本书是数理逻辑方面的经典教材,以可读性强而著称。在美国大学中采用率极高,麻省理工学院、加州大学伯克利分校、哥伦比亚大学、康奈尔大学等众多名校均用它作为教材。本书是第二版,章节组织更加灵活,增加了与计算机科学相关的主题(比如有限模型),还增加了一些示例和阐释文字,更适合本科生和研究生数理逻辑课程使用。
本书是数理逻辑方面的经典教材。书中涵盖了命题逻辑、一阶逻辑、不可判定性以及二阶逻辑等方面的内容,并且包含了与计算机科学有关的主题,如有限模型。本书特点是:内容可读性强:组织结构更灵活,授课教师可根据教学需要节选本书的内容;反映了近几年来理论计算机科学对逻辑学产生的影响;包含较多的示例和说明。本书适合作为计算机及相关专业本科生和研究生数理逻辑课程的教材。
CHAPTER ZERO Useful Facts about Sets
CHAPTER ONE Sentential Logic
1.0 Informal Remarks on Formal Languages
1. 1 The Language of Sentential Logic
1.2 Truth Assignments
1.3 A Parsing Algorithm
1.4 Induction and Recursion
1.5 Sentential Connectives
1.6 Switching Circuits
1.7 Compactness and Effectiveness
CHAPTER TWO First-Order Logic
2.0 Preliminary Remarks
2.1 First-Order Languages
2.2 Truth and Models
2.3 A Parsing Algorithm
2.4 A Deductive Calculus
2.5 Soundness and Completeness Theorems
2.6 Models of Theories
2.7 Interpretations Between Theories
2.8 Nonstandard Analysis
CHAPTER THREE Undecidability
3.0 Number Theory
3.1 Natural Numbers with Successor
3.2 Other Reducts of Number Theory
3.3 A Subtheory of Number Theory
3.4 Arithmetization of Syntax
3.5 Incompleteness and Undecidability
3.6 Recursive Functions
3.7 Second Incompleteness Theorem
3.8 Representing Exponentiation
CHAPTER FOUR Second-Order Logic
4.1 Second-Order Languages
4.2 Skolem Functions
4.3 Many-Sorted Logic
4.4 General Structures
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