《应用逻辑 第2版》PDF下载

  • 购买积分:15 如何计算积分?
  • 作  者:(美)尼罗德(Nerode,A.)等著
  • 出 版 社:北京:机械工业出版社
  • 出版年份:2006
  • ISBN:7111197720
  • 页数:457 页
图书介绍:本是一本结合逻辑在计算机科学中的应用来介绍数理逻辑的教科书,书中强调了演绎作为计算的一种形式的概念。虽然本书覆盖了所有传统的逻辑主题(语法、语义、完备性和紧致性),但是书中大部分内容讨论的是其他主题,诸如消解定理证明、逻辑式程序设计和非经典逻辑(模态逻辑和直觉主义逻辑),而这些主题在现代计算机科学中变得越来越重要。另外,本书还系统介绍了集合论基础知识,并对该主题提供了历史综述。

Introduction 1

Ⅰ Propositional Logic 7

1 Orders and Trees 7

2 Propositions,Connectives and Truth Tables 12

3 Truth Assignments and Valuations 23

4 Tableau Proofs in Propositional Calculus 27

5 Soundness and Completeness of Tableau Proofs 38

6 Deductions from Premises and Compactness 40

7 An Axiomatic Approach 47

8 Resolution 49

9 Refining Resolution 62

10 Linear Resolution,Horn Clauses and PROLOG 66

Ⅱ Predicate Logic 81

1 Predicates and Quantifiers 81

2 The Language:Terms and Formulas 83

3 Formation Trees,Structures and Lists 89

4 Semantics:Meaning and Truth 95

5 Interpretations of PROLOG Programs 100

6 Proofs:Complete Systematic Tableaux 108

7 Soundness and Completeness of Tableau Proofs 120

8 An Axiomatic Approach 127

9 Prenex Normsl Form and Skolemization 128

10 Herbrand’s Theorem 133

11 Unification 137

12 The Unification Algorithm 141

13 Resolution 145

14 Refining Resolution:Linear Resolution 153

Ⅲ PROLOG 159

1 SLD-Resolution 159

2 Implementations:Searching and Backtracking 166

3 Controlling the Implementation:Cut 178

4 Termination Conditions for PROLOG Programs 182

5 Equality 188

6 Negation as Failure 192

7 Negation and Nonmonotonic Logic 203

8 Computability and Undecidability 211

Ⅳ Modal Logic 221

1 Possibility and Necessity:Knowledge or Belief 221

2 Frames and Forcing 224

3 Modal Tableaux 228

4 Soundness and Completeness 239

5 Modal Axioms and Special Accessibility Relations 249

6 An Axiomatic Approach 259

Ⅴ Intuitionistic Logic 263

1 Intuitionism and Constructivism 263

2 Frames and Forcing 265

3 Intuitionistic Tableaux 275

4 Soundness and Completeness 285

5 Decidability and Undecidability 293

6 A Comparative Guide 306

Ⅵ Elements of Set Theory 315

1 Some Basic Axioms of Set Theory 315

2 Boole’8 Algebra of Sets 318

3 Relations.Functions and the Power Set Axiom 321

4 The Natural Numbers,Arithmetic and Infinity 328

5 Replacement.Choice and Foundation 339

6 Zermelo-Fraenkel Set Theory in Predicate Logic 345

7 Cardinality:Finite and Countable 348

8 Ordinal Numbers 354

9 Ordinal Arithmetic and Transfinite Induction 360

10 Transfinite Recursion,Choice and the Ranked Universe 364

11 Cardinals and Cardinal Arithmetic 368

Appendix A:An Historical Overview 375

1 Calculus 375

2 Logic 376

3 Leibniz’8 Dream 379

4 Nineteenth Century Logic 380

5 Nineteenth Century Foundatlons of Mathematics 383

6 Twentieth Century Foundations of Mathematics 387

7 Early Twentieth Century Logic 389

8 Deduction and Computation 392

9 Recent Automation of Logic and PROLOG 395

10 The Future 395

Appendix B:A Genealogical Database 399

Bibliography 409

Index of Symbols 439

Index ofTerms 443