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 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 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 Model Theory for Modal Logic written by K.A. Bowen and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Laws and Explanations Theories and Modal Possibilities written by Arnold Koslow and published by Springer Nature. This book was released on 2020-01-01 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book has two parts: In the first, after a review of some seminal classical accounts of laws and explanations, a new account is proposed for distinguishing between laws and accidental generalizations (LAG). Among the new consequences of this proposal it is proved that any explanation of a contingent generalization shows that the generalization is not accidental. The second part involves physical theories, their modality, and their explanatory power. In particular, it is shown that (1) Each theory has a theoretical implication structure associated with it, such that there are new physical modal operators on these structures and also special modal entities that are in these structures. A special subset of the physical modals, the nomic modals are associated with the laws of theories. (2) The familiar idea that theories always explain laws by deduction of them has to be seriously modified in light of the fact that there are a host of physical theories (including for example, Newtonian Classical mechanics, Hamiltonian, and Lagrangian theory, and probability theory) that we believe are schematic (they do not have any truth value). Nevertheless, we think that there is a kind of non-deductive explanation and generality that they achieve by subsumtion under a schema.
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 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 Musical Theory in the Renaissance written by CristleCollins Judd and published by Routledge. This book was released on 2017-07-05 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of essays draws together recent work on historical music theory of the Renaissance. The collection spans the major themes addressed by Renaissance writers on music and highlights the differing approaches to this body of work by modern scholars, including: historical and theoretical perspectives; consideration of the broader cultural context for writing about music in the Renaissance; and the dissemination of such work. Selected from a variety of sources ranging from journals, monographs and specialist edited volumes, to critical editions, translations and facsimiles, these previously published articles reflect a broad chronological and geographical span, and consider Renaissance sources that range from the overtly pedagogical to the highly speculative. Taken together, this collection enables consideration of key essays side by side aided by the editor‘s introductory essay which highlights ongoing debates and offers a general framework for interpreting past and future directions in the study of historical music theory from the Renaissance.
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 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 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 From Modes to Keys in Early Modern Music Theory written by Michael R. Dodds and published by Oxford University Press. This book was released on 2023-12-05 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Modes to Keys in Early Modern Music Theory addresses one of the broadest and most elusive open topics in music history: the transition from the Renaissance modes to the major and minor keys of the high Baroque. Through deep engagement with the corpus of Western music theory, author Michael R. Dodds presents a model to clarify the factors of this complex shift.
Download or read book The Puzzle of Existence written by Tyron Goldschmidt and published by Routledge. This book was released on 2014-02-05 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This groundbreaking volume investigates the most fundamental question of all: Why is there something rather than nothing? The question is explored from diverse and radical perspectives: religious, naturalistic, platonistic and skeptical. Does science answer the question? Or does theology? Does everything need an explanation? Or can there be brute, inexplicable facts? Could there have been nothing whatsoever? Or is there any being that could not have failed to exist? Is the question meaningful after all? The volume advances cutting-edge debates in metaphysics, philosophy of cosmology and philosophy of religion, and will intrigue and challenge readers interested in any of these subjects.
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 Truth Existence and Explanation written by Mario Piazza and published by Springer. This book was released on 2018-10-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains more than 15 essays that explore issues in truth, existence, and explanation. It features cutting-edge research in the philosophy of mathematics and logic. Renowned philosophers, mathematicians, and younger scholars provide an insightful contribution to the lively debate in this interdisciplinary field of inquiry. The essays look at realism vs. anti-realism as well as inflationary vs. deflationary theories of truth. The contributors also consider mathematical fictionalism, structuralism, the nature and role of axioms, constructive existence, and generality. In addition, coverage also looks at the explanatory role of mathematics and the philosophical relevance of mathematical explanation. The book will appeal to a broad mathematical and philosophical audience. It contains work from FilMat, the Italian Network for the Philosophy of Mathematics. These papers collected here were also presented at their second international conference, held at the University of Chieti-Pescara, May 2016.
