The Theory of Logical Types
The Theory of Logical Types

Author: Irving Copi

Publisher: Routledge

Published: 2011-02-28

Total Pages: 142

ISBN-13: 1136816143

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This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its various different formulations (Simple and Ramified), the difficulties connected with each, and the criticisms that have been directed against it. Professor Copi seeks to make the subject accessible to the non-specialist and yet provide a sufficiently rigorous exposition for the serious student to see exactly what the theory is and how it works.

Categorical Logic and Type Theory
Categorical Logic and Type Theory

Author: B. Jacobs

Publisher: Gulf Professional Publishing

Published: 2001-05-10

Total Pages: 784

ISBN-13: 9780444508539

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This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

Higher-Order Logic and Type Theory
Higher-Order Logic and Type Theory

Author: John L. Bell

Publisher: Cambridge University Press

Published: 2022-03-31

Total Pages: 88

ISBN-13: 1108991955

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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.

Steps to an Ecology of Mind
Steps to an Ecology of Mind

Author: Gregory Bateson

Publisher: University of Chicago Press

Published: 2000

Total Pages: 572

ISBN-13: 9780226039053

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Gregory Bateson was a philosopher, anthropologist, photographer, naturalist, and poet, as well as the husband and collaborator of Margaret Mead. This classic anthology of his major work includes a new Foreword by his daughter, Mary Katherine Bateson. 5 line drawings.