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Categorical Logic and Type Theory

Categorical Logic and Type Theory PDF Author: B. Jacobs
Publisher: Gulf Professional Publishing
ISBN: 9780444508539
Category : Computers
Languages : en
Pages : 784

Book Description
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.

Categorical Logic and Type Theory

Categorical Logic and Type Theory PDF Author: B. Jacobs
Publisher: Gulf Professional Publishing
ISBN: 9780444508539
Category : Computers
Languages : en
Pages : 784

Book Description
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.

Categorical Logic and Type Theory

Categorical Logic and Type Theory PDF Author: B. Jacobs
Publisher: Elsevier
ISBN: 0080528708
Category : Mathematics
Languages : en
Pages : 779

Book Description
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.

Categorical Logic and Type Theory

Categorical Logic and Type Theory PDF Author: B. Jacobs
Publisher: Elsevier Health Sciences
ISBN:
Category : Mathematics
Languages : en
Pages : 790

Book Description
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.

Introduction to Higher-Order Categorical Logic

Introduction to Higher-Order Categorical Logic PDF Author: J. Lambek
Publisher: Cambridge University Press
ISBN: 9780521356534
Category : Mathematics
Languages : en
Pages : 308

Book Description
Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

First Order Categorical Logic

First Order Categorical Logic PDF Author: M. Makkai
Publisher: Springer
ISBN: 3540371001
Category : Mathematics
Languages : en
Pages : 317

Book Description


Basic Category Theory

Basic Category Theory PDF Author: Tom Leinster
Publisher: Cambridge University Press
ISBN: 1107044243
Category : Mathematics
Languages : en
Pages : 193

Book Description
A short introduction ideal for students learning category theory for the first time.

Topoi

Topoi PDF Author: R. Goldblatt
Publisher: Elsevier
ISBN: 148329921X
Category : Mathematics
Languages : en
Pages : 569

Book Description
The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''.The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.

Categories for the Working Philosopher

Categories for the Working Philosopher PDF Author: Elaine M. Landry
Publisher: Oxford University Press
ISBN: 019874899X
Category : Mathematics
Languages : en
Pages : 486

Book Description
This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these areas.

Twenty Five Years of Constructive Type Theory

Twenty Five Years of Constructive Type Theory PDF Author: Giovanni Sambin
Publisher: Clarendon Press
ISBN: 0191606936
Category : Mathematics
Languages : en
Pages : 292

Book Description
Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.

Categories for Types

Categories for Types PDF Author: Roy L. Crole
Publisher: Cambridge University Press
ISBN: 9780521457019
Category : Computers
Languages : en
Pages : 362

Book Description
This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.