Screen LibraryHigher-order logic and type theory /
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...
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| Main Authors: | |
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| Published: |
Cambridge University Press,
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| Publisher Address: | Cambridge : |
| Publication Dates: | 2022. |
| Literature type: | Book |
| Language: | English |
| Series: |
Cambridge elements. Elements in philosophy and logic,
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| Subjects: | |
| Summary: |
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. |
| Carrier Form: | 79 pages : illustrations ; 23 cm. |
| Bibliography: | Includes bibliographical references (pages [75]-79) |
| ISBN: |
9781108986908 1108986900 |
| Index Number: | QA9 |
| CLC: | O141 |
| Call Number: | O141/B433-1 |
| Contents: | 1. Second- 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. |