Foundations of Fuzzy Logic and Semantic Web Languages / Umberto Straccia.

Format:

Book

Author/Creator:

Straccia, Umberto, author.

Language:

English

Subjects (All):

Computers.

Genre:

Electronic books.

Physical Description:

1 online resource (381 pages)

Other Title:

Knowledge Unlatched.

Place of Publication:

Boca Raton : CRC Press, 2013.

System Details:

text file

Summary:

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic.

Contents:

1 The Quest for Fuzzy Logic in Semantic Web Languages 1

I Semantic Web Languages Basics 9

2 Introduction 11

2.1 RDF & RDFS 12

2.2 The OWL Family 13

2.3 The RIF Family 14

2.4 The Query Language SPARQL 15

3 Resource Description Language RDF & RDF Schema 17

3.1 Introduction 17

3.2 RDF and RDFS 18

3.3 Conjunctive Queries 22

3.4 Reasoning 23

4 Web Ontology Language OWL 29

4.1 Introduction 29

4.2 Description Logics Basics 32

4.2.1 The Basic Description Language AL 32

4.2.2 The DL Family 35

4.2.2.1 DLs Naming Convention 35

4.2.2.2 Concrete Domains 37

4.2.2.3 The AL Family and STROIQ(D) 38

4.2.2.4 The EL Family 41

4.2.2.5 The DL-Lite Family 41

4.2.2.6 The Horn-DL Family 44

4.3 Conjunctive Queries 45

4.4 Reasoning 47

4.4.1 The Case of the AL Family 48

4.4.1.1 The Case with Empty TBox 48

4.4.1.2 The Case of Acyclic TBox 50

4.4.1.3 The Case with General TBox 52

4.4.1.4 A Classification Algorithm 55

4.4.2 The Case of the EL Family 60

4.4.3 The Case of the DL-Lite Family 65

4.4.4 The Case of the Horn-DLs Family 69

4.4.5 Reasoning Complexity Summary 71

5 Rule Languages 73

5.1 Introduction 73

5.2 Datalog Basics 74

5.3 Concrete Domains 77

5.4 Conjunctive Queries 78

5.5 Reasoning 79

5.5.1 SLD-Resolution Driven Query Answering 79

5.5.2 Tabling like Query Driven Query Answering 82

6 Query Languages for SWL-based Knowledge Bases 87

6.1 Introduction 87

6.2 Conjunctive and Disjunctive Queries 88

6.3 SPARQL 90

II Fuzzy Logics and Semantic Web Languages 97

7 Introduction 99

8 Fuzzy Sets and Mathematical Fuzzy Logic Basics 101

8.1 Fuzzy Sets Basics 101

8.1.1 From Crisp Sets to Fuzzy Sets 101

8.1.2 Standard Fuzzy Set Operations 107

8.1.3 Norm-Based Fuzzy Set Operations 109

8.1.3.1 T-Norms 109

8.1.3.2 Dual Norms 112

8.1.3.3 Distributive Norms 113

8.1.3.4 T-Norm Representation Theorem 114

8.1.4 Fuzzy Implication 117

8.1.5 Fuzzy Relation 120

8.1.6 Aggregation Operators 121

8.1.7 Matrix-Based Fuzzy Set Operations 124

8.1.8 Fuzzy Modifiers 126

8.2 Mathematical Fuzzy Logic Basics 127

8.2.1 From Classical Logic to Mathematical Fuzzy Logic 127

8.2.1.1 On Witnessed Models 131

8.2.2 Reasoning 132

8.2.2.1 Axiomatizations 132

8.2.2.2 Operational Research-based 137

8.2.2.3 Analytical Fuzzy Tableau 143

8.2.2.4 Reduction to Classical Logic 149

8.2.3 Concrete Domains and Aggregation Operators 153

8.2.4 On Fuzzy IF-THEN Rules 158

9 Fuzzy RDF & RDFS 163

9.1 Introduction 163

9.2 Fuzzy RDF & RDFS 163

9.3 Fuzzy Conjunctive Queries 166

9.4 Reasoning 169

10 Fuzzy OWL 173

10.1 Introduction 173

10.2 Fuzzy Description Logics Basics 174

10.2.1 Syntax and Semantics 174

10.2.2 Some Additional Constructs 178

10.2.3 Acyclic Fuzzy Ontologies 180

10.2.4 On Witnessed Models 181

10.3 Salient Language Extensions 183

10.4 Fuzzy Conjunctive Queries 187

10.5 Representing Fuzzy OWL Ontologies in OWL 190

10.6 Reasoning 193

10.6.1 The Case of the AL Family 195

10.6.1.1 Reduction to Classical Logic 198

10.6.1.2 Analytical Fuzzy Tableau 202

10.6.1.3 Fuzzy Tableau for Finite-Valued DLs 209

10.6.1.4 Operational Research-based Fuzzy Tableau 210

10.6.1.5 A Fuzzy Classification Algorithm 218

10.6.2 The Case of Fuzzy EL 225

10.6.3 The Case of Fuzzy DL-Lite 228

10.6.4 The Case of Fuzzy Horn-DLs 233

10.6.5 The Case of Concrete Domains and Aggregation Operators 235

11 Fuzzy Rule Languages 237

11.1 Introduction 237

11.2 Fuzzy Datalog Basics 238

11.3 Concrete Domains 244

11.4 Fuzzy Conjunctive Queries 245

11.5 Reasoning 245

11.5.1 SLD-Resolution Driven Query Answering 249

11.5.2 Reduction to Classical Logic 252

11.5.3 Top-k Query Answering 253

11.5.3.1 Top-k Retrieval for Non-Recursive KBs 253

11.5.3.2 Top-k Retrieval: The General Case 256.

Notes:

Description based on print version record.

Local Notes:

KU Select 2018: STEM Backlist Books

BiblioBoard internal publisher id: 102703

ISBN:

9781439853474

Access Restriction:

Open Access Unrestricted online access