For more than two generations, W.V. Quine has contributed fundamentally to the substance, the pedagogy and the philosophy of mathematical logic. "Selected Logic Papers", long out of print and now reissued with eight additional essays, includes much of the author's important work on mathematical logic and the philosophy of mathematics from the past 60 years.

Hailed by the "Bulletin of the American Mathematical Society" as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed, and the examples are chosen from a variety of mathematical fields. 1978 edition.

These nine essays are largely concerned with the theory of meaning and references—semantics. At the same time adjacent portions of phil osophy and logic are discussed. To the existence of what objects may a given scientific theory be said to be committed? And what considerations may suitably guide us in accepting or revising such ontological commitments? These are among the questions dealt with in this book, particular attention being devoted to the role of abstract entities in mathematics. There is speculation on the mechanism whereby objects of one sort or another come to be posited a process in which the notion of identity plays an important part.

内容提要 本卷包括两部论著：《威拉德·范·奥曼·蒯因自传》（1986）和《数理逻辑》（1940）。前者是蒯因为“在世哲学家文库”《蒯因哲学》卷所写的简明自传；后者是蒯因的一部重要的逻辑著作，在其中，他仍然坚持逻辑主义纲领，试图从逻辑中推导出数学，把先前在《数理逻辑的新基础》（1937）一文中提出的NF系统，修改为ML系统，这是一个把命题逻辑、量化理论和集合论集为一身的系统，结构简明、特性奇异。 目录 威拉德·范·奥曼·蒯因自传 数理逻辑 导言 第一章 句子 1 合取、析取和否定 2 条件句 3 多重复合 4 使用和谈论 5 谈论句子的句子 6 准引语 7 括号与黑点 8 归约为三个初始联结词 9 归约为一个初始联结词 10 重言式 11 某些重言的形式 第二章 量化 12 量词 13 公式 14 约束、自由、闭包 15 量化的公理 16 定理 17 元定理 18 等值代换 19 存在量词 20 量词的分配 21 字母变体 第三章 项 22 类和分子 23 逻辑公式 24 抽离 25 等同 26 再论抽离 27 摹状词和名字 第四章 关于类的进一步理论 28 层次 29 更进一步的从属关系公理 30 等同可代入性 31 变元的代入 32 进一步的结果 33 逻辑积、和、补 34 包含 35 单类 第五章 关系 36 对和关系 37 关系的抽离 38 逆、象、关系积 39 祖先 40 函数 41 函数的抽离 42 作为关系的等同和从属 第六章 数 43 零、一、后继 44 自然数 45 可数集合 46 有穷的和无穷的 47 关系的幂 48 算术和、积、幂 …… 第七章 句法 附录 参考文献 人名索引 主题词索引

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading.

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an up-to-date and reliable guide essential for the student.

This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraisse's characterization of elementary equivalence, Lindstrom's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

《数学所讲座2010》是中国科学院数学研究所一批中青年学者发起组织的数学所讲座，介绍现代数学的重要内容及其思想、方法，旨在开阔视野，增进交流，提高数学修养。《数学所讲座2010》根据2010年八个讲座的讲稿整理而成，内容涉及数与形的关系、数和形的认识、分析数学、数理逻辑、表示论、数学物理等。

本书脱胎于北京大学哲学系本科“数理逻辑”课程的讲义，针对逻辑学的初学者，尤其是初学逻辑的学生，介绍一阶逻辑的最基本的知识和技术，包括一阶语言的语形和语义、一阶推演系统、一阶逻辑的完全性定理等。

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.

The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of "naive" (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.

集合论的主要概念（基数、序数、超限归纳）对于所有数学家都是最基础的，并非仅限于研究数理逻辑或集合论拓扑的专家。通常分析、代数或拓扑学的课程只会给出基础集合论的一个概貌，然而事实上它足够重要、有趣和简单，值得慢慢地学习品味。 《集合论基础》使得读者能够以悠闲品味的方式学习集合论的内容，它适用于广大范围的各类读者，从本科生直至那些想要最终掌握超限归纳并且理解它为何总被Zorn引理替代的专业数学家。 《集合论基础》介绍了“朴素”（非公理化）集合论的所有主要内容：函数、基数、有序集和良序集、超限归纳及其应用、序数、序数上的运算。《集合论基础》还包括对Cantor-Bernstein定理、Cantor的对角构造、Zorn引理、Zermelo定理和Hamel基的讨论和证明。此外，书中还给出了150多道问题，循序渐进地揭示了集合论基本思想和方法，内容全面完整，具有很好的可读性。

以維也納學派（Vienna Circle）為代表的「邏輯經驗論」，曾在二十世紀的世界思想界風行一時。殷海光即是深受這波學術思潮影響的知識人之一，始終鑽研不倦，本書正是他從事研究教學的心得之作。 殷海光在少年時期即對邏輯發生濃厚興趣，就讀高中一年級時曾將一本英文邏輯教本譯成中文，書名《邏輯基本》，自此與邏輯結下不解之緣。大學求學時期師從金岳霖教授學習邏輯，在大學任教期間也一直擔任邏輯教學工作，雖然未成為專業邏輯家，但對邏輯始終維持高度熱忱。充分使用邏輯概念分析政治及文化問題，乃成為殷海光文章的一大特色。 本書初稿在1943年完成，1956年修訂，由香港亞洲出版社出版，並作為殷海光在臺灣大學教授相關課程的教科書，影響深遠。全書以對話方式介紹邏輯基本原理與法則，深入淺出，對一般初學者容易混淆的概念及不易理解的原理皆詳加說明，引領讀者進入邏輯研究的世界。作者採用對話體的方式，便於暫時離開主題，穿插別的話題，以借此發表他個人對時局、政治、文化等問題的評論。這些題外話可以顯示邏輯的用途，值得特別留意。 閱讀本書，既具有知識學習的價值，也可以領略殷海光如何將邏輯轉化為闡揚自由主義，批判各種不合理權威的利器，有助於進一步深入探索他的思想世界。

《逻辑学导论(第11版》所选用的有关政治、哲学、科学及多领域当代论争的鲜活的论证实例，展示了许多严肃的学者和思想家在解决实际问题的过程中对逻辑原理的应用，使逻辑学习既内容充盈又富有生活气息。书中也选用了许多谬误性论证作为例示与辨谬训练资料，以使学生明了对逻辑法则的忽视或误用如何使论证走入误区。书中也有少量论辩推理的例子，这些例子是为说明逻辑原理而特别编制的，但使本书卓尔不凡的，还是那些精心选自许多不同领域文献的丰富多彩的新颖实例。

《计算理论导引（原书第3版）》由计算理论领域的知名权威 Michael Sipser 所撰写。他以独特的视角，系统地介绍了计算理论的三个主要内容：自动机与语言、可计算性理论和计算复杂性理论。作者以清新的笔触、生动的语言给出了宽泛的数学原理，而没有拘泥于某些低层次的细节。在证明之前，均有“证明思路”，帮助读者理解数学形式下蕴涵的概念。本书可作为计算机专业高年级本科生和研究生的教材，也可作为教师和研究人员的参考书。

Gain a clear understanding of even the most complex, highly theoretical computational theory topics in the approachable presentation found only in the market-leading INTRODUCTION TO THE THEORY OF COMPUTATION, 3E. The number one choice for today's computational theory course, this revision continues the book's well-know, approachable style with timely revisions, additional practice, and more memorable examples in key areas. A new first-of-its-kind theoretical treatment of deterministic context-free languages is ideal for a better understanding of parsing and LR(k) grammars. You gain a solid understanding of the fundamental mathematical properties of computer hardware, software, and applications with a blend of practical and philosophical coverage and mathematical treatments, including advanced theorems and proofs. INTRODUCTION TO THE THEORY OF COMPUTATION, 3E's comprehensive coverage makes this a valuable reference for your continued studies in theoretical computing.

《可计算性与计算复杂性导引(第3版)》是学习计算理论的教材和参考书，内容包括三部分：可计算性、形式语言与自动机、计算复杂性，主要介绍几种计算模型及它们的等价性，函数、谓词和语言的可计算性等基本概念，形式语言及其对应的自动机模型，时间和空间复杂性，NP完全性等。 《可计算性与计算复杂性导引(第3版)》可作为计算机专业本科生和研究生的教材，也可作为从事计算机科学技术的研究和开发人员的参考书，还可作为对计算理论感兴趣的读者的入门读物。