Temporal Type Theory A Topos-Theoretic Approach to Systems and Behavior
tarafından
Schultz, Patrick. author.
Başlık
:
Temporal Type Theory A Topos-Theoretic Approach to Systems and Behavior
Yazar
:
Schultz, Patrick. author.
ISBN
:
9783030007041
Yazar
:
Schultz, Patrick. author.
Edisyon
:
1st ed. 2019.
Fiziksel Niteleme
:
VIII, 235 p. 67 illus., 7 illus. in color. online resource.
Seri
:
Progress in Computer Science and Applied Logic, 29
İçindekiler
:
Introduction -- The Interval Domain -- Translation Invariance -- Logical Preliminaries -- Axiomatics -- Semantics and Soundness -- Local Numeric Types and Derivatives -- Applications -- Appendices -- Bibliography -- Index.
Özet
:
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. .
Konu Başlığı
:
Category theory (Mathematics).
Homological algebra.
Mathematical logic.
System theory.
Aerospace engineering.
Astronautics.
Category Theory, Homological Algebra. https://scigraph.springernature.com/ontologies/product-market-codes/M11035
Mathematical Logic and Foundations. https://scigraph.springernature.com/ontologies/product-market-codes/M24005
Systems Theory, Control. https://scigraph.springernature.com/ontologies/product-market-codes/M13070
Mathematical Logic and Formal Languages. https://scigraph.springernature.com/ontologies/product-market-codes/I16048
Aerospace Technology and Astronautics. https://scigraph.springernature.com/ontologies/product-market-codes/T17050
Yazar Ek Girişi
:
Spivak, David I.
Ek Kurum Yazar
:
SpringerLink (Online service)
Elektronik Erişim
:
Materyal Türü | Barkod | Yer Numarası | Durumu/İade Tarihi |
---|
Electronic Book | 428118-1001 | QA169 | Springer E-Book Collection |