应用逻辑（英文版·第2版）

　　这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。.本书不要求读者具备逻辑基础知识，适合计算机科学和数学系高年级本科生以及低年级研究生使用。...

　　作者：Anil NerodeAnil Nerode康奈尔大学数学系的创始人和教授，于1956年在芝加哥大学获得博士学位。他的研究领域包括数理逻辑、自动机、可计算理论、混合系统等。除本书外，他还与其他人合著了《Effective Completeness Theorems for Modal Logic》、《Tableaux for Constructive Concurrent Dynamic Logic》、《Logic，Categories，Lambda Calculus》等书。.

Introduction
Propositional Logic
1Orders and Trees
2Propositions,Connectives and Truth Tables
3Truth Assignments and Valuations
4Tableau Proofs in Propositional Calculus
5Soundness and Completeness of Tableau Proofs
6Deductions from Premises and Compactness
7An Axiomatic Approach*
8Resolution
9Refining Resolution
10Linear Resolution,Horn Clauses and PROLOG
Predicate Logic
1Predicates and Quantifiers
2The Language:Term and Formulas
3Formaiton Trees,Structures and Lists
4Semantics:Meaning and Truth
5Interpretations of PROLOG Programs
6Proofs:Complete Systematic Tableaux
7Soundness and Completeness of Tableau Proofs
8An Axiomatic Approach*
9Prenex Normal Form and Skolemization
10Herbrand’s Theorem
11Unification
12The Unification Algorithm
13Resolution
14Refining Resolution:Linear Resolution
PROLOG
1SLD-Resolution
2Implementations:Searching and Backtracking
3Controlling the Implementation:Cut
4Termination Conditions for PROLOG Programs
5Epuality
6Negation as Failure
7Negation and Nonmonotonic Logic
8Computability and Undecidability
Modal Lgic
1Possibility and Necessity;Knowledge or Belief
2Frames and Forcing
3Modal Tableaux
4Soundness and Completeness
5Modal Axioms and Special Accessibility Relaitons
6An Axiomatic Approach*
Intutitionistic Logic
1Intuitionism and Constructivism
2Frames and Forcing
3Intuitionistc Tableaux
4Soundness and Completeness
5Decidability and Undecidability
6A Comparative Guide
Elements of Set Theory
1Some Basic Axioms of Set Theory
2Boole’s Algebra of Sets
3Relations,Functions and the Power Set Axiom
4The Natural Numbers,Arithmetic and Infinity
5Replacement,Choice and Foundation
6Zermolo-Fraenkel Set Theory in Predicate Logic
7Cardinality:Finite and Countable
8Ordinal Numbers
9Ordinal Arithmetic and Transfinite Induction
10Transfinite Recursion,Coice and the Ranked Universe
11Cardinals and Cardinal Arithmetic
Appedix A:An Historical Overview
1Calculus
2Logic
3Leibniz’s Dream
4Nineteenth Century Logic
5Nineteenth Century Foundations of Mathematics
6Twentieth  Century Foudations of Mathematics
7Early Twentieth Century Logic
8Deduction and Computation
9Recent Automation of Logic and PROLOG
10The Future
Appendix B:A Genealogical Database
Bibliography
Index of Symbols
Index of Terms