Foundations of Disjunctive Logic Programming

Overview

This monograph provides an intensive course for graduate students in computer science, as well as others interested in extensions of logic programming, on the theoretical foundations of disjunctive logic programming.

Disjunctive logic programming permits the description of indefinite or incomplete information through a disjunction of atoms in the head of a clause. The authors describe model theoretic semantics, proof theoretic semantics, and fix point semantics for disjunctive ...

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Overview

This monograph provides an intensive course for graduate students in computer science, as well as others interested in extensions of logic programming, on the theoretical foundations of disjunctive logic programming.

Disjunctive logic programming permits the description of indefinite or incomplete information through a disjunction of atoms in the head of a clause. The authors describe model theoretic semantics, proof theoretic semantics, and fix point semantics for disjunctive and normal disjunctive programs (a normal disjunctive program permits negated atoms in the body of a clause) and present theories of negation. They conclude with selected applications to knowledge databases.

Jorge Lobo is Assistant Professor in Computer Science at the University of Illinois, Chicago Circle. Jack Minker is Professor in the Department of Computer Science and Institute for Advanced Computer Studies at the University of Maryland. Arcot Rajasekar is Assistant Professor in the Computer Science Department at the University of Kentucky.

Contents: Introduction and Background. Definitions and Terminology. Declarative Semantics. Proof Theory. Negation. Weak Negation. Normal Logic Programs. Procedural Semantics: Normal Programs. Disjunctive Databases. Applications.

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Editorial Reviews

Booknews
A monograph providing an intensive course for graduate students in computer science, as well as for other interested in extensions of logic programming, on the theoretical foundations of disjunctive logic programming. Assumes a background in elementary mathematical logic and a basic course in logic programming. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780262121651
  • Publisher: MIT Press
  • Publication date: 4/17/1992
  • Series: Logic Programming Series
  • Pages: 332
  • Product dimensions: 7.04 (w) x 9.26 (h) x 1.01 (d)

Table of Contents

List of Figures
List of Tables
Series Foreword
Preface
1 Introduction and Background 1
1.1 Motivation 1
1.2 Historical background 11
2 Definitions and Terminology 25
2.1 First order theory--syntax 25
2.2 First order theory--semantics 28
2.3 Logic programs--syntax 32
2.4 Logic programs--semantics: models and interpretations 35
2.5 Substitutions and unifiers 42
2.6 Fixpoint Theory 48
3 Declarative Semantics 55
3.1 Logical consequences 55
3.2 Model theory 57
3.3 Fixpoint theory 61
3.4 Comparison of definite and disjunctive logic programs 65
4 Proof Theory 71
4.1 Query type and correct answers 71
4.2 SLI resolution and SLD resolution 72
4.3 Soundness of SLI resolution 84
4.4 Completeness of SLI resolution 88
4.5 Computation rule 91
4.6 Comparison of SLD and SLI resolution 96
5 Negation 105
5.1 Generalized closed world assumption 106
5.2 Procedural interpretation for the GCWA 113
5.3 Non-Herbrand models and the GCWA 127
5.4 Constructive answers 129
6 Weak Negation 141
6.1 Weak generalized closed world assumption 141
6.2 Finite failure semantics 145
6.3 Fixpoint Characterization 147
6.4 Completion theory 152
6.5 Procedural interpretation 157
7 Normal Logic Programs 163
7.1 Normal disjunctive logic programs 163
7.2 The generalized disjunctive well-founded semantics 167
7.3 Stationary semantics 176
7.4 Comparison of semantics 181
7.5 Normal logic programs 182
8 Proof Theory: Normal Programs 195
8.1 Introduction 195
8.2 SLIS resolution 197
8.3 Soundness of SLIS resolution 203
8.4 Completeness of SLIS resolution 207
9 Disjunctive Deductive Databases 217
9.1 Disjunctive deductive databases 217
9.2 Queries and answers 219
9.3 Incremental evaluation of hierarchical DDDB's 224
9.4 Model trees: a data structure for sets of minimal models 227
9.5 Incremental computation on model trees 229
9.6 Computing answers on trees 234
9.7 Meaningless models and denials 240
9.8 Background 242
10 Applications 245
10.1 View updates 245
10.2 Combining deductive databases 263
Bibliography 275
Index 291
Author Index 305
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