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Cover: 9783030007034 | Temporal Type Theory | David I. Spivak (u. a.) | Buch | Englisch
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Temporal Type Theory
A Topos-Theoretic Approach to Systems and Behavior
Buch von David I. Spivak (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung

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

Inhaltsverzeichnis
Introduction.- The Interval Domain.- Translation Invariance.- Logical Preliminaries.- Axiomatics.- Semantics and Soundness.- Local Numeric Types and Derivatives.- Applications.- Appendices.- Bibliography.- Index.
Details
Erscheinungsjahr: 2019
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 244
Reihe: Progress in Computer Science and Applied Logic
Inhalt: viii
235 S.
60 s/w Illustr.
7 farbige Illustr.
235 p. 67 illus.
7 illus. in color.
ISBN-13: 9783030007034
ISBN-10: 3030007030
Sprache: Englisch
Herstellernummer: 978-3-030-00703-4
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Spivak, David I.
Schultz, Patrick
Auflage: 1st ed. 2019
Hersteller: Springer International Publishing
Progress in Computer Science and Applied Logic
Maße: 241 x 160 x 19 mm
Von/Mit: David I. Spivak (u. a.)
Erscheinungsdatum: 11.02.2019
Gewicht: 0,535 kg
preigu-id: 114174818
Zusammenfassung

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

Inhaltsverzeichnis
Introduction.- The Interval Domain.- Translation Invariance.- Logical Preliminaries.- Axiomatics.- Semantics and Soundness.- Local Numeric Types and Derivatives.- Applications.- Appendices.- Bibliography.- Index.
Details
Erscheinungsjahr: 2019
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 244
Reihe: Progress in Computer Science and Applied Logic
Inhalt: viii
235 S.
60 s/w Illustr.
7 farbige Illustr.
235 p. 67 illus.
7 illus. in color.
ISBN-13: 9783030007034
ISBN-10: 3030007030
Sprache: Englisch
Herstellernummer: 978-3-030-00703-4
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Spivak, David I.
Schultz, Patrick
Auflage: 1st ed. 2019
Hersteller: Springer International Publishing
Progress in Computer Science and Applied Logic
Maße: 241 x 160 x 19 mm
Von/Mit: David I. Spivak (u. a.)
Erscheinungsdatum: 11.02.2019
Gewicht: 0,535 kg
preigu-id: 114174818
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