數理邏輯（第2版） [Mathematical Logic] epub pdf mobi txt 電子書 下載 2024

數理邏輯（第2版） [Mathematical Logic] epub pdf mobi txt 電子書 下載 2024

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數理邏輯（第2版） [Mathematical Logic] epub pdf mobi txt 電子書 下載 2024

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　　A short digression into model theory will help us to analyze the expressive power of the first-order language， and it will turn out that there are certain deficiencies. For example， the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand， this di~culty can be overcome——-even in the framework of first-order logic——by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.
　　Godels incompleteness theorems are presented in connection with several related results (such as Trahtenbrots theorem) which all exemplify the limitatious of machine-oriented proof methods. The notions of computability theory that are relevant to this discussion are given in detail. The concept of computability is made precise by means of the register machine as a

內容簡介

　　What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs?
　　Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godels completeness theorem， which shows that the consequence relation coincides with formal provability： By means of a calculus consisting of simple formal inference rules， one can obtain all consequences of a given axiom system (and in particular， imitate all mathematical proofs)

內頁插圖

目錄

Preface
PART A
ⅠIntroduction
1.An Example from Group Theory
2.An Example from the Theory of Equivalence Relations
3.A Preliminary Analysis
4.Preview
Ⅱ Syntax of First-Order Languages
1.Alphabets
2.The Alphabet of a First-Order Language
3.Terms and Formulas in First-Order Languages
4.Induction in the Calculus of Terms and in the Calculus of Formulas
5.Free Variables and Sentences
Ⅲ Semantics of First-Order Languages
1.Structures and Interpretations
2.Standardization of Connectives
3.The Satisfaction Relation
4.The Consequence Relation
5.Two Lemmas on the Satisfaction Relation
6.Some simple formalizations
7.Some remarks on Formalizability
8.Substitution
Ⅳ A Sequent Calculus
1．Sequent Rules
2．Structural Rules and Connective Rules
3．Derivable Connective Rules
4．Quantifier and Equality Rules
5．Further Derivable Rules and Sequents
6．Summary and Example
7．Consistency
ⅤThe Completeness Theorem
1．Henkin’S Theorem．
2． Satisfiability of Consistent Sets of Formulas（the Countable Casel
3． Satisfiability of Consistent Sets of Formulas（the General Case）
4．The Completeness Theorem
Ⅵ The LSwenheim-Skolem and the Compactness Theorem
1．The L6wenheim-Skolem Theorem．
2．The Compactness Theorem
3．Elementary Classes
4．Elementarily Equivalent Structures
Ⅶ The Scope of First-Order Logic
1．The Notion of Formal Proof
2．Mathematics Within the Framework of Fimt—Order Logic
3．The Zermelo-Fraenkel Axioms for Set Theory．
4．Set Theory as a Basis for Mathematics
Ⅷ Syntactic Interpretations and Normal Forms
1．Term-Reduced Formulas and Relational Symbol Sets
2．Syntactic Interpretations
3．Extensions by Definitions
4．Normal Forms
PART B
Ⅸ Extensions of First-order logic
Ⅹ Limitations of the Formal Method
Ⅺ Free Models and Logic Programming
Ⅻ An Algebraic Characterization of Elementary Equivalence
ⅩⅢ Lindstrom’s Theorems
References
Symbol Index
Subject Index

前言/序言

數理邏輯（第2版） [Mathematical Logic] epub pdf mobi txt 電子書 下載 2024

數理邏輯（第2版） [Mathematical Logic] 下載 epub mobi pdf txt 電子書

評分☆☆☆☆☆

還沒有看，都是經典教材啊

評分☆☆☆☆☆

邏輯一下子

評分☆☆☆☆☆

1847年，英國數學傢布爾發錶瞭《邏輯的數學分析》，建立瞭“布爾代數”，並創造一套符號係統，利用符號來錶示邏輯中的各種概念。布爾建立瞭一係列的運算法則，利用代數的方法研究

評分☆☆☆☆☆

書很不錯，是數理邏輯的經典之作！

評分☆☆☆☆☆

知識是人類在實踐中認識客觀世界的成果。它可能包括事實，信息，描述或在教育和實踐中獲得的技能。它可能是關於理論的，也可能是關於實踐的。在哲學中，關於知識的研究叫做認識論。知識的獲取涉及到許多復雜的過程：感覺，交流，推理。知識也可以看成構成人類智慧的最根本的因素。

評分☆☆☆☆☆

本書從經典的一階語言開始，詳細介紹以數理邏輯進行的推導和證明，之後少量介紹為解決一階語言不足而擴展的二階語言。書中大量的推導證明過程，豐富的實例和練習，是進行頭腦體操的好教材。對於數學不感興趣的人，這本書有些枯燥，但是如果是數學和人工智能專業的高手，肯定會喜歡這本書所提供的知識。

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發展

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好

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