Foundations of Knowledge Systems: with Applications to Databases and Agents

309 Pages·1998·25.67 MB·English

by  Gerd Wagner (auth.)

FOUNDATIONS OF
KNOWLEDGE SYSTEMS:
with Applications to
Databases and Agents
The Kluwer International Series on
ADVANCES IN DATABASE SYSTEMS
Series Editor
Ahmed K. Elmagarmid
Purdue University
West Lafayette, IN 47907
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FOUNDATIONS OF
KNOWLEDGE SYSTEMS:
with Applications to
Databases and Agents
by
Gerd Wagner
University of Leipzig
GERMANY
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data
A CLP. Catalogue record for this book is available
from the Library of Congress.
ISBN 978-1-4613-7621-7 ISBN 978-1-4615-5723-4 (eBook)
DOI 10.1007/978-1-4615-5723-4
Copyright © 1998 Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 1998
Softcover reprint of the hardcover 1st edition 1998
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system or transmitted in any form or by any means, mechanical, photo
copying, recording, or otherwise, without the prior written permission of the
publisher, Springer Science+Business Media, LLC .
Printed on acid-free paper.
Contents
List ofFigures XIII
list ofTables XV
Preface xvii
Acknowledgments XXI
Introduction xxiii
1.1 The SuccessofDatabase Systems xxiii
1.2 The Difficulties of 'Expert Systems' xxiii
1.3 What is a Knowledge System? XXIV
1.4 Knowledge Systemsand Logic xxv
1.5 About this Book XXVI
Part I Tables and Objects
1. CONCEPTUAL MODELING OF KNOWLEDGE BASES 3
1.1 Introduction 3
1.2 Predicate Logic 4
1.3 Entity-Relationship Modeling 5
1.3.1 Entities and Entity Types 6
1.3.2 Relationships and Relationship Types 8
1.3.3 Application Domain Predicates 10
1.3.4 ER Modeling Is Object-Oriented 11
1.4 Identifying Qualified Predicates 11
1.5 Identifying Incomplete Predicates 11
1.6 Identifying Intensional Predicates 13
1.7 Entity-Relationship Modeling in 7 Steps 13
vi FOUNDATIONS OFKNOWLEDGESYSTEMS
1.8 Agent-Object-Relationship Modeling 15
1.8.1 Interaction Framesand Agent Roles 16
1.8.2 Mental Attributes 17
1.9 SummilFY 17
1.10 Further Reading 17
1.11 Exercises 17
2. RELATIONAL DATABASES 19
2.1 Introduction 20
2.2 Basic Concepts 21
2.2.1 Tables 21
2.2.2 Keys 23
2.2.3 Table Schema. Table Type and Table Instance 23
2.2.4 DatabaseSchema and Database State 25
2.2.5 A Database as a Set ofSentences 27
2.3 Query Answering 27
2.3.1 Logical Formulas 27
2.3.2 Database Queries as Logical Formulas 28
2.4 Conjunctive Queries 30
2.4.1 Inference-Based AnsweringofConjunctiveQueries 31
2.4.2 Compositional Evaluation ofConjunctive Queries 31
2.4.3 Correctness and Completeness ofthe Answer Operation 34
2.4.4 Conjunctive Queries and SQL 35
2.5 General Queries 36
2.5.1 Not All Queries Can Be Answered Sensibly 37
2.5.2 Compositional Evaluation ofOpen Queries 40
2.5.3 Correctnessand Completeness ofthe AnswerOperation 41
2.5.4 The Database Completeness Assumption 42
2.5.5 Relational Database Queries Cannot ExpressTransitive Closure 43
2.5.6 Views 44
2.6 Integrity Constraints 44
2.6.1 Functional Dependencies 45
2.6.2 Inclusion Dependencies 45
2.6.3 Integrity Constraintsin SQL 46
2.7 Transforming an ER Model into a Relational Database Schema 47
2.8 Information Order and Relative Information Distance 48
2.9 Updating Relational Databases 49
2.9.1 Insertion 50
2.9.2 Deletion 50
2.9.3 Non-Literal Inputs 50
2.9.4 On the Semantics of Updates 51
2.9.5 Updates in the PresenceofIntegrity Constraints 53
2.10 Incomplete Information in Relational Databases 55
Contents vii
2.10.1 The Null Value UNKNOWN 56
2.10.2 The Null Value INAPPLICABLE 59
2.10.3 Null Values in SQL 59
2.11 ARelational Databasewithout Nulls Represents a Herbrand Interpretation 59
2.11.1 The Language Lr. 59
2.11.2 The Interpretation It!. 60
2.12 Reiter's Database Completion Theory 61
2.13 Database Inference as Preferential Entailment Based on Minimal Models 62
2.14 Deficiencies ofthe Relational Database Model 63
2.14.1 General Purpose Extensions 64
2.14.2 Special Purpose Extensions 65
2.15 Summary 66
2.16 Further Reading 67
2.17 Exercises 67
2.17.1 AFurther Example: The Library Database 67
2.17.2 Database Completion 68
2.17.3 Miscellaneous 69
3. OBJECT-RELATIONAL DATABASES 71
3.1 ADT-Relational Databases 73
3.1.1 Complex Values and Types 73
3.1.2 ADT Tables 75
3.1.3 ADT Terms and Formulas 75
3.1.4 ADT Queries Can ExpressTransitive Closure 77
3.2 Introducing Objects and Classes 77
3.2.1 Classesas Object Tables 77
3.2.2 Object-Relational Databases 80
3.3 Further Reading 82
3.4 Exercises 82
Part II Adding Rules
4. REACTION RULES 87
4.1 Introduction 88
4.1.1 Production Rules 88
4.1.2 DatabaseTriggers 89
4.1.3 AGENT-O Commitment Rules 90
4.2 Communication Events 91
4.3 Epistemic ar.d Communicative Reactions 93
4.3.1 TELL 94
4.3.2 ASK-IF 95
4.3.3 REPLY-IF 96
viii FOUNDATIONS OFKNOWLEDGESYSTEMS
4.4 Operational Semanticsof Reaction Rules 96
4.5 Multidatabases 97
4.6 Summary 100
4.7 Further Reading 100
4.8 Exercises 100
5. DEDUCTION RULES 103
5.1 Introduction 103
5.1.1 Datalog Rules 106
5.1.2 Normal Deduction Rules 107
5.1.3 Semantics 108
5.2 Closure Semantics 109
5.2.1 Datalog Rules III
5.2.2 Stratified Deductive Databases 112
5.2.3 Normal Deduction Rules - The General Case 114
5.3 Model-Theoretic Semantics 119
5.3.1 Datalog Rules 119
5.3.2 Normal Deduction Rules- The General Case 120
5.4 Summary 121
5.5 Further Reading 121
5.6 Exercises 122
Part III Positive Knowledge Systems: Concepts, Properties and Examples
6. PRINCIPLES OF POSITIVE KNOWLEDGE SYSTEMS 127
6.1 Introduction 127
6.2 Basic Concepts 128
6.3 Formal PropertiesofKnowledge Systems 132
6.4 Vivid Knowledge Systems 135
6.5 Knowledge Update and Knowledge Integration 135
6.6 Summary 136
7. TEMPORAL DATABASES 139
7.1 Introduction 139
7.2 The Timestamp Algebra 140
7.3 Temporal Tables 141
7.4 Natural Inference in Temporal Databases 142
7.5 Updatesand Information Order 143
7.6 Indexical Temporal Null Values 143
7.7 Temporal Table Operations 145
Contents ix
7.7.1 Correctnessand Completeness 146
7.7.2 Four Kinds ofQueries 147
7.8 Temporal Deduction Rules 147
7.9 Bitemporal Databases 148
7.10 Further Reading 148
7.11 Summary 148
7.12 Exercises 149
8. FUZZY DATABASES 151
8.1 Introduction 151
8.1.1 Disjunctive Imprecision 152
8.1.2 Vagueness 153
8.1.3 Gradual Uncertainty 153
8.2 Certainty Scales 153
8.3 Fuzzy Tables 154
8.4 Natural Inference in Fuzzy Databases 155
8.5 Update, Knowledge Integration and Information Order 156
8.6 Fuzzy Table Operations 157
8.6.1 Correctnessand Completeness 159
8.6.2 Four KindsofQueries 159
8.7 Fuzzy Deduction Rules 159
8.8 Further Reading 161
8.9 Summary 161
8.10 Exercises 161
9. FURTHER EXAMPLES OF POSITIVE KNOWLEDGE SYSTEMS 165
9.1 Multi-level Secure Databases 165
9.2 lineage Databases 169
9.3 Disjunctive Databases 171
9.4 S5-Epistemic Databases 173
9.4.1 S5-Epistemic Deduction Rules 174
9.5 Summary 175
Part IV Admitting Negative Information: From Tablesto Bitables
10. PRINCIPLES OF NON-POSITIVE KNOWLEDGE SYSTEMS 179
10.1 Introduction 179
10.2 Basic Concepts 180
10.2.1 Consistency 181
10.2.2 Vivid Knowledge Systems 183
x FOUNDATIONSOFKNOWLEDGESYSTEMS
10.3 Standard Logics as Knowledge Systems 183
11. RELATIONAL FACTBASES 187
11.1 Introduction 187
11.2 Birelational Databases 188
11.2.1 ShortcomingsofBirelational Databases 190
11.3 Relational Factbases 191
11.3.1 Reaction Rules for the Caseof Unknown Information 194
11.3.2 Heuristic Deduction and Default Rules 194
12. POSSIBILISTIC DATABASES 195
12.1 Introduction 195
12.2 Possibilistic Tables 196
12.3 Natural Inference in Possibilistic Databases 197
12.4 Updatesand Information Order 199
12.5 Knowledge Integration 200
12.6 Possibilistic Deductive Databases 200
12.7 Possibilistic Deduction Rules and EMYCIN 202
13. FURTHER EXAMPLES OF NON-POSITIVE KNOWLEDGE SYSTEMS 205
13.1 Multi-Level Secure Factbases 205
13.2 Lineage Factbases 207
13.3 Disjunctive Factbases 209
13.3.1 Total Predicatesand the Closed-World Assumption 211
13.3.2 Reasoning with Three Kindsof Predicates 212
13.3.3 Deduction Rules in Disjunctive Factbases 214
PartV More on Reaction and Deduction Rules
14. COMMUNICATION AND COOPERATION 219
14.1 Multi-Knowledge Bases 219
14.1.1 Operational Semantics of Reaction Rules 220
14.1.2 Reactive Knowledge Bases as Transition Systems 221
14.1.3 Assertional Reasoning 223
14.2 Distributed Updating and Query Answering 224
14.2.1 Distributed QueryAnswering 225
14.2.2 Distributed Updating 227
14.2.3 Distributed Updating Using Replication 227
14.2.4 Correctness 228
14.3 Cooperative Knowledge Bases 229
14.3.1 The Contract Net Protocol for Cooperative Query Answering 229
14.3.2 Running the CNP 232