Logic for Computer Science and Artificial Intelligence

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

2.2. Somehistoric landmarks 32

Chapter 3. Propositional Logic 39

3.1. Syntaxand semantics 40

3.2. Themethodof semantic tableaux 54

3.3. Formal systems 64

3.4. Aformal systemforPL(PC) 78

3.5. ThemethodofDavis andPutnam 92

3.6. Semantic trees inPL 96

3.7. The resolutionmethodinPL 101

3.8. Problems, strategies, andstatements 109

3.9. Hornclauses 113

3.10. Algebraic point of view of propositional logic 114

Chapter 4. First-order Terms 121

4.1. Matchingandunification 121

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

5.3. Semantic tableauxin FOL 154

5.4. Unification in the method of semantic tableaux 166

5.5. Toward a semi-decision procedure for FOL 169

5.6. Semantic trees inFOL 186

5.7. The resolutionmethodinFOL 190

5.8. Adecidable class: themonadic class 202

5.9. Limits: Godel¢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. Logicprogramming: examples 222

6.4. Computability and Horn clauses 241

Chapter 7. Artificial Intelligence 245

7.1. Intelligent systems: AI 245

7.2. What approaches to studyAI? 249

7.3. Toward an operational definition of intelligence 249

7.4. Can we identify human intelligence with mechanicalintelligence? 251

7.5. Somehistory 254

7.6. Some undisputed themes in AI 256

Chapter 8. Inference 259

8.1. Deductiveinference 260

8.2. An important concept: clause subsumption 266

8.3. Abduction 273

8.4. Inductive inference 278

8.5. Generalization: the generation of inductive hypotheses 284

Chapter 9. Problem Specification in Logical Languages 291

9.1. Equality 291

9.2. Constraints 309

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

Chapter 10. Non-classical Logics 327

10.1. Many-valuedlogics 327

10.2. Inaccurate concepts: fuzzy logic 337

10.3. Modal logics 353

10.4. Some elements of temporal logic 371

Chapter 11. Knowledge and Logic: Some Notions 385

11.1. What is knowledge? 386

11.2. Knowledge and modal logic 389

Chapter 12. Solutions to the Exercises 395

Bibliography 515

Index 517