國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Temporal type theorya topos-theoreti...

Schultz, Patrick.

Temporal type theorya topos-theoretic approach to systems and behavior /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Temporal type theoryby 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.
出版者:	Cham :Springer International Publishing :2019.
面頁冊數:	viii, 235 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	System theory.
電子資源:	https://doi.org/10.1007/978-3-030-00704-1
ISBN:	9783030007041$q(electronic bk.)

Temporal type theorya 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. - Cham :Springer International Publishing :2019. - viii, 235 p. :ill., digital ;24 cm. - Progress in computer science and applied logic,292297-0576 ;. - Progress in computer science and applied logic ;v.26..

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$q(electronic bk.)

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

183989
System theory.

LC Class. No.: Q295 / .S385 2019

Dewey Class. No.: 003

Temporal type theorya topos-theoretic approach to systems and behavior /
LDR:02832nmm a2200349 a 4500 001 552924
003 DE-He213
005 20190808105701.0
006 m d
007 cr nn 008maaau
008 191107s2019 gw s 0 eng d
020 $a 9783030007041$q(electronic bk.)
020 $a 9783030007034$q(paper)
024 7 $a 10.1007/978-3-030-00704-1 $2 doi
035 $a 978-3-030-00704-1
040 $a GP $c GP
041 0 $a eng
050 4 $a Q295 $b .S385 2019
072 7 $a PBC $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBC $2 thema
072 7 $a PBF $2 thema
082 0 4 $a 003 $2 23
090 $a Q295 $b .S387 2019
100 1 $a Schultz, Patrick. $3 833889
245 1 0 $a Temporal type theory $h [electronic resource] : $b a topos-theoretic approach to systems and behavior / $c by Patrick Schultz, David I. Spivak.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2019.
300 $a viii, 235 p. : $b ill., digital ; $c 24 cm.
490 1 $a Progress in computer science and applied logic, $x 2297-0576 ; $v 29
505 0 $a Introduction -- The Interval Domain -- Translation Invariance -- Logical Preliminaries -- Axiomatics -- Semantics and Soundness -- Local Numeric Types and Derivatives -- Applications -- Appendices -- Bibliography -- Index.
520 $a 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.
650 0 $a System theory. $3 183989
650 1 4 $a Category Theory, Homological Algebra. $3 275954
650 2 4 $a Mathematical Logic and Foundations. $3 274479
650 2 4 $a Systems Theory, Control. $3 274654
650 2 4 $a Mathematical Logic and Formal Languages. $3 275383
650 2 4 $a Aerospace Technology and Astronautics. $3 309707
700 1 $a Spivak, David I. $3 833890
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Progress in computer science and applied logic ; $v v.26. $3 684056
856 4 0 $u https://doi.org/10.1007/978-3-030-00704-1
950 $a Mathematics and Statistics (Springer-11649)