圖書標籤: 邏輯學 數理邏輯 數學 英文原版 logic Math 教科書 MathLogic
发表于2024-11-05
Mathematical Logic pdf epub mobi txt 電子書 下載 2024
Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic, Mathematics, Philosophy, and Computer Science.
大一的時候數理邏輯課的教材
評分在眾多的數理邏輯教材中,這本並不突齣。對於完全沒有基礎的人,這本並不閤適;而對於已經學過數理基礎的人來說,這本又淺瞭一些。其中一些非常直觀簡單的概念,作者為瞭追求嚴謹,寫得過於囉嗦。而一些比較難理解的概念和證明,作者又沒有給予充分的、直觀的解釋。不過這本書有一個優點——就是每一個定理,不管難不難,都有證明,也基本能夠證清楚。能做到這點也是不容易的。但總得來說,這本書寫得不夠清晰明瞭。
評分比較簡單 natural deduction部分比較好
評分做瞭本科生數理邏輯的助教,這本是教材,寫得足夠清晰,但總感覺有些概念的引入,比如樹,對於剛入門的學生來說不是很必要。總體而言是入門的好書,但最好有素樸集閤論基礎。
評分做瞭本科生數理邏輯的助教,這本是教材,寫得足夠清晰,但總感覺有些概念的引入,比如樹,對於剛入門的學生來說不是很必要。總體而言是入門的好書,但最好有素樸集閤論基礎。
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Mathematical Logic pdf epub mobi txt 電子書 下載 2024