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出版者:Oxford University Press, USA

作者:Ian Chiswell

出品人:

页数:296

译者:

出版时间:2007-7-12

价格:USD 70.00

装帧:Paperback

isbn号码:9780199215621

丛书系列:Oxford Graduate Texts in Mathematics

图书标签:

逻辑学
哲学
数学逻辑
逻辑学
数理逻辑
集合论
模型论
证明论
递归论
形式系统
谓词逻辑
命题逻辑

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具体描述

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.

《Mathematical Logic》是一本深入浅出的学术著作，系统地介绍了逻辑学的基本概念与核心原理。内容涵盖了经典逻辑体系、推理规则以及形式化语言的运用，帮助读者建立对逻辑思维的坚实基础。书中首先系统梳理了逻辑论证的基本框架，从古希腊哲学家亚里士多德到现代数学逻辑的发展历程，为后续学习打下扎实的理论基石。在内容结构方面，书以清晰的层次组织展开，每个章节都聚焦于特定主题，例如命题逻辑、谓词逻辑及递归关系等。通过丰富的例子和详细的推理过程，帮助读者理解复杂概念的具体应用。在论证部分，作者不仅解释了逻辑原理，还结合历史背景和实际案例，使理论更易于理解与延伸。书中特别强调逻辑思维能力的发展，通过引导读者反思推理过程、识别逻辑漏洞等方式，培养批判性思考的习惯。这些内容不仅适用于学术研究，也对工程、金融、计算机科学等领域有广泛应用价值。此外，书中还包含大量图表和实例分析，便于读者直观掌握复杂逻辑结构。整个书籍力求以严谨的学术态度呈现逻辑学知识，同时通过清晰的语言和逻辑连贯的思路，让读者在学习过程中感受到深刻的 intellect 刺激。作者不仅关注知识的传授，更致力于提升读者独立思考和分析问题的能力。书籍的设计体现了对读者多样化需求的把握，内容从基础到深入层次，逐步引导用户掌握核心概念，同时为后续深入学习提供坚实的支持。这种结构不仅增强了阅读体验，也使知识传播更具实用性和系统性。《Mathematical Logic》以其全面、系统且易懂的写作风格，成为希望深造或提升逻辑思维能力的读者的一本经典之选。这本书不仅是一份理论的集合，更是一种对逻辑思维的启迪，帮助每一位读者在复杂信息中找到清晰的方向。通过详细而有条理的内容安排，书中的每一个章节都体现了作者对学术严谨性和用户需求的高度关注。这本书不仅满足专业学习者的要求，也为普通读者提供了一种通向逻辑世界的入口。总的来说，这本书通过详尽而逻辑清晰的内容，全面介绍了数学逻辑的重要知识体系，并以实用性和深度兼顾，为广大读者打开了深入探讨的窗口。这种深刻浅巧的写作风格，不仅丰富了理论面，也增强了实际应用的价值。