A Modern Perspective On Type Theory
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A Modern Perspective On Type Theory
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Author : F.D. Kamareddine
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-10
A Modern Perspective On Type Theory written by F.D. Kamareddine 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 2006-03-10 with Mathematics categories.
This book provides an overview of type theory. The first part of the book is historical, yet at the same time, places historical systems in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or proofs as terms. The third part proposes new systems that bring more advantages together.
Modern Perspectives In Type Theoretical Semantics
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Author : Stergios Chatzikyriakidis
language : en
Publisher: Springer
Release Date : 2017-02-07
Modern Perspectives In Type Theoretical Semantics written by Stergios Chatzikyriakidis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-07 with Language Arts & Disciplines categories.
This book is a collective volume that reports the state of the art in the applications of type theory to linguistic semantics. The volume fills a 20 year gap from the last published book on the issue and aspires to bring researchers closer to cutting edge alternatives in formal semantics research. It consists of unpublished work by some key researchers on various issues related to the type theoretical study of formal semantics and further exemplifies the advantages of using modern type theoretical approaches to linguistic semantics. Themes that are covered include modern developments of type theories in formal semantics, foundational issues in linguistic semantics like anaphora, modality and plurals, innovational interdisciplinary research like the introduction of probability theory to type theories as well as computational implementations of type theoretical approaches. This volume will be of great interest to formal semanticists that are looking for alternative ways to study linguistic semantics, but will also be of interest to theoretical computer scientists and mathematicians that are interested in the applications of type theory.
Type Theory And Formal Proof
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Author : Rob Nederpelt
language : en
Publisher: Cambridge University Press
Release Date : 2014-11-06
Type Theory And Formal Proof written by Rob Nederpelt 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 2014-11-06 with Computers categories.
A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.
Homotopy Type Theory Univalent Foundations Of Mathematics
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Author :
language : en
Publisher: Univalent Foundations
Release Date :
Homotopy Type Theory Univalent Foundations Of Mathematics written by and has been published by Univalent Foundations this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Mathesis Universalis Computability And Proof
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Author : Stefania Centrone
language : en
Publisher: Springer Nature
Release Date : 2019-10-25
Mathesis Universalis Computability And Proof written by Stefania Centrone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-25 with Philosophy categories.
In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gründe”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.
Sets And Extensions In The Twentieth Century
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Author :
language : en
Publisher: Elsevier
Release Date : 2012-01-24
Sets And Extensions In The Twentieth Century written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-24 with Mathematics categories.
Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights
Perspectives On Digital Pathology
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Author : M. García-Rojo
language : en
Publisher: IOS Press
Release Date : 2012-08-28
Perspectives On Digital Pathology written by M. García-Rojo and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-28 with Medical categories.
Multimedia information and digital images are increasingly important in the field of healthcare, but establishing an adequate technological framework for their management, and workable international standards to ensure compatibility and interoperability, are crucial if they are to be employed effectively. This book presents the main research efforts of EURO-TELEPATH, an initiative of the European Corporation in Science and Technology (COST) Action, IC0604. This program began in November 2007, and ran until November 2011. Its aim was to develop the standards and solutions necessary to represent, interpret, browse and retrieve digital medical images, while preserving their diagnostic quality for clinical purposes, education and research. At the end of the project, the most relevant researchers in the field of digital pathology – many of whom had been active members of EURO-TELEPATH – were asked to contribute to a book which would compile the main research efforts of the European COST Action consortium. The book is divided into six parts. The first is an introduction to the instruments and activities of COST. This is followed by sections dealing with: the state-of-the-art in pathology; pathology business modeling; standards and specifications in pathology; the analysis, processing, retrieval and management of images; technology and automation in pathology; and strategic developments and emerging research. As well as being a comprehensive overview of the IC0604 COST program, the book includes a selection of papers from American and Japanese researchers working in the same field.
Applied Logic For Computer Scientists
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Author : Mauricio Ayala-Rincón
language : en
Publisher: Springer
Release Date : 2017-02-04
Applied Logic For Computer Scientists written by Mauricio Ayala-Rincón and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-04 with Computers categories.
This book provides an introduction to logic and mathematical induction which are the basis of any deductive computational framework. A strong mathematical foundation of the logical engines available in modern proof assistants, such as the PVS verification system, is essential for computer scientists, mathematicians and engineers to increment their capabilities to provide formal proofs of theorems and to certify the robustness of software and hardware systems. The authors present a concise overview of the necessary computational and mathematical aspects of ‘logic’, placing emphasis on both natural deduction and sequent calculus. Differences between constructive and classical logic are highlighted through several examples and exercises. Without neglecting classical aspects of computational logic, the authors also highlight the connections between logical deduction rules and proof commands in proof assistants, presenting simple examples of formalizations of the correctness of algebraic functions and algorithms in PVS. Applied Logic for Computer Scientists will not only benefit students of computer science and mathematics but also software, hardware, automation, electrical and mechatronic engineers who are interested in the application of formal methods and the related computational tools to provide mathematical certificates of the quality and accuracy of their products and technologies.
Lambda Calculus And Combinators
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Author : J. Roger Hindley
language : en
Publisher: Cambridge University Press
Release Date : 2008-07-24
Lambda Calculus And Combinators written by J. Roger Hindley 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 2008-07-24 with Computers categories.
Combinatory logic and lambda-calculus, originally devised in the 1920s, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambda-calculus for over 20 years: this version is thoroughly revised and offers an account of the subject with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.
Semantic Technology
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Author : Yuan-Fang Li
language : en
Publisher: Springer
Release Date : 2016-11-24
Semantic Technology written by Yuan-Fang Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-24 with Computers categories.
This book constitutes the thoroughly refereed proceedings of the 6th Joint International Semantic Technology Conference, JIST 2016, held in Singapore, Singapore, in November 2016. The main topics of JIST 2016 include among others ontology and reasoning; linked data; knowledge graph. The JIST 2016 conference consists of two keynotes, a main technical track, including (full and short papers) from the research and the in-use tracks, a Poster and Demo session, a workshop and two tutorials. The 16 full and 8 short papers presented were carefully reviewed and selected from 34 submissions. The papers cover the following topics: ontology and data management; linked data; information retrieval and knowledge discovery; RDF and query; knowledge graph; application of semantic technologies.