Overview
- 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
Part of the book series: Progress in Computer Science and Applied Logic (PCS, volume 29)
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Table of contents (8 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Temporal Type Theory
Book Subtitle: A Topos-Theoretic Approach to Systems and Behavior
Authors: Patrick Schultz, David I. Spivak
Series Title: Progress in Computer Science and Applied Logic
DOI: https://doi.org/10.1007/978-3-030-00704-1
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2019
Hardcover ISBN: 978-3-030-00703-4Published: 11 February 2019
eBook ISBN: 978-3-030-00704-1Published: 29 January 2019
Series ISSN: 2297-0576
Series E-ISSN: 2297-0584
Edition Number: 1
Number of Pages: VIII, 235
Number of Illustrations: 60 b/w illustrations, 7 illustrations in colour
Topics: Category Theory, Homological Algebra, Mathematical Logic and Foundations, Systems Theory, Control, Mathematical Logic and Formal Languages, Aerospace Technology and Astronautics