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Temporal Type Theory = A Topos-Theoretic Approach to Systems and Behavior /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Temporal Type Theory/ by Patrick Schultz, David I. Spivak.
其他題名:	A Topos-Theoretic Approach to Systems and Behavior /
作者:	Schultz, Patrick.
其他作者:	Spivak, David I.
面頁冊數:	VIII, 235 p. 67 illus., 7 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Category theory (Mathematics). -
電子資源:	https://doi.org/10.1007/978-3-030-00704-1
ISBN:	9783030007041

Temporal Type Theory = A Topos-Theoretic Approach to Systems and Behavior /
Schultz, Patrick.

Temporal Type TheoryA Topos-Theoretic Approach to Systems and Behavior /[electronic resource] :by Patrick Schultz, David I. Spivak. - 1st ed. 2019. - VIII, 235 p. 67 illus., 7 illus. in color.online resource. - Progress in Computer Science and Applied Logic,292297-0576 ;. - Progress in Computer Science and Applied Logic,28.

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

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. .

ISBN: 9783030007041

Standard No.: 10.1007/978-3-030-00704-1doiSubjects--Topical Terms:

1255325
Category theory (Mathematics).

LC Class. No.: QA169

Dewey Class. No.: 512.6

Temporal Type Theory = A Topos-Theoretic Approach to Systems and Behavior /
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