Logic And Foundations Of Mathematics
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The Logical Foundations Of Mathematics
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Author : William S. Hatcher
language : en
Publisher: Elsevier
Release Date : 2014-05-09
The Logical Foundations Of Mathematics written by William S. Hatcher and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-09 with Mathematics categories.
The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems. The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory. Comprised of eight chapters, this book begins with an introduction to first-order logic. In particular, two complete systems of axioms and rules for the first-order predicate calculus are given, one for efficiency in proving metatheorems, and the other, in a "natural deduction" style, for presenting detailed formal proofs. A somewhat novel feature of this framework is a full semantic and syntactic treatment of variable-binding term operators as primitive symbols of logic. Subsequent chapters focus on the origin of modern foundational studies; Gottlob Frege's formal system intended to serve as a foundation for mathematics and its paradoxes; the theory of types; and the Zermelo-Fraenkel set theory. David Hilbert's program and Kurt Gödel's incompleteness theorems are also examined, along with the foundational systems of W. V. Quine and the relevance of categorical algebra for foundations. This monograph will be of interest to students, teachers, practitioners, and researchers in mathematics.
Foundations Of Logic And Mathematics
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Author : Yves Nievergelt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Foundations Of Logic And Mathematics written by Yves Nievergelt 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.
This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.
Mathematical Logic And The Foundations Of Mathematics
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Author : G. T. Kneebone
language : en
Publisher: Dover Publications
Release Date : 2001
Mathematical Logic And The Foundations Of Mathematics written by G. T. Kneebone and has been published by Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Logic, Symbolic and mathematical categories.
Ideal for students intending to specialize in the topic. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics. Part III focuses on the philosophy of mathematics.
Foundations Of Mathematical Logic
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Author : Haskell Brooks Curry
language : en
Publisher: Courier Corporation
Release Date : 1977-01-01
Foundations Of Mathematical Logic written by Haskell Brooks Curry and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-01-01 with Mathematics categories.
Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.
Logic And Foundations Of Mathematics
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Author : Arend Heyting
language : en
Publisher:
Release Date : 1969
Logic And Foundations Of Mathematics written by Arend Heyting and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Logic, Symbolic and mathematical categories.
Le Niewski S Systems Of Logic And Foundations Of Mathematics
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Author : Rafal Urbaniak
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-24
Le Niewski S Systems Of Logic And Foundations Of Mathematics written by Rafal Urbaniak 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 2013-09-24 with Science categories.
This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw Leśniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsaw school. The author’s nuanced survey eschews secondary commentary, analyzing Leśniewski's core philosophical views and evaluating the formulations that were to have such a profound influence on the evolution of mathematical logic. One of the undisputed leaders of the cohort of brilliant logicians that congregated in Poland in the early twentieth century, Leśniewski was a guide and mentor to a generation of celebrated analytical philosophers (Alfred Tarski was his PhD student). His primary achievement was a system of foundational mathematical logic intended as an alternative to the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. Its three strands—‘protothetic’, ‘ontology’, and ‘mereology’, are detailed in discrete sections of this volume, alongside a wealth other chapters grouped to provide the fullest possible coverage of Leśniewski’s academic output. With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great pioneers.
Logical Foundations Of Mathematics And Computational Complexity
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Author : Pavel Pudlák
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-22
Logical Foundations Of Mathematics And Computational Complexity written by Pavel Pudlák 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 2013-04-22 with Mathematics categories.
The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.
Logic And Foundations Of Mathematics
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Author : Andrea Cantini
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Logic And Foundations Of Mathematics written by Andrea Cantini 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 Mathematics categories.
The IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science. The final program counted 51 invited lectures and around 700 contributed papers, distributed in 15 sections. Following the tradition of previous LMPS-meetings, some authors, whose papers aroused particular interest, were invited to submit their works for publication in a collection of selected contributed papers. Due to the large number of interesting contributions, it was decided to split the collection into two distinct volumes: one covering the areas of Logic, Foundations of Mathematics and Computer Science, the other focusing on the general Philosophy of Science and the Foundations of Physics. As a leading choice criterion for the present volume, we tried to combine papers containing relevant technical results in pure and applied logic with papers devoted to conceptual analyses, deeply rooted in advanced present-day research. After all, we believe this is part of the genuine spirit underlying the whole enterprise of LMPS studies.
Mathematical Logic
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Author : Wei Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-26
Mathematical Logic written by Wei Li 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 2010-02-26 with Mathematics categories.
Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.
Mathematical Logic And The Foundations Of Mathematics
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Author : G. T. Kneebone
language : en
Publisher:
Release Date : 1963
Mathematical Logic And The Foundations Of Mathematics written by G. T. Kneebone and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Logic, Symbolic and mathematical categories.