Knowledge Integration Methods for Probabilistic Knowledge-based Systems

203 Pages·2022·22.474 MB·English

by  Van Tham Nguyen, Ngoc Thanh Nguyen, Trong Hieu Tran

Knowledge Integration
Methods for Probabilistic
Knowledge-Based Systems
Knowledge-based systems and solving knowledge integrating problems have seen a great surge
of research activity in recent years. Knowledge Integration Methods for Probabilistic Knowledge-
Based Systems provides a wide snapshot of building knowledge-based systems, inconsistency
measures, methods for handling consistency, and methods for integrating knowledge bases. The
book also provides the mathematical background to solving problems of restoring consistency
and integrating probabilistic knowledge bases in the integrating process. The research results
presented in the book can be applied in decision support systems, semantic web systems, mul-
timedia information retrieval systems, medical imaging systems, cooperative information sys-
tems, and more. This text will be useful for computer science graduates and PhD students, in
addition to researchers and readers working on knowledge management and ontology interpre-
tation.
Taylor & Francis
Taylor & Francis Group
http://taylorandfrancis.com
Knowledge Integration
Methods for Probabilistic
Knowledge-Based Systems
Van Tham Nguyen
Ngoc Thanh Nguyen
Trong Hieu Tran
First edition published 2023
by CRC Press
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Library of Congress Cataloging-in-Publication Data
Names: Nguyen, Van Tham (Researcher on computational intelligence), author.
| Nguyen, Ngoc Thanh (Computer scientist), author. | Tran, Trong Hieu,
author.
Title: Knowledge integration methods for probabilistic knowledge-based
systems / Van Tham Nguyen, Ngoc Thanh Nguyen, Trong Hieu Tran.
Description: First edition. | Boca Raton : CRC Press, 2023. | Includes
bibliographical references and index. | Identifiers: LCCN 2022028082 | ISBN 9781032232188
(hardback) | ISBN
9781032233888 (paperback) | ISBN 9781003277019 (ebook)
Subjects: LCSH: Expert systems (Computer science) | Probabilistic
databases.
Classification: LCC QA76.76.E95 N4995 2022 | DDC 006.3/3--dc23/eng/20220815
LC record available at https://lccn.loc.gov/2022028082
ISBN: 978-1-032-23218-8 (hbk)
ISBN: 978-1-032-23388-8 (pbk)
ISBN: 978-1-003-27701-9 (ebk)
DOI: 10.1201/9781003277019
Typeset in Latin Modern font
by KnowledgeWorks Global Ltd.
Publisher’s note: This book has been prepared from camera-ready copy provided by the authors.
Contents
Preface ix
Authors xi
Chapter 1(cid:4) Introduction 1
1.1 MOTIVATION 1
1.2 THEOBJECTIVESOFTHISBOOK 5
1.3 THESTRUCTUREOFTHISBOOK 6
Chapter 2(cid:4) Probabilistic knowledge-based systems 8
2.1 KNOWLEDGEBASEREPRESENTATION 8
2.1.1 Knowledge Representation Methods 8
2.1.2 Probabilistic Knowledge Base Representation 10
2.2 TYPESOFKNOWLEDGE-BASEDSYSTEMS 14
2.3 THEKNOWLEDGE-BASEDSYSTEMDEVELOPMENT 16
2.4 COMPONENTSOFAPROBABILISTICKNOWLEDGE-BASED
SYSTEM 17
2.5 COMPARINGPROBABILISTICKNOWLEDGE-BASEDSYSTEM
WITHOTHERSYSTEMS 19
2.6 CONCLUDINGREMARKS 22
Chapter 3(cid:4) Inconsistency measures for probabilistic knowledge bases 23
3.1 OVERVIEWOFINCONSISTENCYMEASURES 23
3.1.1 Distance Functions 23
3.1.2 Development of Inconsistency Measures 24
3.2 REPRESENTING THE INCONSISTENCY OF THE PROBABILISTIC
KNOWLEDGEBASE 27
3.2.1 Basic Notions 27
3.2.2 Characteristic Model 29
3.2.3 Desired Properties of Inconsistency Measures 31
3.3 INCONSISTENCYMEASURESFORPROBABILISTIC
KNOWLEDGEBASES 33
3.3.1 The Basic Inconsistency Measures 33
v
vi (cid:4) Contents
3.3.2 The Norm-based Inconsistency Measures 40
3.3.3 The Unnormalized Inconsistency Measure 45
3.4 ALGORITHMSFORCOMPUTINGTHEINCONSISTENCY
MEASURES 49
3.4.1 The Computational Complexity 49
3.4.2 The General Methods 50
3.4.3 Algorithms 51
3.5 CONCLUDINGREMARKS 57
Chapter 4(cid:4) Methods for restoring consistency in probabilistic knowledge
bases 58
4.1 OVERVIEWOFHANDLINGINCONSISTENCIES 58
4.1.1 The Inconsistency Resolution Problem 58
4.1.2 Methods of Handling Inconsistencies 60
4.2 RESTORINGCONSISTENCYINPROBABILISTICKNOWLEDGE
BASES 63
4.2.1 Basic Notions 63
4.2.2 Desired Properties of Consistency-Restoring Operator 64
4.2.3 A General Model for Restoring Consistency 66
4.3 METHODSFORRESTORINGCONSISTENCY 67
4.3.1 The Norm-based Consistency-restoring Problem 67
4.3.2 The Unnormalized Consistency-Restoring Problem 77
4.4 ALGORITHMSFORRESTORINGCONSISTENCY 84
4.5 CONCLUDINGREMARKS 90
Chapter 5(cid:4) Distance-based methods for integrating probabilistic
knowledge bases 91
5.1 OVERVIEWOFKNOWLEDGEINTEGRATIONMETHODS 91
5.1.1 The Knowledge Integration Problem 91
5.1.2 Methods for Integrating Knowledge Bases 94
5.2 PROBABILISTICKNOWLEDGEINTEGRATION 98
5.2.1 Divergence Functions 98
5.2.2 Distance-based Model for Integrating Probabilistic
Knowledge Bases 102
5.2.3 Desired Properties of Distance-based Probabilistic
Integrating Operator 104
5.2.4 Finding the Satisfying Probability Vector 106
5.3 THEPROBLEMSWITHDISTANCE-BASEDINTEGRATING
PROBABILISTICKNOWLEDGEBASES 110
5.4 DISTANCE-BASEDINTEGRATINGOPERATORS 112
5.4.1 The Class of Probabilistic Integrating Operators Γϑ 112
5.4.2 The Class of Probabilistic Integrating Operators ΓHU 115
Contents (cid:4) vii
5.5 INTEGRATIONALGORITHMS 127
5.5.1 Algorithm for Finding the Satisfying Probability Vector 127
5.5.2 The Distance-based Integration Algorithm 128
5.5.3 The HULL Algorithm 130
5.6 CONCLUDINGREMARKS 131
Chapter 6(cid:4) Value-based method for integrating probabilistic
knowledge bases 132
6.1 VALUE-BASEDPROBABILISTICKNOWLEDGEINTEGRATION 132
6.1.1 Basic Notions 132
6.1.2 Value-based Model for Integrating Probabilistic Knowledge
Bases 136
6.1.3 Desired Properties of Value-based Probabilistic Integrating
Operator 137
6.2 THEPROBABILITYVALUE-BASEDINTEGRATINGOPERATORS 138
6.3 THEPROBABILITYVALUE-BASEDINTEGRATIONALGORITHMS 141
6.3.1 Algorithm for Deducting Probabilistic Constraints 141
6.3.2 Probability Value-based Integration Algorithms 143
6.4 CONCLUDINGREMARKS 146
Chapter 7(cid:4) Experiments and Applications 147
7.1 EXPERIMENT 147
7.1.1 Experimental Purpose and Assumptions 147
7.1.2 Experiment Settings 149
7.1.3 Experimental Implementation 151
7.1.4 Results and Analysis 152
7.2 APPLICATIONS 162
7.2.1 Artificial Intelligence and Machine Learning 162
7.2.1.1 Machine Learning 162
7.2.1.2 Recommendation Systems 164
7.2.1.3 Group Decision-making 165
7.2.2 Knowledge Systems 165
7.2.3 Software Engineering 166
7.2.4 Other Applications 167
Chapter 8(cid:4) Conclusions and open problems 168
8.1 CONCLUSIONS 168
8.2 OPENPROBLEMS 170
Bibliography 171
Index 186
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Preface
Inconsistency of knowledge often takes place when the knowledge is gathered from
various sources. This phenomenon often occurs in social networks and generally in
distributed environments. Resolving knowledge inconsistency and recovering knowl-
edge consistency are a common subject of Knowledge Management and Knowledge
Integration areas. The inconsistency of knowledge may be considered on two levels,
namely syntactic and semantic. At the syntactic level, inconsistency may appear as
the contradiction of logical formulas without interpretation. On the semantic level,
on the other hand, inconsistency appears when referring to the same real world;
these formulas have different logical values. In this sense inconsistency at the seman-
tic level is more general than inconsistency at the syntactic level. The problem of
solving knowledge inconsistency is very important because it enables to achieve the
consistency of knowledge bases, which is an essential feature of the bases to func-
tion. There are many models for knowledge consistency recovering presented in the
worldwide literature. In this book we deal with the probabilistic model for this aim.
The need for knowledge inconsistency resolution arises in many practical applica-
tions of computer systems. This book provides a wide snapshot of some intelligent
technologies for knowledge inconsistency resolution based on probabilistic approach.
It completes the newest research results of the authors in the period of the last five
years. For practical requirements: the research results of this research can be widely
applied in decision support systems, automated e-commerce systems, semantic web
systems, as well as expert systems to enhance the accuracy of disease diagnostic sys-
tems;weatherforecastingsystemsandeconomicforecasts;systemstocombatclimate
change and prevent natural disasters and epidemics; and other fields. These systems
serve many aspects of social life as well as national security The authors hope that
the book can be useful for graduate and Ph.D. students in Computer Science; partic-
ipants of courses: knowledge engineering and collective intelligence; researchers and
all readers working on knowledge management and ontology integration; and special-
ists of social media. For related fields of science and technology: The results of this
research should provide theoretical models, evaluation results on the rationality, and
computational complexity for the community to do research and development. We
wish to express great gratitude to the reviewers for their valuable comments. Special
thanks go to Randi Cohel from the Publisher for Computer Science and IT at Taylor
and Francis Group for her kind contacts and advices in preparing this book.
Van Tham Nguyen, Ngoc Thanh Nguyen and Trong Hieu Tran
ix