HigheOrder Logic and Type Theory | 2.03 MB
Title: HigheOrder Logic and Type Theory
Author: John L. Bell
Language: English | 88 Pages | ISBN: 1108986900
Description:
This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 introduces Local Set Theory (also known as higher-order intuitionistic logic), an important form of type theory based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called ‘doctrine of propositions as types’. We conclude with an Appendix in which the semantics for Local Set Theory – based on category theory – is outlined.
This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 introduces Local Set Theory (also known as higher-order intuitionistic logic), an important form of type theory based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called ‘doctrine of propositions as types’. We conclude with an Appendix in which the semantics for Local Set Theory – based on category theory – is outlined.
DOWNLOAD:
rapidgator.net/file/1315c30549f9c73750b08b73ee864233/Higher-Order_Logic_and_Type_Theory.rar
nitroflare.com/view/B6B1FFFA433ECFE/Higher-Order_Logic_and_Type_Theory.rar
