Proof And Computation Digitization In Mathematics Computer Science And Philosophy
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Proof And Computation Digitization In Mathematics Computer Science And Philosophy
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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2018-05-30
Proof And Computation Digitization In Mathematics Computer Science And Philosophy written by Klaus Mainzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-30 with Mathematics categories.
This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes Predicative Foundations, Constructive Mathematics and Type Theory, Computation in Higher Types, Extraction of Programs from Proofs, and Algorithmic Aspects in Financial Mathematics. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification
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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2021-07-27
Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification written by Klaus Mainzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-27 with Mathematics categories.
This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
Artificial Intelligence Algorithm Design For Systems
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Author : Radek Silhavy
language : en
Publisher: Springer Nature
Release Date : 2024-11-25
Artificial Intelligence Algorithm Design For Systems written by Radek Silhavy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-25 with Computers categories.
This volume delves into the application of Artificial Intelligence within systems and network environments. Highlighted papers investigate the latest in neural network applications, optimisation strategies, and hybrid bio-inspired algorithms. It includes the rigorously reviewed proceedings of the Artificial Intelligence Application in Networks and Systems session of the 13th Computer Science Online Conference 2024 (CSOC 2024), held online in April 2024.
Temporal Logic From Philosophy And Proof Theory To Artificial Intelligence And Quantum Computing
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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2023-05-12
Temporal Logic From Philosophy And Proof Theory To Artificial Intelligence And Quantum Computing written by Klaus Mainzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-12 with Mathematics categories.
Calculi of temporal logic are widely used in modern computer science. The temporal organization of information flows in the different architectures of laptops, the Internet, or supercomputers would not be possible without appropriate temporal calculi. In the age of digitalization and High-Tech applications, people are often not aware that temporal logic is deeply rooted in the philosophy of modalities. A deep understanding of these roots opens avenues to the modern calculi of temporal logic which have emerged by extension of modal logic with temporal operators. Computationally, temporal operators can be introduced in different formalisms with increasing complexity such as Basic Modal Logic (BML), Linear-Time Temporal Logic (LTL), Computation Tree Logic (CTL), and Full Computation Tree Logic (CTL*). Proof-theoretically, these formalisms of temporal logic can be interpreted by the sequent calculus of Gentzen, the tableau-based calculus, automata-based calculus, game-based calculus, and dialogue-based calculus with different advantages for different purposes, especially in computer science.The book culminates in an outlook on trendsetting applications of temporal logics in future technologies such as artificial intelligence and quantum technology. However, it will not be sufficient, as in traditional temporal logic, to start from the everyday understanding of time. Since the 20th century, physics has fundamentally changed the modern understanding of time, which now also determines technology. In temporal logic, we are only just beginning to grasp these differences in proof theory which needs interdisciplinary cooperation of proof theory, computer science, physics, technology, and philosophy.
Contemporary Natural Philosophy And Philosophies Part 1
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Author : Gordana Dodig-Crnkovic
language : en
Publisher: MDPI
Release Date : 2019-06-11
Contemporary Natural Philosophy And Philosophies Part 1 written by Gordana Dodig-Crnkovic and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Philosophy categories.
Modern information communication technology eradicates barriers of geographic distances, making the world globally interdependent, but this spatial globalization has not eliminated cultural fragmentation. The Two Cultures of C.P. Snow (that of science–technology and that of humanities) are drifting apart even faster than before, and they themselves crumble into increasingly specialized domains. Disintegrated knowledge has become subservient to the competition in technological and economic race leading in the direction chosen not by the reason, intellect, and shared value-based judgement, but rather by the whims of autocratic leaders or fashion controlled by marketers for the purposes of political or economic dominance. If we want to restore the authority of our best available knowledge and democratic values in guiding humanity, first we have to reintegrate scattered domains of human knowledge and values and offer an evolving and diverse vision of common reality unified by sound methodology. This collection of articles responds to the call from the journal Philosophies to build a new, networked world of knowledge with domain specialists from different disciplines interacting and connecting with other knowledge-and-values-producing and knowledge-and-values-consuming communities in an inclusive, extended, contemporary natural–philosophic manner. In this process of synthesis, scientific and philosophical investigations enrich each other—with sciences informing philosophies about the best current knowledge of the world, both natural and human-made—while philosophies scrutinize the ontological, epistemological, and methodological foundations of sciences, providing scientists with questions and conceptual analyses. This is all directed at extending and deepening our existing comprehension of the world, including ourselves, both as humans and as societies, and humankind.
Artificial Intelligence When Do Machines Take Over
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Author : Klaus Mainzer
language : en
Publisher: Springer Nature
Release Date : 2019-10-14
Artificial Intelligence When Do Machines Take Over written by Klaus Mainzer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-14 with Technology & Engineering categories.
Everybody knows them. Smartphones that talk to us, wristwatches that record our health data, workflows that organize themselves automatically, cars, airplanes and drones that control themselves, traffic and energy systems with autonomous logistics or robots that explore distant planets are technical examples of a networked world of intelligent systems. Machine learning is dramatically changing our civilization. We rely more and more on efficient algorithms, because otherwise we will not be able to cope with the complexity of our civilizing infrastructure. But how secure are AI algorithms? This challenge is taken up in the 2nd edition: Complex neural networks are fed and trained with huge amounts of data (big data). The number of necessary parameters explodes exponentially. Nobody knows exactly what is going on in these "black boxes". In machine learning we need more explainability and accountability of causes and effects in order to be able to decide ethical and legal questions of responsibility (e.g. in autonomous driving or medicine)! Besides causal learning, we also analyze procedures of tests and verification to get certified AI-programs. Since its inception, AI research has been associated with great visions of the future of mankind. It is already a key technology that will decide the global competition of social systems. "Artificial Intelligence and Responsibility" is another central supplement to the 2nd edition: How should we secure our individual liberty rights in the AI world? This book is a plea for technology design: AI must prove itself as a service in society.
The Digital And The Real World
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Author : Klaus Mainzer
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017
The Digital And The Real World written by Klaus Mainzer and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
In the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy. Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT).
Computational Thinking
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Author : Peter J. Denning
language : en
Publisher: MIT Press
Release Date : 2019-05-14
Computational Thinking written by Peter J. Denning and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-14 with Computers categories.
This pocket-sized introduction to computational thinking and problem-solving traces its genealogy centuries before the digital computer. A few decades into the digital era, scientists discovered that thinking in terms of computation made possible an entirely new way of organizing scientific investigation. Eventually, every field had a computational branch: computational physics, computational biology, computational sociology. More recently, “computational thinking” has become part of the K–12 curriculum. But what is computational thinking? This volume in the MIT Press Essential Knowledge series offers an accessible overview—tracing a genealogy that begins centuries before digital computers and portraying computational thinking as the pioneers of computing have described it. The authors explain that computational thinking (CT) is not a set of concepts for programming; it is a way of thinking that is honed through practice: the mental skills for designing computations to do jobs for us, and for explaining and interpreting the world as a complex of information processes. Mathematically trained experts (known as “computers”) who performed complex calculations as teams engaged in CT long before electronic computers. In each chapter, the author identify different dimensions of today's highly developed CT: • Computational Methods • Computing Machines • Computing Education • Software Engineering • Computational Science • Design Along the way, they debunk inflated claims for CT and computation while making clear the power of CT in all its complexity and multiplicity.
Digital And The Real World The Computational Foundations Of Mathematics Science Technology And Philosophy
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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2017-11-17
Digital And The Real World The Computational Foundations Of Mathematics Science Technology And Philosophy written by Klaus Mainzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-17 with Mathematics categories.
In the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy.Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT).
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.