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Author: Patrick Schultz
Publisher: Springer
ISBN: 3030007049
Category : Mathematics
Languages : en
Pages : 237
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Book Description
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.
Author: Patrick Schultz
Publisher: Springer
ISBN: 3030007049
Category : Mathematics
Languages : en
Pages : 237
Get Book Here
Book Description
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.
Author: David Corfield
Publisher: Oxford University Press
ISBN: 0192595032
Category : Philosophy
Languages : en
Pages : 191
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Book Description
"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.
Author: Patrick Blackburn
Publisher: Elsevier
ISBN: 9780080466668
Category : Mathematics
Languages : en
Pages : 1260
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Book Description
The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners approaching the subject for the first time, and advanced articles, which will help those already familiar with the field to deepen their expertise. Please visit: http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html - Compact modal logic reference - Computational approaches fully discussed - Contemporary applications of modal logic covered in depth
Author: Dean Rickles
Publisher: Clarendon Press
ISBN: 0191515027
Category : Science
Languages : en
Pages : 288
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Book Description
Quantum gravity is the name given to a theory that unites general relativity - Einstein's theory of gravitation and spacetime - with quantum field theory, our framework for describing non-gravitational forces. The Structural Foundations of Quantum Gravity brings together philosophers and physicists to discuss a range of conceptual issues that surface in the effort to unite these theories, focusing in particular on the ontological nature of the spacetime that results. Although there has been a great deal written about quantum gravity from the perspective of physicists and mathematicians, very little attention has been paid to the philosophical aspects. This volume closes that gap, with essays written by some of the leading researchers in the field. Individual papers defend or attack a structuralist perspective on the fundamental ontologies of our physical theories, which offers the possibility of shedding new light on a number of foundational problems. It is a book that will be of interest not only to physicists and philosophers of physics but to anyone concerned with foundational issues and curious to explore new directions in our understanding of spacetime and quantum physics.
Author: Stefan Sudhoff
Publisher: Walter de Gruyter
ISBN: 3110914646
Category : Language Arts & Disciplines
Languages : en
Pages : 405
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Book Description
This book contains a collection of cutting-edge papers on methodological aspects of prosody research. Current approaches to the gathering, treatment, and interpretation of prosodic data are discussed by experts in the field, illustrated by their own empirical research. Contributions focus on the choice and measurement of prosodic parameters, the establishment of prosodic categories, annotation structures for spoken-language data, and experimental methods for production and perception studies (including the construction of materials, modes of presentation, online vs. offline tasks, judgement scales, data processing, and statistical evaluation). The volume will serve as a handbook linking data collection and interpretation, allowing researchers in linguistics and related fields to make more informed decisions concerning their empirical work in prosody.
Author: Arend Rensink
Publisher: Springer
ISBN: 3319933175
Category : Computers
Languages : en
Pages : 203
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Book Description
This book constitutes the refereed proceedings of the 11th International Conference on Model Transformation, ICMT 2018, held as part of STAF 2018, in Toulouse, France, in June 2018. The 9 full papers were carefully reviewed and selected from 24 submissions. This book also presents 1 invited paper. The papers include research, application, and tool demonstration papers presented in the context of four sessions on verification of model transformations, model transformation tools, transformation reuse and graph transformations.
Author: S. Mehlberg
Publisher: Springer Science & Business Media
ISBN: 9400989350
Category : Science
Languages : en
Pages : 321
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Book Description
An intermittent but mentally quite disabling illness prevented Henry Mehlberg from becoming recognized more widely as the formidable scholar he was, when at his best. During World War II, he had lived in hiding under the false identity of an egg farmer, when the Nazis occupied his native Poland. After relatively short academic appointments at the University of Toronto and at Princeton University, he taught at the University of Chicago until reaching the age of normal retirement. But partly at the initiative of his Chicago colleague Charles Morris, who had preceded him to a 'post-retirement' profes sorship at the University of Florida in Gainesville, and with the support of Eugene Wigner, he then received an appointment at that University, where he remained until his death in 1979. In Chicago, he organized a discussion group of scholars from that area as a kind of small scale model of the Vienna Circle, which met at his apart ment, where he lived with his first wife Janina, a mathematician. It was during this Chicago period that the functional disturbances from his illness were pronounced and not infrequent. The very unfortunate result was that colleagues who had no prior knowledge of the caliber of his writings in Polish and French or of his very considerable intellectual powers, had little incentive to read his published work, which he had begun to write in English.
Author: Henry Mehlberg
Publisher: Springer Science & Business Media
ISBN: 9789027707215
Category : Causality (Physics)
Languages : en
Pages : 338
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Book Description
Author: B. Jacobs
Publisher: Gulf Professional Publishing
ISBN: 9780444508539
Category : Computers
Languages : en
Pages : 784
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Book Description
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
Author: William Lawless
Publisher: Academic Press
ISBN: 0128176377
Category : Computers
Languages : en
Pages : 306
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Book Description
Artificial Intelligence for the Internet of Everything considers the foundations, metrics and applications of IoE systems. It covers whether devices and IoE systems should speak only to each other, to humans or to both. Further, the book explores how IoE systems affect targeted audiences (researchers, machines, robots, users) and society, as well as future ecosystems. It examines the meaning, value and effect that IoT has had and may have on ordinary life, in business, on the battlefield, and with the rise of intelligent and autonomous systems. Based on an artificial intelligence (AI) perspective, this book addresses how IoE affects sensing, perception, cognition and behavior. Each chapter addresses practical, measurement, theoretical and research questions about how these "things may affect individuals, teams, society or each other. Of particular focus is what may happen when these "things begin to reason, communicate and act autonomously on their own, whether independently or interdependently with other "things. - Considers the foundations, metrics and applications of IoE systems - Debates whether IoE systems should speak to humans and each other - Explores how IoE systems affect targeted audiences and society - Discusses theoretical IoT ecosystem models
