Temporal Type Theory: A Topos-Theoretic Approach to Systems and Behavior: 29 (Progress in Computer Science and Applied Logic, 29) - Tapa dura

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9783030007034: Temporal Type Theory: A Topos-Theoretic Approach to Systems and Behavior: 29 (Progress in Computer Science and Applied Logic, 29)
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ISBN 10: 3030007030 ISBN 13: 9783030007034
Editorial: Springer, 2019

Sinopsis

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. 

"Sinopsis" puede pertenecer a otra edición de este libro.

De la contraportada

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 resultsare 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. 

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2019
Idioma
Inglés
ISBN 10 
3030007030
ISBN 13 
9783030007034
Encuadernación
Tapa dura
Número de edición
1
Número de páginas
244
Contacto del fabricante
no disponible
Persona responsable
ProductSafety@springernature.com
ProductSafety@springernature.com

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