Mechanizing Mathematical Reasoning

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Mechanizing Mathematical Reasoning

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Author : Dieter Hutter
language : en
Publisher: Springer
Release Date : 2011-03-29

Mechanizing Mathematical Reasoning written by Dieter Hutter and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-29 with Computers categories.

By presenting state-of-the-art results in logical reasoning and formal methods in the context of artificial intelligence and AI applications, this book commemorates the 60th birthday of Jörg H. Siekmann. The 30 revised reviewed papers are written by former and current students and colleagues of Jörg Siekmann; also included is an appraisal of the scientific career of Jörg Siekmann entitled "A Portrait of a Scientist: Logics, AI, and Politics." The papers are organized in four parts on logic and deduction, applications of logic, formal methods and security, and agents and planning.

Mathematical Reasoning

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Author : Raymond Nickerson
language : en
Publisher: Taylor & Francis
Release Date : 2011-02-25

Mathematical Reasoning written by Raymond Nickerson and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-25 with Psychology categories.

The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.

Mechanization Of Reasoning In A Historical Perspective

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Author :
language : en
Publisher: Rodopi
Release Date : 1995

Mechanization Of Reasoning In A Historical Perspective written by and has been published by Rodopi this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Computers categories.

This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section of the research project Logical Systems and Algorithms for Automatic Testing of Reasoning, 1986-1990, in which participated nine Polish universities; the project was coordinated by the Department of Logic, Methodology and Philosophy of Science of the Bia l ystok Branch of the University of Warsaw, and supported by the Ministry of Education (some of its results are reported in (Srzednicki (Ed.) 1987). The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE (Multi-Sorted first-order logic with Equality, reported in (Marciszewski 1994a)) due to Dr. Andrzej Trybulec. He and other colleagues deserve a grateful mention for a hands-on experience and theoretical stimulants owed to their collaboration.

Mechanization Of Reasoning In A Historical Perspective

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Author :
language : en
Publisher: BRILL
Release Date : 2023-03-13

Mechanization Of Reasoning In A Historical Perspective written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-13 with Language Arts & Disciplines categories.

This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section of the research project Logical Systems and Algorithms for Automatic Testing of Reasoning, 1986-1990, in which participated nine Polish universities; the project was coordinated by the Department of Logic, Methodology and Philosophy of Science of the Bia??l??ystok Branch of the University of Warsaw, and supported by the Ministry of Education (some of its results are reported in (Srzednicki (Ed.) 1987). The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE (Multi-Sorted first-order logic with Equality, reported in (Marciszewski 1994a)) due to Dr. Andrzej Trybulec. He and other colleagues deserve a grateful mention for a hands-on experience and theoretical stimulants owed to their collaboration.

Mechanizing Proof

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Author : Donald MacKenzie
language : en
Publisher: MIT Press
Release Date : 2004-01-30

Mechanizing Proof written by Donald MacKenzie and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-30 with Social Science categories.

Most aspects of our private and social lives—our safety, the integrity of the financial system, the functioning of utilities and other services, and national security—now depend on computing. But how can we know that this computing is trustworthy? In Mechanizing Proof, Donald MacKenzie addresses this key issue by investigating the interrelations of computing, risk, and mathematical proof over the last half century from the perspectives of history and sociology. His discussion draws on the technical literature of computer science and artificial intelligence and on extensive interviews with participants. MacKenzie argues that our culture now contains two ideals of proof: proof as traditionally conducted by human mathematicians, and formal, mechanized proof. He describes the systems constructed by those committed to the latter ideal and the many questions those systems raise about the nature of proof. He looks at the primary social influence on the development of automated proof—the need to predict the behavior of the computer systems upon which human life and security depend—and explores the involvement of powerful organizations such as the National Security Agency. He concludes that in mechanizing proof, and in pursuing dependable computer systems, we do not obviate the need for trust in our collective human judgment.

Mechanizing Mathematical Reasoning

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Author : Werner Stephan (informatico.)
language : en
Publisher:
Release Date : 2005

Mechanizing Mathematical Reasoning written by Werner Stephan (informatico.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.

Logic Language Information And Computation

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Author : Ulrich Kohlenbach
language : en
Publisher: Springer
Release Date : 2014-08-23

Logic Language Information And Computation written by Ulrich Kohlenbach and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-23 with Mathematics categories.

Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 21st Workshop on Logic, Language, Information and Communication, WoLLIC 2014, held in Valparaiso, Chile, in September 2014. The 15 contributed papers presented together with 6 invited lectures were carefully reviewed and selected from 29 submissions. The focus of the workshop was on the following subjects Inter-Disciplinary Research involving Formal Logic, Computing and Programming Theory, and Natural Language and Reasoning.

Proof Technology In Mathematics Research And Teaching

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Author : Gila Hanna
language : en
Publisher: Springer Nature
Release Date : 2019-10-02

Proof Technology In Mathematics Research And Teaching written by Gila Hanna and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-02 with Education categories.

This book presents chapters exploring the most recent developments in the role of technology in proving. The full range of topics related to this theme are explored, including computer proving, digital collaboration among mathematicians, mathematics teaching in schools and universities, and the use of the internet as a site of proof learning. Proving is sometimes thought to be the aspect of mathematical activity most resistant to the influence of technological change. While computational methods are well known to have a huge importance in applied mathematics, there is a perception that mathematicians seeking to derive new mathematical results are unaffected by the digital era. The reality is quite different. Digital technologies have transformed how mathematicians work together, how proof is taught in schools and universities, and even the nature of proof itself. Checking billions of cases in extremely large but finite sets, impossible a few decades ago, has now become a standard method of proof. Distributed proving, by teams of mathematicians working independently on sections of a problem, has become very much easier as digital communication facilitates the sharing and comparison of results. Proof assistants and dynamic proof environments have influenced the verification or refutation of conjectures, and ultimately how and why proof is taught in schools. And techniques from computer science for checking the validity of programs are being used to verify mathematical proofs. Chapters in this book include not only research reports and case studies, but also theoretical essays, reviews of the state of the art in selected areas, and historical studies. The authors are experts in the field.

Towards Mechanized Mathematical Assistants

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Author : Manuel Kauers
language : en
Publisher: Springer
Release Date : 2007-08-15

Towards Mechanized Mathematical Assistants written by Manuel Kauers and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-15 with Mathematics categories.

This book constitutes the refereed proceedings of the 6th International Conference on Mathematical Knowledge Management, MKM 2007, and the 14th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2006, held in Hagenberg, Austria in June 2007 as events of the RISC Summer 2007, organized by the Research Institute for Symbolic Computation.

Logical Dynamics Of Information And Interaction

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Author : Johan van Benthem
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-29

Logical Dynamics Of Information And Interaction written by Johan van Benthem 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 2011-09-29 with Mathematics categories.

This book develops a view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science.