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 typ...

Ausführliche Beschreibung

Bibliographische Detailangaben

1. Verfasser:	Bell, John L. 1945- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Cambridge Cambridge University Press 2022
Schlagworte:	Logic, Symbolic and mathematical Type theory Set theory
Online-Zugang:	BSB01 UBG01 Volltext
Zusammenfassung:	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
Beschreibung:	Title from publisher's bibliographic system (viewed on 21 Mar 2022)
Beschreibung:	1 Online-Ressource (79 Seiten)
ISBN:	9781108981804
DOI:	10.1017/9781108981804