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Higher-Order Logic and Type Theory: Elements in Philosophy and Logic

Autor John L. Bell
en Limba Engleză Paperback – 30 mar 2022
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.
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Specificații

ISBN-13: 9781108986908
ISBN-10: 1108986900
Pagini: 75
Dimensiuni: 152 x 229 x 5 mm
Greutate: 0.13 kg
Ediția:Nouă
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Elements in Philosophy and Logic

Locul publicării:Cambridge, United Kingdom

Cuprins

1. Second- Order Logic and Higher-Order Logic; 2. Type Theory and its Origins; 3. Local set theory; 4. Newer Forms of Type Theory Based on the Doctrine of 'Propositions as Types'; Appendix; The Semantics of Local Set Theory/Intuitionistic Higher-Order Logic.

Descriere

The Element provides a wide-ranging, but unified account of higher-order logic and contemporary type theory.