Temporal Type Theory
Temporal Type Theory

Author: Patrick Schultz

Publisher: Springer

Published: 2019-01-29

Total Pages: 237

ISBN-13: 3030007049

DOWNLOAD EBOOK

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
Modal Homotopy Type Theory

Author: David Corfield

Publisher: Oxford University Press

Published: 2020-02-06

Total Pages: 208

ISBN-13: 0192595032

DOWNLOAD EBOOK

"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.

Methods in Empirical Prosody Research
Methods in Empirical Prosody Research

Author: Stefan Sudhoff

Publisher: Walter de Gruyter

Published: 2012-02-13

Total Pages: 405

ISBN-13: 3110914646

DOWNLOAD EBOOK

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.

Programming Languages and Systems
Programming Languages and Systems

Author: Thomas Wies

Publisher: Springer Nature

Published: 2023-04-16

Total Pages: 579

ISBN-13: 3031300440

DOWNLOAD EBOOK

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.

The Ontology of Time
The Ontology of Time

Author: L. Nathan Oaklander

Publisher: Prometheus Books

Published: 2013-05-24

Total Pages: 366

ISBN-13: 1615923217

DOWNLOAD EBOOK

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.

The Handbook of Contemporary Semantic Theory
The Handbook of Contemporary Semantic Theory

Author: Shalom Lappin

Publisher: John Wiley & Sons

Published: 2019-02-12

Total Pages: 771

ISBN-13: 1119046823

DOWNLOAD EBOOK

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

Sheaf Theory through Examples
Sheaf Theory through Examples

Author: Daniel Rosiak

Publisher: MIT Press

Published: 2022-10-25

Total Pages: 454

ISBN-13: 0262542153

DOWNLOAD EBOOK

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.

History and Philosophy of Constructive Type Theory
History and Philosophy of Constructive Type Theory

Author: Giovanni Sommaruga

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 377

ISBN-13: 9401593930

DOWNLOAD EBOOK

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.

Mathematics for Future Computing and Communications
Mathematics for Future Computing and Communications

Author: Liao Heng

Publisher: Cambridge University Press

Published: 2021-12-16

Total Pages: 400

ISBN-13: 100908223X

DOWNLOAD EBOOK

For 80 years, mathematics has driven fundamental innovation in computing and communications. This timely book provides a panorama of some recent ideas in mathematics and how they will drive continued innovation in computing, communications and AI in the coming years. It provides a unique insight into how the new techniques that are being developed can be used to provide theoretical foundations for technological progress, just as mathematics was used in earlier times by Turing, von Neumann, Shannon and others. Edited by leading researchers in the field, chapters cover the application of new mathematics in computer architecture, software verification, quantum computing, compressed sensing, networking, Bayesian inference, machine learning, reinforcement learning and many other areas.

Theorem Proving in Higher Order Logics
Theorem Proving in Higher Order Logics

Author: Mark Aagaard

Publisher: Springer

Published: 2007-07-23

Total Pages: 546

ISBN-13: 3540446591

DOWNLOAD EBOOK

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.