rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Temporal Type Theory
    sub title: A Topos-Theoretic Approach to Systems and Behavior
  name:
    name part: Schultz, Patrick.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Spivak, David I.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2019
    edition: 1st ed. 2019.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 235 p. 67 illus., 7 illus. in color. online resource.
  abstract: 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. .
  table of contents: Introduction -- The Interval Domain -- Translation Invariance -- Logical Preliminaries -- Axiomatics -- Semantics and Soundness -- Local Numeric Types and Derivatives -- Applications -- Appendices -- Bibliography -- Index.
  note: by Patrick Schultz, David I. Spivak.
  subject:
    topic: Category theory (Mathematics)
  subject:
    topic: Homological algebra
  subject:
    topic: Mathematical logic
  subject:
    topic: System theory
  subject:
    topic: Aerospace engineering
  subject:
    topic: Astronautics
  subject:
    topic: Category Theory, Homological Algebra
  subject:
    topic: Mathematical Logic and Foundations
  subject:
    topic: Systems Theory, Control
  subject:
    topic: Mathematical Logic and Formal Languages
  subject:
    topic: Aerospace Technology and Astronautics
  classification: QA169
  classification: 512.6
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Progress in Computer Science and Applied Logic, 29
  identifier: 9783030007041
  identifier: https://doi.org/10.1007/978-3-030-00704-1
  record info:
    record creation date: 190129
    record change date: 20191024072347.0
    record identifier: 978-3-030-00704-1