such computations are directly amenable to set-oriented fact processing. However, the classical fixpoint procedures based on bottom-up processing — the naive and semi-naive methods — are rather primitive and often inefficient. In this article, we rely on bottom-up meta-interpretation for formalizing a new fixpoint procedure that performs a different kind of reasoning: We specify a top-down query answering method, which we call the Backward Fixpoint Procedure. Then, we reconsider query evaluation methods for recursive databases. First, we show that the methods based on rewriting on the one hand, and the methods based on resolution on the other hand, implement the Backward Fixpoint Procedure. Second, we interpret the rewritings of the Alexander and Magic Set methods as specializations of the Backward Fixpoint Procedure. Finally, we argue that such a rewriting is also needed in a database context for implementing efficiently the resolution-based methods. Thus, the methods based on rewriting and the methods based on resolution implement the same top-down evaluation of the original database rules by means of auxiliary rules processed bottom-up.     

Answering atomic queries in indefinite deductive databases

Answering queries in indefinite systems is a difficult problem both computationally, since it involves non-Horn clauses and factoring, and conceptually, concerning producing beliefs for formulas not derivable from the system. to provide a basis for reasonable beliefs, we propose new criteria as an alternative to the Full Information Principle. Then an approach to producing stable beliefs, called Plausible World Assumption (PWA), is introduced. It is shown how a set of non-Horn clauses can be transformed into a set of so called singleton-head-rules such that evaluation of a given query is reduced to processing of a set of Horn clauses relevant to the query. Finally, algorithms are presented for computing facts and beliefs for atomic queries in accord with the PWA. This method is shown to be more efficient than the known techniques for query evaluation in indefinite systems.     

Fixpoint iteration with subsumption in deductive databases

Declarative languages for deductive and object-oriented databases require some high-level mechanism for specifying semantic control knowledge. This paper proposes user-supplied subsumption information as a paradigm to specify desired, prefered or useful deductions at the meta level. For this purpose we augment logic programming by subsumption relations and succeed to extend the classical theorems for least models, fixpoints and bottom-up evaluation accordingly. Moreover, we provide a differential fixpoint operator for efficient query evaluation in deductive databases. This operator discards subsumed tuples on the fly. We also exemplify the ease of use of this programming methodology. In particular, we demonstrate how heuristic AI search procedures can be integrated into deductive databases in this way.This article is a revised and extended version of (Köstler et al., 1993)     

Efficient processing of integrity constraints in deductive databases

One major operation in a deductive database is to verify the contents of the database with integrity constraints whenever the database is changed. The number of facts and integrity constraints in a deductive database often makes the validation process the bottleneck of the system. In this paper, we describe a set of approaches to process integrity constraints efficiently on sequential computers and on massively parallel computers.     

Data mining in deductive databases using query flocks

Data mining can be defined as a process for finding trends and patterns in large data. An important technique for extracting useful information, such as regularities, from usually historical data, is called as association rule mining. Most research on data mining is concentrated on traditional relational data model. On the other hand, the query flocks technique, which extends the concept of association rule mining with a ‘generate-and-test’ model for different kind of patterns, can also be applied to deductive databases. In this paper, query flocks technique is extended with view definitions including recursive views. Although in our system query flock technique can be applied to a data base schema including both the intensional data base (IDB) or rules and the extensible data base (EDB) or tabled relations, we have designed an architecture to compile query flocks from datalog into SQL in order to be able to use commercially available data base management systems (DBMS) as an underlying engine of our system. However, since recursive datalog views (IDB's) cannot be converted directly into SQL statements, they are materialized before the final compilation operation. On this architecture, optimizations suitable for the extended query flocks are also introduced. Using the prototype system, which is developed on a commercial database environment, advantages of the new architecture together with the optimizations, are also presented.     

Update operations in deductive databases with functional dependencies

We study the problem of updating intensional relations in the framework of deductive databases on which integrity constraints (specifically functional dependencies) are defined. First, a formalization of a model-theoretic semantics of updates is provided: the notions ofrepresentability, consistency anddeterminism are introduced to characterize the various cases. Then, a proof-theoretic approach, based on a variant of resolution integrated with the chase procedure, is defined, showing that the method exactly captures the above notions. It turns out that using functional dependencies it is possible to resolve potential ambiguities in several practical cases. Also, precomputations can be performed at definition time to execute update requests more efficiently.Work partially supported by Consiglio Nazionale delle Ricerche, within Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo, LRC Logidata+, and by System & Management S.p.A.A preliminary version of this paper appeared in [33].