Temporal Type Theory
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Temporal Type Theory
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Author : Patrick Schultz
language : en
Publisher: Springer
Release Date : 2019-01-29
Temporal Type Theory written by Patrick Schultz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-29 with Mathematics categories.
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.
Modal Homotopy Type Theory
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Author : David Corfield
language : en
Publisher: Oxford University Press
Release Date : 2020-02-06
Modal Homotopy Type Theory written by David Corfield and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-06 with Philosophy categories.
"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.
An Invitation To Applied Category Theory
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Author : Brendan Fong
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-18
An Invitation To Applied Category Theory written by Brendan Fong and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-18 with Computers categories.
Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.
Mathematics For Future Computing And Communications
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Author : Liao Heng
language : en
Publisher: Cambridge University Press
Release Date : 2021-12-16
Mathematics For Future Computing And Communications written by Liao Heng and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-16 with Computers categories.
A panorama of new ideas in mathematics that are driving innovation in computing and communications.
Sheaf Theory Through Examples
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Author : Daniel Rosiak
language : en
Publisher: MIT Press
Release Date : 2022-10-25
Sheaf Theory Through Examples written by Daniel Rosiak and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-25 with Mathematics categories.
An approachable introduction to elementary sheaf theory and its applications beyond pure math. Sheaves are mathematical constructions concerned with passages from local properties to global ones. They have played a fundamental role in the development of many areas of modern mathematics, yet the broad conceptual power of sheaf theory and its wide applicability to areas beyond pure math have only recently begun to be appreciated. Taking an applied category theory perspective, Sheaf Theory through Examples provides an approachable introduction to elementary sheaf theory and examines applications including n-colorings of graphs, satellite data, chess problems, Bayesian networks, self-similar groups, musical performance, complexes, and much more. With an emphasis on developing the theory via a wealth of well-motivated and vividly illustrated examples, Sheaf Theory through Examples supplements the formal development of concepts with philosophical reflections on topology, category theory, and sheaf theory, alongside a selection of advanced topics and examples that illustrate ideas like cellular sheaf cohomology, toposes, and geometric morphisms. Sheaf Theory through Examples seeks to bridge the powerful results of sheaf theory as used by mathematicians and real-world applications, while also supplementing the technical matters with a unique philosophical perspective attuned to the broader development of ideas.
Programming Languages And Systems
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Author : Thomas Wies
language : en
Publisher: Springer Nature
Release Date : 2023-04-16
Programming Languages And Systems written by Thomas Wies and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-16 with Computers categories.
This open access book constitutes the proceedings of the 32nd European Symposium on Programming, ESOP 2023, which was held during April 22-27, 2023, in Paris, France, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2023. The 20 regular papers presented in this volume were carefully reviewed and selected from 55 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems.
Theorem Proving In Higher Order Logics
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Author : Mark Aagaard
language : en
Publisher: Springer
Release Date : 2007-07-23
Theorem Proving In Higher Order Logics written by Mark Aagaard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-23 with Computers categories.
This volume is the proceedings of the 13th International Conference on Theo rem Proving in Higher Order Logics (TPHOLs 2000) held 14-18 August 2000 in Portland, Oregon, USA. Each of the 55 papers submitted in the full rese arch category was refereed by at least three reviewers who were selected by the program committee. Because of the limited space available in the program and proceedings, only 29 papers were accepted for presentation and publication in this volume. In keeping with tradition, TPHOLs 2000 also offered a venue for the presen tation of work in progress, where researchers invite discussion by means of a brief preliminary talk and then discuss their work at a poster session. A supplemen tary proceedings containing associated papers for work in progress was published by the Oregon Graduate Institute (OGI) as technical report CSE-00-009. The organizers are grateful to Bob Colwell, Robin Milner and Larry Wos for agreeing to give invited talks. Bob Colwell was the lead architect on the Intel P6 microarchitecture, which introduced a number of innovative techniques and achieved enormous commercial success. As such, he is ideally placed to offer an industrial perspective on the challenges for formal verification. Robin Milner contributed many key ideas to computer theorem proving, and to functional programming, through his leadership of the influential Edinburgh LCF project.
Fundamentals Of Hearing
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Author : William Yost
language : en
Publisher: BRILL
Release Date : 2022-11-14
Fundamentals Of Hearing written by William Yost and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-14 with Medical categories.
Cooperative Multimodal Communication
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Author : Harry Bunt
language : en
Publisher: Springer
Release Date : 2003-06-30
Cooperative Multimodal Communication written by Harry Bunt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-30 with Computers categories.
This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Cooperative Multimodal Communication, CMC'98, held in Tilburg, The Netherlands, in January 1998. The 13 revised full papers presented together with an introductory survey by the volume editors have passed through two rounds of reviewing, selection, and revision. The book offers topical sections on multimodal generation, multimodal cooperation, multimodal interpretation, and multimedia platforms and test environments.
Modern Perspectives In Type Theoretical Semantics
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Author : Stergios Chatzikyriakidis
language : en
Publisher: Springer
Release Date : 2017-02-07
Modern Perspectives In Type Theoretical Semantics written by Stergios Chatzikyriakidis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-07 with Language Arts & Disciplines categories.
This book is a collective volume that reports the state of the art in the applications of type theory to linguistic semantics. The volume fills a 20 year gap from the last published book on the issue and aspires to bring researchers closer to cutting edge alternatives in formal semantics research. It consists of unpublished work by some key researchers on various issues related to the type theoretical study of formal semantics and further exemplifies the advantages of using modern type theoretical approaches to linguistic semantics. Themes that are covered include modern developments of type theories in formal semantics, foundational issues in linguistic semantics like anaphora, modality and plurals, innovational interdisciplinary research like the introduction of probability theory to type theories as well as computational implementations of type theoretical approaches. This volume will be of great interest to formal semanticists that are looking for alternative ways to study linguistic semantics, but will also be of interest to theoretical computer scientists and mathematicians that are interested in the applications of type theory.