ISBN-10:
1848213018
ISBN-13:
9781848213012
Pub. Date:
08/30/2011
Publisher:
Wiley
Logic for Computer Science and Artificial Intelligence / Edition 1

Logic for Computer Science and Artificial Intelligence / Edition 1

by Ricardo Caferra
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Product Details

ISBN-13: 9781848213012
Publisher: Wiley
Publication date: 08/30/2011
Series: ISTE Series , #569
Pages: 523
Product dimensions: 6.40(w) x 9.20(h) x 1.40(d)

About the Author

Ricardo Caferra, LIG, CNRS/Grenoble INP, France.

Table of Contents

Preface xi

Chapter 1 Introduction 1

1.1 Logic, foundations of computer science, and applications of logic to computer science 1

1.2 On the utility of logic for computer engineers 3

Chapter 2 A Few Thoughts Before the Formalization 7

2.1 What is logic? 7

2.1.1 Logic and paradoxes 8

2.1.2 Paradoxes and set theory 9

l2.1.2.1 The answer 10

2.1.3 Paradoxes in arithmetic and set theory 13

2.1.3.1 The halting problem 13

2.1.4 On formalisms and well-known notions 15

2.1.4.1 Some "well-known" notions that could turn out to be difficult to analyze 19

2.1.5 Back to the definition of logic 23

2.1.5.1 Some definitions of logic for all 24

2.1.5.2 A few more technical definitions 24

2.1.5.3 Theory and meta-theory (language and meta-language) 30

2.1.6 A few thoughts about logic and computer science 30

2.2 Some historic landmarks 32

Chapter 3 Propositional Logic 39

3.1 Syntax and semantics 40

3.1.1 Language and meta-language 43

3.1.2 Transformation rules for cnf and dnf 49

3.2 The method of semantic tableaux 54

13.2.1 A slightly different formalism: signed tableaux 58

3.3 Formal systems 64

3.3.1 A capital notion: the notion of proof 64

3.3.2 What do we learn from the way we do mathematics? 72

3.4 A formal system for PL (PC) 78

3.4.1 Some properties of formal systems 84

3.4.2 Another formal system for PL (PC) 86

3.4.3 Another formal system 86

3.5 The method of Davis and Putnam 92

3.5.1 The Davis-Putnam method and the SAT problem 95

3.6 Semantic trees in PL 96

3.7 The resolution method in PL 101

3.8 Problems, strategies, and statements 109

3.8.1 Strategies 110

3.9 Horn clauses 113

3.10 Algebraic point of view of propositional logic 114

Chapter 4 First-order Terms 121

4.1 Matching and unification 121

4.1.1 A motivation for searching for a matching algorithm 121

4.1.2 A classification of trees 123

4.2 First-order terms, substitutions, unification 125

Chapter 5 First-Order Logic (FOL) or Predicate Logic (PL1, PC1) 131

5.1 Syntax 133

5.2 Semantics 137

5.2.1 The notions of truth and satisfaction 139

5.2.2 A variant: multi-sorted structures 150

5.2.2.1 Expressive power, sort reduction 150

5.2.3 Theories and their models 152

5.2.3.1 How can we reason in FOL? 153

5.3 Semantic tableaux in FOL 154

5.4 Unification in the method of semantic tableaux 166

5.5 Toward a semi-decision procedure for FOL 169

5.5.1 Prenex normal form 169

5.5.1.1 Skolemization 174

5.5.2 Skolem normal form 176

5.6 Semantic trees in FOL 186

5.6.1 Skolemization and clausal form 188

5.7 The resolution method in FOL 190

5.7.1 Variables must be renamed 201

5.8 A decidable class: the monadic class 202

5.8.1 Some decidable classes 205

5.9 Limits: Gödel's (first) incompleteness theorem 206

Chapter 6 Foundations of Logic Programming 213

6.1 Specifications and programming 213

6.2 Toward a logic programming language 219

6.3 Logic programming: examples 222

6.3.1 Acting on the execution control: cut"/" 229

6.3.1.1 Translation of imperative structures 231

6.3.2 Negation as failure (NAF) 232

6.3.2.1 Some remarks about the strategy used by LP and negation as failure 238

6.3.2.2 Can we simply deduce instead of using NAF? 239

6.4 Computability and Horn clauses 241

Chapter 7 Artificial Intelligence 245

7.1 Intelligent systems: AI 245

7.2 What approaches to study AI? 249

7.3 Toward an operational definition of intelligence 249

7.3.1 The imitation game proposed by Turing 250

7.4 Can we identify human intelligence with mechanical intelligence? 251

7.4.1 Chinese room argument 252

7.5 Some history 254

7.5.1 Prehistory 254

7.5.2 History 255

7.6 Some undisputed themes in AI 256

Chapter 8 Inference 259

8.1 Deductive inference 260

8.2 An important concept: clause subsumption 266

8.2.1 An important problem 268

8.3 Abduction 273

8.3.1 Discovery of explanatory theories 274

8.3.1.1 Required conditions 275

8.4 Inductive inference 278

8.4.1 Deductive inference 279

8.4.2 Inductive inference 280

8.4.3 Hempel's paradox (1945) 280

8.5 Generalization: the generation of inductive hypotheses 284

8.5.1 Generalization from examples and counter examples 288

Chapter 9 Problem Specification in Logical Languages 291

9.1 Equality 291

9.1.1 When is it used? 292

9.1.2 Some questions about equality 292

9.1.3 Why is equality needed? 293

9.1.4 Whatis equality? 293

9.1.5 How to reason with equality? 295

9.1.6 Specification without equality 296

9.1.7 Axiomatization of equality 297

9.1.8 Adding the definition of = and using the resolution method 297

9.1.9 By adding specialized rules to the method of semantic tableaux 299

9.1.10 By adding specialized rules to resolution 300

9.1.10.1 Paramodulation and demodulation 300

9.2 Constraints 309

9.3 Second Order Logic (SOL): a few notions 319

9.3.1 Syntax and semantics 324

9.3.1.1 Vocabulary 324

9.3.1.2 Syntax 325

9.3.1.3 Semantics 325

Chapter 10 Non-classical Logics 327

l0.l Many-valued logics 327

10.1.1 How to reason with p-valued logics? 334

10.1.1.1 Semantic tableaux for p-valued logics 334

10.2 Inaccurate concepts: fuzzy logic 337

10.2.1 Inference in FL 348

10.2.1.1 Syntax 349

10.2.1.2 Semantics 349

10.2.2 Herbrand's method in FL 350

10.2.2.1 Resolution andFL 351

10.3 Modal logics 353

10.3.1 Toward a semantics 355

10.3.1.1 Syntax (language of modal logic) 357

10.3.1.2 Semantics 358

10.3.2 How to reason with modallogics? 360

10.3.2.1 Formal systems approach 360

10.3.2.2 Translation approach 361

10.4 Some elements of temporal logic 371

10.4.1 Temporal operators and semantics 374

10.4.1.1 A famous argument 375

10.4.2 A temporal logic 377

10.4.3 How to reason with temporal logics? 378

10.4.3.1 The method of semantic tableaux 379

10.4.4 An example of a PL for linear and discrete time; PTL (or PLTL) 381

10.4.4.1 Syntax 331

10.4.4.2 Semantics 382

10.4.4.3 Method of semantic tableaux for PLTL (direct method) 333

Chapter 11 Knowledge and Logic: Some Notions 385

11.1 What is knowledge? 335

11.2 Knowledge and modal logic 389

11.2.1 Toward a formalization 389

11.2.2 Syntax 339

11.2.2.1 What expressive power? An example 389

11.2.2.2 Semantics 339

11.2.3 New modal operators 391

11.2.3.1 Syntax (extension) 391

11.2.3.2 Semantics (extension) 391

11.2.4 Application examples 392

11.2.4.1 Modeling the muddy children puzzle 392

11.2.4.2 Corresponding Kripke worlds 392

11.2.4.3 Properties of the (formalization chosen for the) knowledge 394

Chapter 12 Solutions to the Exercises 395

Bibliography 515

Index 517

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