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Temporal type theory = a topos-theor...

Schultz, Patrick.

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Temporal type theory = a topos-theoretic approach to systems and behavior /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Temporal type theory/ by Patrick Schultz, David I. Spivak.
Reminder of title:	a topos-theoretic approach to systems and behavior /
Author:	Schultz, Patrick.
other author:	Spivak, David I.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	viii, 235 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- The Interval Domain -- Translation Invariance -- Logical Preliminaries -- Axiomatics -- Semantics and Soundness -- Local Numeric Types and Derivatives -- Applications -- Appendices -- Bibliography -- Index.
Contained By:	Springer eBooks
Subject:	System theory. -
Online resource:	https://doi.org/10.1007/978-3-030-00704-1
ISBN:	9783030007041

Temporal type theory = a topos-theoretic approach to systems and behavior /
Schultz, Patrick.

Temporal type theorya topos-theoretic approach to systems and behavior /[electronic resource] :by Patrick Schultz, David I. Spivak. - Cham :Springer International Publishing :2019. - viii, 235 p. :ill., digital ;24 cm. - Progress in computer science and applied logic,292297-0576 ;. - Progress in computer science and applied logic ;29..

Introduction -- The Interval Domain -- Translation Invariance -- Logical Preliminaries -- Axiomatics -- Semantics and Soundness -- Local Numeric Types and Derivatives -- Applications -- Appendices -- Bibliography -- Index.

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.

ISBN: 9783030007041

Standard No.: 10.1007/978-3-030-00704-1doiSubjects--Topical Terms:

525574
System theory.

LC Class. No.: Q295 / .S385 2019

Dewey Class. No.: 003

Temporal type theory = a topos-theoretic approach to systems and behavior /
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245 1 0 $a Temporal type theory $h [electronic resource] : $b a topos-theoretic approach to systems and behavior / $c by Patrick Schultz, David I. Spivak.
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300 $a viii, 235 p. : $b ill., digital ; $c 24 cm.
490 1 $a Progress in computer science and applied logic, $x 2297-0576 ; $v 29
505 0 $a Introduction -- The Interval Domain -- Translation Invariance -- Logical Preliminaries -- Axiomatics -- Semantics and Soundness -- Local Numeric Types and Derivatives -- Applications -- Appendices -- Bibliography -- Index.
520 $a 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.
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