“數(shù)理邏輯”是一門(mén)基礎(chǔ)性學(xué)科，選一本好的“數(shù)理邏輯”的教材，對(duì)于培養(yǎng)新一代計(jì)算機(jī)科學(xué)家及IT從業(yè)人員是非常重要的。經(jīng)專(zhuān)家推薦，我們選了劍橋大學(xué)出版社的，由A.G.Hamilton著“Logic for Mathematicians”一書(shū)影印出版，希望本書(shū)的影印版能為國(guó)內(nèi)高?！皵?shù)理邏輯”課程的開(kāi)設(shè)提供支持。本書(shū)系統(tǒng)地講解了數(shù)理邏輯的基礎(chǔ)部分——命題演算與謂詞演算。第一章直觀地講解了命題邏輯基本思想和概念；第二章講解命題邏輯的形式化系統(tǒng)；第三章直觀地講解了謂詞邏輯；第四章講解謂詞邏輯的形式化系統(tǒng)；第五章介紹數(shù)學(xué)系統(tǒng)；第六章以很不的篇幅完整地介紹了哥德?tīng)柌煌陚涠ɡ硪杂羞f歸函數(shù)的初步知識(shí)；第七章簡(jiǎn)要介紹了可計(jì)算性與可判定性理論。由于數(shù)理邏輯（特別是其基礎(chǔ)部分）是一門(mén)定形的老學(xué)科，其理論體系沒(méi)有什么變化。本書(shū)第一版由劍橋大學(xué)出版社于1978年出版，然后，于1988年出了修訂版。自從出版以來(lái)，幾乎第年都要重印，可見(jiàn)其受歡迎的程度。本書(shū)是適合作本科生教學(xué)的，難得的好教材，既適用于計(jì)算機(jī)專(zhuān)業(yè)，也適用于數(shù)學(xué)專(zhuān)業(yè)，對(duì)哲學(xué)專(zhuān)業(yè)的學(xué)生同樣也是適用的。
作者簡(jiǎn)介
暫缺《數(shù)理邏輯》作者簡(jiǎn)介
圖書(shū)目錄
Preface 1 Informal statement calculus 1.1 Statements and connectives 1.2 Truth functions and truth tables 1.3 Rules for manipulation and substitution 1.4 Normal forms 1.5 Adequate sets of connectives 1.6 Arguments and validity 2 Formal statement calculus 2.1 The formal system L 2.2 The Adequacy Theorem for L 3 Informal predicate calculus 3.1 Predicates and quantifiers 3.2 First order languages 3.3 Interpretations 3.4 Satisfaction, truth 3.5 Skolemisation 4 Formal predicate calculus 4.1 The formal system K L 4.2 Equivalence, substitution 4.3 Prenex form 4.4 The Adequacy Theorem for K 4.5 Models 5 Mathematical systems 5.1 Introduction 5.2 First order systems with equality 5.3 The theory of groups 5.4 First order arithmetic 5.5 Formal set theory 5.6 Consistency and models 6 The Godel Incompleteness Theorem 6.1 Introduction 6.2 Expressibility 6.3 Recursive functions and relations 6.4 Godel numbers 6.5 The incompleteness proof 7 Computability, unsolvability, undecidability 7.1 Algorithms and computability 7.2 Turing machines 7.3 Word problems 7.4 Undecidability of formal systems Appendix Countable and uncountable sets Hints and solutions to selected exercises References and further reading Glossary of symbols Index
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