Models for Modalities


Book Description

The papers collected in this volume were written over a period of some eight or nine years, with some still earlier material incorporated in one of them. Publishing them under the same cover does not make a con tinuous book of them. The papers are thematically connected with each other, however, in a way which has led me to think that they can naturally be grouped together. In any list of philosophically important concepts, those falling within the range of application of modal logic will rank high in interest. They include necessity, possibility, obligation, permission, knowledge, belief, perception, memory, hoping, and striving, to mention just a few of the more obvious ones. When a satisfactory semantics (in the sense of Tarski and Carnap) was first developed for modal logic, a fascinating new set of methods and ideas was thus made available for philosophical studies. The pioneers of this model theory of modality include prominently Stig Kanger and Saul Kripke. Several others were working in the same area independently and more or less concurrently. Some of the older papers in this collection, especially 'Quantification and Modality' and 'Modes of Modality', serve to clarify some of the main possibilities in the semantics of modal logics in general.




Mathematics of Modality


Book Description

Modal logic is the study of modalities - expressions that qualify assertions about the truth of statements - like the ordinary language phrases necessarily, possibly, it is known/believed/ought to be, etc., and computationally or mathematically motivated expressions like provably, at the next state, or after the computation terminates. The study of modalities dates from antiquity, but has been most actively pursued in the last three decades, since the introduction of the methods of Kripke semantics, and now impacts on a wide range of disciplines, including the philosophy of language and linguistics ('possible words' semantics for natural language), constructive mathematics (intuitionistic logic), theoretical computer science (dynamic logic, temporal and other logics for concurrency), and category theory (sheaf semantics). This volume collects together a number of the author's papers on modal logic, beginning with his work on the duality between algebraic and set-theoretic modals, and including two new articles, one on infinitary rules of inference, and the other about recent results on the relationship between modal logic and first-order logic. Another paper on the 'Henkin method' in completeness proofs has been substantially extended to give new applications. Additional articles are concerned with quantum logic, provability logic, the temporal logic of relativistic spacetime, modalities in topos theory, and the logic of programs.




Modal Homotopy Type Theory


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.




Therapeutic Modalities


Book Description

Ideal for exercise science, athletic training, and physical therapy students, this updated edition of Knight and Draper’sTherapeutic Modalities: The Art and Science covers the knowledge and skills needed to select the best therapeutic modality for each client injury. This edition helps students hone their clinical decision-making skills by teaching both the how and the why of each therapeutic modality, offering the application that today’s student craves. Retaining the accessible student-friendly writing style and focus on kinesthetic learning that made the book so successful, the third edition is enhanced by new chapters, new photos, and significant updates throughout that reflect the latest research and advances in the field.




Modalities and Multimodalities


Book Description

In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would ?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? no one could have foreseen that in a short time modal logic would become a lively source of ideas and methods for analytical philosophers,historians of philosophy,linguists, epistemologists and computer scientists. The aim which oriented the composition of this book was not to write a new manual of modal logic (there are a lot of excellent textbooks on the market, and the expert reader will realize how much we bene?ted from manyofthem)buttoo?ertoeveryreader,evenwithnospeci?cbackground in logic, a conceptually linear path in the labyrinth of the current panorama of modal logic. The notion which in our opinion looked suitable to work as a compass in this enterprise was the notion of multimodality, or, more speci?cally, the basic idea of grounding systems on languages admitting more than one primitive modal operator.




Interpretable Machine Learning


Book Description

This book is about making machine learning models and their decisions interpretable. After exploring the concepts of interpretability, you will learn about simple, interpretable models such as decision trees, decision rules and linear regression. Later chapters focus on general model-agnostic methods for interpreting black box models like feature importance and accumulated local effects and explaining individual predictions with Shapley values and LIME. All interpretation methods are explained in depth and discussed critically. How do they work under the hood? What are their strengths and weaknesses? How can their outputs be interpreted? This book will enable you to select and correctly apply the interpretation method that is most suitable for your machine learning project.




Teaching Ethics


Book Description

Teaching Ethics: Instructional Models, Methods, and Modalities for University Studies encourages teachers and students to approach their work with a deep awareness that people, not as disinterested reasoners devoid of or effectively cut-off from passions, make ethical judgments. An individual’s social and emotional constitution should be taken into account. This collaborative publication offers salient instructional models, methods and modalities centered on the whole person.




Neighborhood Semantics for Modal Logic


Book Description

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.




The Intentions of Intentionality and Other New Models for Modalities


Book Description

The leisure to do the thinking whose results are gathered here has largely been provided by the Academy of Finland, whose support has also made possible the help and co-operation of a group of younger logicians and philosophers. Less tangible support and help is unfortunately harder to record and to thank for. Once again, in working on the many themes I have tried to weave together in this book I have incurred more intellectual and moral debts I can in so many words acknowledge here. Let me only say that the closer to home I get the greater they become. I have especially in mind my colleagues and students at Stanford; my colleagues in Helsinki; the past and present members of my research group in Helsinki; and incom parably more than anybody else my wife Soili. Helsinki, April 1975 JAAKKO HINTIKKA INTRODUCTION A literal-minded reader might easily object to the (sub)title of this volume. What is to be found here, he might allege, are neither models, nor modalities stricto sensu, nor yet any completely new applications of modal logic. Even though the purpose of the title is only to signal the con tinuity between the present volume and its predecessor, Models for Modalities (D. Reidel Publishing Co., Dordrecht, 1969), the objection is sufficiently well taken to serve as an excuse for an attempt to put my enterprise in a wider perspective.




Michlovitz's Modalities for Therapeutic Intervention


Book Description

A volume in the Contemporary Perspectives in Rehabilitation Series, curated by Steven L. Wolf, PhD, PT, FAPTA Implement a current, evidence-based approach to the selection, application, and uses of therapeutic modalities as an essential tool for functionally based rehabilitation and as a complement to other types of interventions in a patient-centered model of care. The 7th Edition of this groundbreaking text fosters an in-depth understanding of the science behind each modality, its advantages and limitations, its appropriateness for specific conditions, and its implementation. A hands-on problem-solving approach promotes the development of essential clinical decision-making skills through a wealth of full-color photographs and illustrations, special features, and challenging cases studies. See what students and practitioners are saying about the previous edition… Recommend this book. “Great clinical reference for young therapists and seasoned therapists alike. Great information in a nicely organized book.”—Jane D., Online Reviewer Excellent book “Excellent content. Therapeutic modalities and many more... including spinal decompression devices.”—Online Reviewer




Recent Books