Perspectives In Logic
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Proofs And Computations
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Author : Helmut Schwichtenberg
language : en
Publisher: Cambridge University Press
Release Date : 2011-12-15
Proofs And Computations written by Helmut Schwichtenberg and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-15 with Mathematics categories.
Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
Model Theoretic Logics
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Author : J. Barwise
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-02
Model Theoretic Logics written by J. Barwise and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Mathematics categories.
This book brings together several directions of work in model theory between the late 1950s and early 1980s.
An Introduction To Service Dominant Logic
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Author : Robert F. Lusch
language : en
Publisher: Cambridge University Press
Release Date : 2014-01-30
An Introduction To Service Dominant Logic written by Robert F. Lusch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-30 with Business & Economics categories.
The first accessible introduction to the principles and applications of Service-Dominant Logic, written by the world-leading authors of this perspective.
Higher Recursion Theory
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Author : Gerald E. Sacks
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-02
Higher Recursion Theory written by Gerald E. Sacks and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Computers categories.
This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
Subsystems Of Second Order Arithmetic
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Author : Stephen G. Simpson
language : en
Publisher: Cambridge University Press
Release Date : 2009-05-29
Subsystems Of Second Order Arithmetic written by Stephen G. Simpson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-29 with Mathematics categories.
Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics. In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic.
The Semantic Conception Of Logic
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Author : Gil Sagi
language : en
Publisher: Cambridge University Press
Release Date : 2021-09-09
The Semantic Conception Of Logic written by Gil Sagi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-09 with Mathematics categories.
This collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on the role of the semantic tradition in their disciplines. This book will be invaluable to philosophers and logicians alike.
Rethinking Logic Logic In Relation To Mathematics Evolution And Method
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Author : Carlo Cellucci
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-09
Rethinking Logic Logic In Relation To Mathematics Evolution And Method written by Carlo Cellucci and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-09 with Philosophy categories.
This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. trigger
Modern Mathematical Logic
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Author : Joseph Mileti
language : en
Publisher: Cambridge University Press
Release Date : 2022-09-22
Modern Mathematical Logic written by Joseph Mileti and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-22 with Mathematics categories.
This textbook gives a complete and modern introduction to mathematical logic. The author uses contemporary notation, conventions, and perspectives throughout, and emphasizes interactions with the rest of mathematics. In addition to covering the basic concepts of mathematical logic and the fundamental material on completeness, compactness, and incompleteness, it devotes significant space to thorough introductions to the pillars of the modern subject: model theory, set theory, and computability. Requiring only a modest background of undergraduate mathematics, the text can be readily adapted for a variety of one- or two-semester courses at the upper-undergraduate or beginning-graduate level. Numerous examples reinforce the key ideas and illustrate their applications, and a wealth of classroom-tested exercises serve to consolidate readers' understanding. Comprehensive and engaging, this book offers a fresh approach to this enduringly fascinating and important subject.
Logical Foundations Of Proof Complexity
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Author : Stephen Cook
language : en
Publisher: Cambridge University Press
Release Date : 2014-03-06
Logical Foundations Of Proof Complexity written by Stephen Cook and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-06 with Mathematics categories.
This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.
Sexual Disorders
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Author : Peter J. Fagan
language : en
Publisher: JHU Press
Release Date : 2004-12-01
Sexual Disorders written by Peter J. Fagan and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-01 with Psychology categories.
Sexual disorders may arise from multiple causes. Their clinical assessment, diagnosis, and treatment must take into account the patient's underlying biology, history, and behaviors. Using an approach pioneered at the Johns Hopkins Medical Institutions, Peter Fagan applies the four "perspectives of psychiatry" (disease, dimension, behavior, and life story) to the diagnosis and treatment of sexual disorders. This book offers therapists an efficient and clinically proven way to organize the range of theoretical methodologies currently available, presenting a framework that is both conceptually cohesive and readily applicable in clinical settings. After an introduction, each chapter offers a case study followed by an analysis based on one perspective methodology as well as a discussion of the clinical implications of that perspective. The book closes with a chapter integrating the approaches. This book will be of interest to mental health care professionals, including psychiatrists, psychologists, and social workers, who treat patients with sexual disorders.