History And Philosophy Of Constructive Type Theory
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History And Philosophy Of Constructive Type Theory
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Author : Giovanni Sommaruga
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
History And Philosophy Of Constructive Type Theory written by Giovanni Sommaruga 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 2013-03-09 with Philosophy categories.
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.
Twenty Five Years Of Constructive Type Theory
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Author : Giovanni Sambin
language : en
Publisher: Clarendon Press
Release Date : 1998-10-15
Twenty Five Years Of Constructive Type Theory written by Giovanni Sambin and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-15 with Mathematics categories.
Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.
Treatise On Intuitionistic Type Theory
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Author : Johan Georg Granström
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-02
Treatise On Intuitionistic Type Theory written by Johan Georg Granström 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 2011-06-02 with Philosophy categories.
Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.
Explanation
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Author : Giora Hon
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Explanation written by Giora Hon 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 2013-04-17 with Science categories.
For some years we have been conducting at the University of Haifa an interdisciplinary seminar on explanation in philosophy and psychology. We habitually begin the seminar with some philosophical reflections on explanation - an analysis of the concept and its metaphysical underpinnings. We discuss the various models and proceed to examine explanation in the setting of psychology. Thus, from the outset, we have focused not only on the concept itself but also on its application. The objective that we have set for the seminar, attended by students from both departments, Philosophy and Psychology, has been a critical understanding of the concept of explanation, its use and limitations. We were keen on deepening our understanding of the concept and on exploring its applications in fields of knowledge other than psychology. This was the motivation for convening an international conference on explanation and its application. The conference took place in the spring of 1998 under the auspices of the University of Haifa. The present book is the fruit of this meeting. The reader should note that the second part of the Introduction presents a detailed analytical account of the book. We hope that this overview will facilitate efficient use of the book by directing the reader's attention to those issues that might be of interest to him or her.
Collected Papers Of Stig Kanger With Essays On His Life And Work
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Author : Ghita Holmström-Hintikka
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Collected Papers Of Stig Kanger With Essays On His Life And Work written by Ghita Holmström-Hintikka 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 2012-12-06 with Mathematics categories.
Stig Kanger (1924-1988) made important contributions to logic and formal philosophy. Kanger's dissertation Provability in Logic, 1957, contained significant results in proof theory as well as the first fully worked out model-theoretic interpretation of quantified modal logic. It is generally accepted nowadays that Kanger was one of the originators of possible worlds semantics for modal logic. Kanger's most original achievements were in the areas of general proof theory, the semantics of modal and deontic logic, and the logical analysis of the concept of rights. He also contributed to action theory, preference logic, and the theory of measurement. This is the first of two volumes dedicated to the work of Stig Kanger. The present volume is a complete collection of Kanger's philosophical papers. The second volume contains critical essays on Kanger's work, as well as biographical essays on Kanger written by colleagues and friends.
Collected Papers Of Stig Kanger With Essays On His Life And Work
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Author : Stig Kanger
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-12-31
Collected Papers Of Stig Kanger With Essays On His Life And Work written by Stig Kanger 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 2001-12-31 with Law categories.
Stig Kanger (1924-1988) made important contributions to logic and formal philosophy. Kanger's most original achievements were in the areas of general proof theory, the semantics of modal and deontic logic, and the logical analysis of the concept of rights. But he contributed significantly to action theory, preference logic and the theory of measurement as well. This is the second of two volumes dedicated to the work of Stig Kanger. The first volume is a complete collection of Kanger's philosophical papers. The present volume contains critical essays on the various aspects of Kanger's work as well as some biographical sketches. Lennart Åqvist, Jan Berg, Brian Chellas, Anatoli Degtyarev, Lars Gustafsson, Sören Halldén, Kaj Børge Hansen, Sven Ove Hansson, Risto Hilpinen, Jaakko Hintikka, Ghita Holmström-Hintikka, Lars Lindahl, Sten Lindström, Ingmar Pörn, Dag Prawitz, Wlodek Rabinowicz, Krister Segerberg, Amartya Sen, Sören Stenlund, Göran Sundholm, and Andrei Voronkov have contributed to this volume.
Axiomatic Method And Category Theory
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Author : Andrei Rodin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-14
Axiomatic Method And Category Theory written by Andrei Rodin 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 2013-10-14 with Philosophy categories.
This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.
The Logic Of Metaphor
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Author : Eric Steinhart
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-07-31
The Logic Of Metaphor written by Eric Steinhart 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 2001-07-31 with Computers categories.
Some sentences in natural languages like English have multiple meanings. Steinhart (William Paterson U. of New Jersey) divides the meanings into literal and metaphorical, denies that they are the same, and denies that the metaphorical function is necessarily false or necessarily true. He argues that most metaphors are based on analogies, which he defines as the relative structural indiscernibility of parts of worlds, and that a metaphor is true for a particular world if and only if certain parts of that world are relatively structurally indiscernible, that is, are analogous. c. Book News Inc.
Types And Programming Languages
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Author : Benjamin C. Pierce
language : en
Publisher: MIT Press
Release Date : 2002-01-04
Types And Programming Languages written by Benjamin C. Pierce and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-04 with Computers categories.
A comprehensive introduction to type systems and programming languages. A type system is a syntactic method for automatically checking the absence of certain erroneous behaviors by classifying program phrases according to the kinds of values they compute. The study of type systems—and of programming languages from a type-theoretic perspective—has important applications in software engineering, language design, high-performance compilers, and security. This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages. The approach is pragmatic and operational; each new concept is motivated by programming examples and the more theoretical sections are driven by the needs of implementations. Each chapter is accompanied by numerous exercises and solutions, as well as a running implementation, available via the Web. Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material. The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators. Extended case studies develop a variety of approaches to modeling the features of object-oriented languages.
Probability Theory
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Author : Vincent F. Hendricks
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-30
Probability Theory written by Vincent F. Hendricks 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 2001-06-30 with Mathematics categories.
A collection of papers presented at the conference on Probability Theory - Philosophy, Recent History and Relations to Science, University of Roskilde, Denmark, September 16-18, 1998. Since the measure theoretical definition of probability was proposed by Kolmogorov, probability theory has developed into a mature mathematical theory. It is today a fruitful field of mathematics that has important applications in philosophy, science, engineering, and many other areas. The measure theoretical definition of probability and its axioms, however, are not without their problems; some of them even puzzled Kolmogorov. This book sheds light on some recent discussions of the problems in probability theory and their history, analysing their philosophical and mathematical significance, and the role pf mathematical probability theory in other sciences.