Conceptual Graphs and Fuzzy Logic: A Fusion for Representing and Reasoning with Linguistic Information / Edition 1

by Tru Hoang Cao

Overview

In this volume, first we formulate a framework of fuzzy types to represent both partial truth and uncertainty about concept and relation types in conceptual graphs. Like fuzzy attribute values, fuzzy types also form a lattice laying a common ground for lattice-based computation of fuzzy granules. Second, for automated reasoning with fuzzy conceptual graphs, we develop foundations of order-sorted fuzzy set logic programming, extending the theory of annotated logic programs of Kifer and Subrahmanian (1992). Third, we show some recent applications of fuzzy conceptual graphs to modelling and computing with generally quantified statements, approximate knowledge retrieval, and natural language query understanding.

Product Details

ISBN-13:	9783642140860
Publisher:	Springer Berlin Heidelberg
Publication date:	07/12/2010
Series:	Studies in Computational Intelligence , #306
Edition description:	2010
Pages:	240
Product dimensions:	6.10(w) x 9.20(h) x 0.60(d)

Table of Contents

1 Introduction 1

1.1 Motivation and Outline 1

1.2 Symbol and Abbreviation Conventions 4

2 Fuzzy Conceptual Graphs 5

2.1 Overview 5

2.2 Conceptual Graphs 6

2.3 Functional Relation Types and Conjunctive Types 11

2.4 Extended Conceptual Graphs 14

2.5 Fuzzy Sets and Fuzzy Logics 18

2.6 Fuzzy Types 26

2.7 Fuzzy Conceptual Graphs 36

2.8 Summary 44

3 Annotated Fuzzy Logic Programming 47

3.1 Overview 47

3.2 AFLP Syntax 49

3.3 AFLP Model-Theoretic Semantics 52

3.4 AFLP Fixpoint Semantics 56

3.5 AFLP Reductants and Constraints 59

3.6 AFLP Procedural Semantics 63

3.7 Order-Sorted AFLPs 66

3.8 Generalized and Specialized AFLPs 71

3.9 Summary 78

4 Fuzzy Conceptual Graph Programming 79

4.1 Overview 79

4.2 FCGP Syntax 80

4.3 FCGP Model-Theoretic Semantics 84

4.4 FCGP Fixpoint Semantics 88

4.5 General Issues of CG Unification and Resolution 91

4.6 FCG Unification and FCGP Reductants 96

4.7 FCGP Procedural Semantics 99

4.8 Summary 103

5 Modelling and Computing with Generally Quantified Statements 105

5.1 Overview 105

5.2 Fuzzy Arithmetic 107

5.3 Fuzzy Conditional Probability 111

5.4 Universally Quantified Conceptual Graphs 112

5.5 Generally Quantified Conceptual Graphs 117

5.6 Computing with Linguistic Quantifiers 120

5.7 Summary 124

6 Approximate Knowledge Retrieval 127

6.1 Overview 127

6.2 Matching Measures for Entity Types, Names, and Attributes 128

6.3 Storing and Querying Knowledge Graphs 134

6.4 Approximate Knowledge Graph Matching 138

6.5 Knowledge Management in VN-KIM 141

6.6 Summary 144

7 Natural Language Query Understanding 145

7.1 Overview 145

7.2 Ontology-Based Information Retrieval 146

7.3 Nested Query Conceptual Graphs 151

7.4 Ontology-Based Query Understanding 154

7.5 Evaluation Experiments 161

7.6 VN-KIM Search 163

7.7 Summary 166

Appendices 167

A.1 Proofs for Chapter 2 167

A.2 Proofs for Chapter 3 174

A.3 Proofs for Chapter 4 181

A.4 Proofs for Chapter 5 185

References 193

Editorial Reviews

From the reviews:

“This research monograph is devoted to the idea of fuzzy conceptual graphs, their analysis, algorithms and applications. … One of the outstanding features of the monograph is a formal and systematic coverage of the fundamental concepts. Overall, the book can serve as a valuable, well-structured reference book for all those interested in the effective representation and processing of fuzzy information.” (Witold Pedrycz, Zentralblatt MATH, Vol. 1208, 2011)

From the Publisher