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应用逻辑 第2版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

应用逻辑 第2版
  • （美）尼罗德（Nerode，A.）等著 著
  • 出版社： 北京：机械工业出版社
  • ISBN：7111197720
  • 出版时间：2006
  • 标注页数：457页
  • 文件大小：240MB
  • 文件页数：470页
  • 主题词：数理逻辑－英文

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图书目录

Introduction1

Ⅰ Propositional Logic7

1 Orders and Trees7

2 Propositions,Connectives and Truth Tables12

3 Truth Assignments and Valuations23

4 Tableau Proofs in Propositional Calculus27

5 Soundness and Completeness of Tableau Proofs38

6 Deductions from Premises and Compactness40

7 An Axiomatic Approach47

8 Resolution49

9 Refining Resolution62

10 Linear Resolution,Horn Clauses and PROLOG66

Ⅱ Predicate Logic81

1 Predicates and Quantifiers81

2 The Language：Terms and Formulas83

3 Formation Trees，Structures and Lists89

4 Semantics：Meaning and Truth95

5 Interpretations of PROLOG Programs100

6 Proofs：Complete Systematic Tableaux108

7 Soundness and Completeness of Tableau Proofs120

8 An Axiomatic Approach127

9 Prenex Normsl Form and Skolemization128

10 Herbrand’s Theorem133

11 Unification137

12 The Unification Algorithm141

13 Resolution145

14 Refining Resolution：Linear Resolution153

Ⅲ PROLOG159

1 SLD-Resolution159

2 Implementations：Searching and Backtracking166

3 Controlling the Implementation：Cut178

4 Termination Conditions for PROLOG Programs182

5 Equality188

6 Negation as Failure192

7 Negation and Nonmonotonic Logic203

8 Computability and Undecidability211

Ⅳ Modal Logic221

1 Possibility and Necessity：Knowledge or Belief221

2 Frames and Forcing224

3 Modal Tableaux228

4 Soundness and Completeness239

5 Modal Axioms and Special Accessibility Relations249

6 An Axiomatic Approach259

Ⅴ Intuitionistic Logic263

1 Intuitionism and Constructivism263

2 Frames and Forcing265

3 Intuitionistic Tableaux275

4 Soundness and Completeness285

5 Decidability and Undecidability293

6 A Comparative Guide306

Ⅵ Elements of Set Theory315

1 Some Basic Axioms of Set Theory315

2 Boole’8 Algebra of Sets318

3 Relations．Functions and the Power Set Axiom321

4 The Natural Numbers，Arithmetic and Infinity328

5 Replacement．Choice and Foundation339

6 Zermelo-Fraenkel Set Theory in Predicate Logic345

7 Cardinality：Finite and Countable348

8 Ordinal Numbers354

9 Ordinal Arithmetic and Transfinite Induction360

10 Transfinite Recursion，Choice and the Ranked Universe364

11 Cardinals and Cardinal Arithmetic368

Appendix A：An Historical Overview375

1 Calculus375

2 Logic376

3 Leibniz’8 Dream379

4 Nineteenth Century Logic380

5 Nineteenth Century Foundatlons of Mathematics383

6 Twentieth Century Foundations of Mathematics387

7 Early Twentieth Century Logic389

8 Deduction and Computation392

9 Recent Automation of Logic and PROLOG395

10 The Future395

Appendix B：A Genealogical Database399

Bibliography409

Index of Symbols439

Index ofTerms443

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