Introduction to Higher-Order Categorical Logic 2024 pdf epub mobi 电子书

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发表于2024-06-16

Introduction to Higher-Order Categorical Logic 2024 pdf epub mobi 电子书

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出版者:Cambridge University Press

作者:J. Lambek

出品人:

页数:304

译者:

出版时间:1988-3-25

价格:USD 53.00

装帧:Paperback

isbn号码:9780521356534

丛书系列:

图书标签: 范畴论数理逻辑范畴逻辑类型论 MathLogic 高阶范畴逻辑语言学 nemlophics

Introduction to Higher-Order Categorical Logic 2024 pdf epub mobi 电子书图书描述

In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic (intuitionistic type theories) is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludes with a set of exercises. Thus it is well-suited for graduate courses and research in mathematics and logic. Researchers in theoretical computer science, artificial intelligence and mathematical linguistics will also find this an accessible introduction to a subject of increasing application to these disciplines.

Introduction to Higher-Order Categorical Logic 2024 pdf epub mobi 电子书

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前言非常好玩，说你变换不同的角度看问题，会把各种派别得罪个遍，然后本书试图给个调解！这听起来就像悖论一样好玩儿。作者的这些观点，成书时已是88年，算上其考虑的时间，如今已经四十年了，在学术界也不见什么影响力，毕竟抽象到没什么用的程度也就不是工作所参考的东西了。现代比较主流一点的观点，多是直接从计算机的应用的出发了。第一章说明Cartesion闭范畴与有类型lambda演算等价，因为都是公理化地描述代入过程；第二章介绍带有乘积类型自然数类型以及真值类型的，分别与直觉谓词演算以及用等式定义逻辑连接与量词对应的，两种类型论等价，其中后者在描述拓扑斯方面非常方便；同时讨论拓扑斯的内语言，以及与某些类型论以及其他拓扑斯的等价问题；第三章研究不同范畴中的数值函数表达问题。

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