Datalog

About: Datalog is a research topic. Over the lifetime, 2388 publications have been published within this topic receiving 66183 citations.

Foundations of databases

Abstract: A. ANTECHAMBER. Database Systems. The Main Principles. Functionalities. Complexity and Diversity. Past and Future. Ties with This Book. Bibliographic Notes. Theoretical Background. Some Basics. Languages, Computability, and Complexity. Basics from Logic. The Relational Model. The Structure of the Relational Model. Named versus Unnamed Perspectives. Notation. Bibliographic Notes. B. BASICS: RELATIONAL QUERY LANGUAGES. Conjunctive Queries. Getting Started. Logic-Based Perspectives. Query Composition and Views. Algebraic Perspectives. Adding Union. Bibliographic Notes. Exercises. Adding Negation: Algebra and Calculus. The Relational Algebras. Nonrecursive Datalog with Negation. The Relational Calculus. Syntactic Restrictions for Domain Independence. Aggregate Functions. Digression: Finite Representations of Infinite Databases. Bibliographic Notes. Exercises. Static Analysis and Optimization. Issues in Practical Query Optimization. Global Optimization. Static Analysis of the Relational Calculus. Computers with Acyclic Joins. Bibliographic Notes. Exercises. Notes on Practical Languages. SQL: The Structured Query Language. Query-by-Example and Microsoft Access. Confronting the Real World. Bibliographic Notes. Exercises. C. CONSTRAINTS. Functional and Join Dependency. Motivation. Functional and Key Dependencies. join and Multivalued Dependencies. The Chase. Bibliographic Notes. Exercises. Inclusion Dependency. Inclusion Dependency in Isolation. Finite versus Infinite Implication. Nonaxiomatizability of fd's + ind's. Restricted Kinds of Inclusion Dependency. Bibliographic Notes. Exercises. A Larger Perspective. A Unifying Framework. The Chase revisited. Axiomatization. An Algebraic Perspective. Bibliographic Notes. Exercises. Design and Dependencies. Semantic Data Models. Normal Forms. Universal Relation Assumption. Bibliographic Notes. Exercises. D. DATALOG AND RECURSION. Datalog. Syntax of Datalog. Model-Theoretic Semantics. Fixpoint Semantics. Proof-Theoretic Approach. Static Program Analysis. Bibliographic Notes. Exercises. Evaluation of Datalog. Seminaive Evaluation. Top-Down Techniques. Magic. Two Improvements. Bibliographic Notes. Exercises. Recursion and Negation. Algebra + While. Calculus + Fixpoint. Datalog with Negation. Equivalence. Recursion in Practical Language. Bibliographic Notes. Exercises. Negation in Datalog. The Basic Problem. Stratified Semantics. Well-Founded Semantics. Expressive Power. Negation as Failure of Brief. Bibliographic Notes. Exercises. E. EXPRESSIVENESS AND COMPLEXITY. Sizing up Languages. Queries. Complexity of Queries. Languages and Complexity. Bibliographic Notes. Exercises. First Order, Fixpoint and While. Complexity of First-Order Queries. Expressiveness of First-Order Queries. Fixpoint and While Queries. The Impact of Order. Bibliographic Notes. Exercises. Highly Expressive Languages. While(N)-while with Arithmetic. While(new)-while with New Values. While(uty)-An Untyped Extension of while. Bibliographic Notes. Exercises. F. FINALE. Incomplete Information. Warm-Up. Weak Representation Systems. Conditional Tables. The Complexity of Nulls. Other Approaches. Bibliographic Notes. Exercises. Complex Values. Complex Value Databases. The Algebra. The Caculas. Examples. Equivalence Theorems. Fixpoint and Deduction. Expressive Power and Complexity. A Practicle Query Language for Complex Values. Bibliographic Notes. Exercises. Object Databases. Informal Presentation. Formal Definition of an OODB Model. Languages for OODB Queries. Languages for Methods. Further Issues for OODB's. Bibliographic Notes. Exercises. Dynamic Aspects. Updated Languages. Transactional Schemas. Updating Views and Deductive Databases. Active Databases. Temporal Databases and Constraints. Bibliographic Notes. Exercises. Bibliography. Symbol Index. Index. 0201537710T04062001

The DLV system for knowledge representation and reasoning

Abstract: Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows one to express every property of finite structures that is decidable in the complexity class ΣP2 (NPNP). Thus, under widely believed assumptions, DLP is strictly more expressive than normal (disjunction-free) logic programming, whose expressiveness is limited to properties decidable in NP. Importantly, apart from enlarging the class of applications which can be encoded in the language, disjunction often allows for representing problems of lower complexity in a simpler and more natural fashion.This article presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to ΔP3-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of DLV, and by deriving new complexity results we chart a complete picture of the complexity of this language and important fragments thereof.Furthermore, we illustrate the general architecture of the DLV system, which has been influenced by these results. As for applications, we overview application front-ends which have been developed on top of DLV to solve specific knowledge representation tasks, and we briefly describe the main international projects investigating the potential of the system for industrial exploitation. Finally, we report about thorough experimentation and benchmarking, which has been carried out to assess the efficiency of the system. The experimental results confirm the solidity of DLV and highlight its potential for emerging application areas like knowledge management and information integration.

The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory

Abstract: This paper starts with the project of finding a large subclass of NP which exhibits a dichotomy. The approach is to find this subclass via syntactic prescriptions. While the paper does not achieve this goal, it does isolate a class (of problems specified by) "monotone monadic SNP without inequality" which may exhibit this dichotomy. We justify the placing of all these restrictions by showing, essentially using Ladner's theorem, that classes obtained by using only two of the above three restrictions do not show this dichotomy. We then explore the structure of this class. We show that all problems in this class reduce to the seemingly simpler class CSP. We divide CSP into subclasses and try to unify the collection of all known polytime algorithms for CSP problems and extract properties that make CSP problems NP-hard. This is where the second part of the title, "a study through Datalog and group theory," comes in. We present conjectures about this class which would end in showing the dichotomy.

Analysis of recursive game graphs using data flow equations

Abstract: Given a finite-state abstraction of a sequential program with potentially recursive procedures and input from the environment, we wish to check statically whether there are input sequences that can drive the system into bad/good executions. Pushdown games have been used in recent years for such analyses and there is by now a very rich literature on the subject. (See, e.g., [BS92,Tho95,Wal96,BEM97,Cac02a,CDT02].) In this paper we use recursive game graphs to model such interprocedural control flow in an open system. These models are intimately related to pushdown systems and pushdown games , but more directly capture the control flow graphs of recursive programs ([AEY01,BGR01,ATM03b]). We describe alternative algorithms for the well-studied problems of determining both reachability and Buchi winning strategies in such games. Our algorithms are based on solutions to second-order data flow equations, generalizing the Datalog rules used in [AEY01] for analysis of recursive state machines. This offers what we feel is a conceptually simpler view of these well-studied problems and provides another example of the close links between the techniques used in program analysis and those of model checking. There are also some technical advantages to the equational approach. Like the approach of Cachat [Cac02a], our solution avoids the necessarily exponential-space blow-up incurred by Walukiewicz's algorithms for pushdown games. However, unlike [Cac02a], our approach does not rely on a representation of the space of winning configurations of a pushdown graph by (alternating) automata. Only minimal sets of exits that can be forced need to be maintained, and this provides the potential for greater space efficiency. In a sense, our algorithms can be viewed as an automaton-free version of the algorithms of [Cac02a].

Information integration using logical views

Abstract: A number of ideas concerning information-integration tools can be thought of as constructing answers to queries using views that represent the capabilities of information sources. We review the formal basis of these techniques, which are closely related to containment algorithms for conjunctive queries and/or Datalog programs. Then we compare the approaches taken by AT&T Labs' “Information Manifold” and the Stanford “Tsimmis” project in these terms.