Download or read book Modal Homotopy Type Theory written by David Corfield and published by Oxford University Press. This book was released on 2020-02-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Download or read book Many Dimensional Modal Logics Theory and Applications written by A. Kurucz and published by Elsevier. This book was released on 2003-10-21 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects.To study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery.We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics.The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources.The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well.Key Features:• Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science• Written by internationally leading researchers in the field of pure and applied logic• Combines mathematical theory of modal logic and applications in artificial intelligence and computer science• Numerous open problems for further research• Well illustrated with pictures and tables

Download or read book Modalogy written by Jeff Brent and published by Hal Leonard Corporation. This book was released on 2011-10-01 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Jazz Instruction). Primarily a music theory reference, Modalogy presents a unique perspective on the origins, interlocking aspects, and usage of the most common scales and modes in occidental music. Anyone wishing to seriously explore the realms of scales, modes, and their real-world functions will find the most important issues dealt with in meticulous detail within these pages. Logical illustrations accompany in-depth examinations of chordal harmonies, cadential motions, and progressions. This book is perfect for both music students and teachers, as either a course in itself or to augment any theory curriculum.

Download or read book Modal Testing written by D. J. Ewins and published by John Wiley & Sons. This book was released on 2009-07-20 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: All the steps involved in planning, executing, interpreting and applying the results from a modal test are described in straightforward terms. This edition has brought the previous book up to date by including all the new and improved techniques that have emerged during the 15 years since the first edition was written, especially those of signal processing and modal analysis. New topics are introduced, notable amongst them are the application of modal testing to rotating machinery and the use of scanning laser vibrometer.

Download or read book The Medieval Heritage in Early Modern Metaphysics and Modal Theory 1400 1700 written by R.L. Friedman and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores key aspects of the transmission of learning and the transformation of thought from the late Middle Ages to the early modern period. The topics dealt with include metaphysics as a science, the rise of probabilistic modality, freedom of the human will, as well as the role and validity of logical reasoning in speculative theology. The volume will be of interest to scholars who work on medieval and early modern philosophy, theology, and intellectual history.

Download or read book The Berklee Book of Jazz Harmony written by Joe Mulholland and published by Hal Leonard Corporation. This book was released on 2013-08-01 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Berklee Guide). Learn jazz harmony, as taught at Berklee College of Music. This text provides a strong foundation in harmonic principles, supporting further study in jazz composition, arranging, and improvisation. It covers basic chord types and their tensions, with practical demonstrations of how they are used in characteristic jazz contexts and an accompanying recording that lets you hear how they can be applied.

Download or read book Aristotle s Modal Syllogistic written by Marko Malink and published by Harvard University Press. This book was released on 2013-11-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aristotle was the founder not only of logic but also of modal logic. In the Prior Analytics he developed a complex system of modal syllogistic which, while influential, has been disputed since antiquity—and is today widely regarded as incoherent. In this meticulously argued new study, Marko Malink presents a major reinterpretation of Aristotle’s modal syllogistic. Combining analytic rigor with keen sensitivity to historical context, he makes clear that the modal syllogistic forms a consistent, integrated system of logic, one that is closely related to other areas of Aristotle’s philosophy. Aristotle’s modal syllogistic differs significantly from modern modal logic. Malink considers the key to understanding the Aristotelian version to be the notion of predication discussed in the Topics—specifically, its theory of predicables (definition, genus, differentia, proprium, and accident) and the ten categories (substance, quantity, quality, and so on). The predicables introduce a distinction between essential and nonessential predication. In contrast, the categories distinguish between substantial and nonsubstantial predication. Malink builds on these insights in developing a semantics for Aristotle’s modal propositions, one that verifies the ancient philosopher’s claims of the validity and invalidity of modal inferences. Malink recognizes some limitations of this reconstruction, acknowledging that his proof of syllogistic consistency depends on introducing certain complexities that Aristotle could not have predicted. Nonetheless, Aristotle’s Modal Syllogistic brims with bold ideas, richly supported by close readings of the Greek texts, and offers a fresh perspective on the origins of modal logic.

Download or read book The Modal Future written by Fabrizio Cariani and published by Cambridge University Press. This book was released on 2021-07 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the interactions between the semantics, epistemology and metaphysics of the future.

Download or read book Proof Theory of Modal Logic written by Heinrich Wansing and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

Download or read book The Nature of Contingency written by Alastair Wilson and published by Oxford University Press, USA. This book was released on 2020-01-30 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book defends a radical new theory of contingency as a physical phenomenon. Drawing on the many-worlds approach to quantum theory and cutting-edge metaphysics and philosophy of science, it argues that quantum theories are best understood as telling us about the space of genuine possibilities, rather than as telling us solely about actuality. When quantum physics is taken seriously in the way first proposed by Hugh Everett III, it provides the resources for a new systematic metaphysical framework encompassing possibility, necessity, actuality, chance, counterfactuals, and a host of related modal notions. Rationalist metaphysicians argue that the metaphysics of modality is strictly prior to any scientific investigation; metaphysics establishes which worlds are possible, and physics merely checks which of these worlds is actual. Naturalistic metaphysicians respond that science may discover new possibilities and new impossibilities. This book's quantum theory of contingency takes naturalistic metaphysics one step further, allowing that science may discover what it is to be possible. As electromagnetism revealed the nature of light, as acoustics revealed the nature of sound, as statistical mechanics revealed the nature of heat, so quantum physics reveals the nature of contingency.

Download or read book Modal Logic as Metaphysics written by Timothy Williamson and published by Oxford University Press. This book was released on 2013-03-28 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

Download or read book Modal Logic written by Patrick Blackburn and published by Cambridge University Press. This book was released on 2002-08-22 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.

Download or read book Between Modes and Keys written by Joel Lester and published by Pendragon Press. This book was released on 1989 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study of music theory examines in detail the persistence of modal thinking in German-speaking areas, which coexisted with major-minor principles, and its impact on German music from the Baroque through the High Classical period.

Download or read book A Companion to Spinoza written by Yitzhak Y. Melamed and published by John Wiley & Sons. This book was released on 2021-07-06 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: An unparalleled collection of original essays on Benedict de Spinoza's contributions to philosophy and his enduring legacy A Companion to Spinoza presents a panoramic view of contemporary Spinoza studies in Europe and across the Anglo-American world. Designed to stimulate fresh dialogue between the analytic and continental traditions in philosophy, this extraordinary volume brings together 53 original essays that explore Spinoza's contributions to Western philosophy and intellectual history. A diverse team of established and emerging international scholars discuss new themes and classic topics to provide a uniquely comprehensive picture of one of the most influential metaphysicians of all time. Rather than simply summarizing the body of existing scholarship, the Companion develops new ideas, examines cutting-edge scholarship, and suggests directions for future research. The text is structured around six thematically-organized sections, exploring Spinoza's life and background, his contributions to metaphysics and natural philosophy, his epistemology, politics, ethics, and aesthetics, the reception of Spinoza in the work of philosophers such as Kant, Schelling, Schopenhauer, and Hegel, and more. This unparalleled research collection combines a timely overview of the current state of research with deep coverage of Spinoza's philosophy, legacy, and influence. Part of the celebrated Blackwell Companions to Philosophy series, A Companion to Spinoza is an ideal text for advanced courses in modern philosophy, intellectual history, and the history of metaphysics, and an indispensable reference for researchers and scholars in Spinoza studies.

Download or read book The Cambridge History of Western Music Theory written by Thomas Christensen and published by Cambridge University Press. This book was released on 2006-04-20 with total page 1033 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cambridge History of Western Music Theory is the first comprehensive history of Western music theory to be published in the English language. A collaborative project by leading music theorists and historians, the volume traces the rich panorama of music-theoretical thought from the Ancient Greeks to the present day. Recognizing the variety and complexity of music theory as an historical subject, the volume has been organized within a flexible framework. Some chapters are defined chronologically within a restricted historical domain, whilst others are defined conceptually and span longer historical periods. Together the thirty-one chapters present a synthetic overview of the fascinating and complex subject that is historical music theory. Richly enhanced with illustrations, graphics, examples and cross-citations as well as being thoroughly indexed and supplemented by comprehensive bibliographies of the most important primary and secondary literature, this book will be an invaluable resource for students and scholars alike.

Download or read book Modal Analysis written by Zhi-Fang Fu and published by Elsevier. This book was released on 2001-09-04 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modal Analysis provides a detailed overview of the theory of analytical and experimental modal analysis and its applications. Modal Analysis is the processes of determining the inherent dynamic characteristics of any system and using them to formulate a mathematical model of the dynamic behavior of the system. In the past two decades it has become a major technological tool in the quest for determining, improving and optimizing dynamic characteristics of engineering structures. Its main application is in mechanical and aeronautical engineering, but it is also gaining widespread use in civil and structural engineering, biomechanical problems, space structures, acoustic instruments and nuclear engineering. - The only book to focus on the theory of modal analysis before discussing applications - A relatively new technique being utilized more and more in recent years which is now filtering through to undergraduate courses - Leading expert in the field

Download or read book Neighborhood Semantics for Modal Logic written by Eric Pacuit and published by Springer. This book was released on 2017-11-15 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic (the so-called non-normal modal logics). In addition, the book discusses a broad range of topics, including standard modal logic results (i.e., completeness, decidability and definability); bisimulations for neighborhood models and other model-theoretic constructions; comparisons with other semantics for modal logic (e.g., relational models, topological models, plausibility models); neighborhood semantics for first-order modal logic, applications in game theory (coalitional logic and game logic); applications in epistemic logic (logics of evidence and belief); and non-normal modal logics with dynamic modalities. The book can be used as the primary text for seminars on philosophical logic focused on non-normal modal logics; as a supplemental text for courses on modal logic, logic in AI, or philosophical logic (either at the undergraduate or graduate level); or as the primary source for researchers interested in learning about the uses of neighborhood semantics in philosophical logic and game theory.