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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 : 208
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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: 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: Thomas Wies
Publisher: Springer Nature
ISBN: 3031300440
Category : Computers
Languages : en
Pages : 579
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Book Description
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.
Author: L. Nathan Oaklander
Publisher: Prometheus Books
ISBN: 1615923217
Category : Philosophy
Languages : en
Pages : 366
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Book Description
Studies in Analytic PhilosophySeries Editor: Quentin Smith, Western Michigan UniversityL. Nathan Oaklander is one of the leading philosophers of time defending the tenseless or B-Theory of time. He has remained at the forefront of this field since the early 1980s and today he is arguably the most formidable opponent of the tensed or A-theory of time. Much of the direction of the debate in this field for the past twenty years or so, especially in regards to the new tenseless theory of time, has been influenced by Oaklander's work. This book presents a carefully argued defense of the tenseless theory of time.The topics discussed include: the ontology of A- and B-theories of time; presentism; the open future theory; the A/B theory; defending the B-theory of time; temporal experience; temporal semantics; and time, identity, responsibility, and freedom.L. Nathan Oaklander (Flint, MI) is professor of philosophy and chair of the Department of Philosophy at the University of Michigan, Flint. He is the author or editor of numerous books on philosophy and the problem of time, including Time, Change and Freedom and The Importance of Time.
Author: Fred Kröger
Publisher: Springer Science & Business Media
ISBN: 3540674012
Category : Computers
Languages : en
Pages : 440
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Book Description
Temporal logic has developed over the last 30 years into a powerful formal setting for the specification and verification of state-based systems. Based on university lectures given by the authors, this book is a comprehensive, concise, uniform, up-to-date presentation of the theory and applications of linear and branching time temporal logic; TLA (Temporal Logic of Actions); automata theoretical connections; model checking; and related theories. All theoretical details and numerous application examples are elaborated carefully and with full formal rigor, and the book will serve as a basic source and reference for lecturers, graduate students and researchers.
Author: Shalom Lappin
Publisher: John Wiley & Sons
ISBN: 1119046823
Category : Language Arts & Disciplines
Languages : en
Pages : 771
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Book Description
The second edition of The Handbook of Contemporary Semantic Theory presents a comprehensive introduction to cutting-edge research in contemporary theoretical and computational semantics. Features completely new content from the first edition of The Handbook of Contemporary Semantic Theory Features contributions by leading semanticists, who introduce core areas of contemporary semantic research, while discussing current research Suitable for graduate students for courses in semantic theory and for advanced researchers as an introduction to current theoretical work
Author: Daniel Rosiak
Publisher: MIT Press
ISBN: 0262542153
Category : Mathematics
Languages : en
Pages : 454
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Book Description
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.
Author: Giovanni Sommaruga
Publisher: Springer Science & Business Media
ISBN: 9401593930
Category : Philosophy
Languages : en
Pages : 377
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Book Description
A comprehensive survey of Martin-Löf's constructive type theory, considerable parts of which have only been presented by Martin-Löf in lecture form or as part of conference talks. Sommaruga surveys the prehistory of type theory and its highly complex development through eight different stages from 1970 to 1995. He also provides a systematic presentation of the latest version of the theory, as offered by Martin-Löf at Leiden University in Fall 1993. This presentation gives a fuller and updated account of the system. Earlier, brief presentations took no account of the issues related to the type-theoretical approach to logic and the foundations of mathematics, while here they are accorded an entire part of the book. Readership: Comprehensive accounts of the history and philosophy of constructive type theory and a considerable amount of related material. Readers need a solid background in standard logic and a first, basic acquaintance with type theory.
Author: Brendan Fong
Publisher: Cambridge University Press
ISBN: 1108582249
Category : Mathematics
Languages : en
Pages : 351
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Book Description
Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.
