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Progress in Computer Science and Applied Logic
cover

Temporal Type Theory

A Topos-Theoretic Approach to Systems and Behavior

Authors: Schultz, Patrick, Spivak, David I.

  • Describes a new approach, developed by the authors, for proving properties about the behaviors of systems using temporal logic
  • Review of the prerequisite material included where needed in order to make a difficult topic more accessible
  • A case study involving aircraft separation illustrates a real-world application of temporal type theory
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Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-030-00704-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-030-00703-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This innovative monograph explores a new mathematical formalism in higher-order temporal logic for proving properties about the behavior of systems. Developed by the authors, the goal of this novel approach is to explain what occurs when multiple, distinct system components interact by using a category-theoretic description of behavior types based on sheaves. The authors demonstrate how to analyze the behaviors of elements in continuous and discrete dynamical systems so that each can be translated and compared to one another. Their temporal logic is also flexible enough that it can serve as a framework for other logics that work with similar models. 
The book begins with a discussion of behavior types, interval domains, and translation invariance, which serves as the groundwork for temporal type theory. From there, the authors lay out the logical preliminaries they need for their temporal modalities and explain the soundness of those logical semantics. These results are then applied to hybrid dynamical systems, differential equations, and labeled transition systems. A case study involving aircraft separation within the National Airspace System is provided to illustrate temporal type theory in action.  
Researchers in computer science, logic, and mathematics interested in topos-theoretic and category-theory-friendly approaches to system behavior will find this monograph to be an important resource.  It can also serve as a supplemental text for a specialized graduate topics course. 

Table of contents (8 chapters)

Table of contents (8 chapters)
  • Introduction

    Schultz, Patrick (et al.)

    Pages 1-15

  • The Interval Domain

    Schultz, Patrick (et al.)

    Pages 17-37

  • Translation Invariance

    Schultz, Patrick (et al.)

    Pages 39-45

  • Logical Preliminaries

    Schultz, Patrick (et al.)

    Pages 47-86

  • Axiomatics

    Schultz, Patrick (et al.)

    Pages 87-114

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-030-00704-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-030-00703-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Temporal Type Theory
Book Subtitle
A Topos-Theoretic Approach to Systems and Behavior
Authors
Series Title
Progress in Computer Science and Applied Logic
Series Volume
29
Copyright
2019
Publisher
Birkhäuser Basel
Copyright Holder
The Author(s)
eBook ISBN
978-3-030-00704-1
DOI
10.1007/978-3-030-00704-1
Hardcover ISBN
978-3-030-00703-4
Series ISSN
2297-0576
Edition Number
1
Number of Pages
VIII, 235
Number of Illustrations
60 b/w illustrations, 7 illustrations in colour
Topics