عنوان

Temporal type theory :

(Number (ISBN

3030007049

(Number (ISBN

9783030007041

Erroneous ISBN

3030007030

Erroneous ISBN

9783030007034

Title Proper

Temporal type theory :

General Material Designation

[Book]

Other Title Information

a topos-theoretic approach to systems and behavior /

First Statement of Responsibility

Patrick Schultz, David I. Spivak.

Place of Publication, Distribution, etc.

Cham, Switzerland :

Name of Publisher, Distributor, etc.

Birkhauser,

Date of Publication, Distribution, etc.

[2019]

Specific Material Designation and Extent of Item

1 online resource

Series Title

Progress in computer science and applied logic,

Volume Designation

v. 29

ISSN of Series

2297-0576 ;

Text of Note

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

0

Text of Note

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.

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9783030007041

Title

Temporal type theory.

International Standard Book Number

9783030007034

System theory.

System theory.

Number

Edition

Class number

Book number

Schultz, Patrick

Spivak, David I.,1978-

Date of Transaction

20200823072120.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y