Topics In Logic Philosophy And Foundations Of Mathematics And Computer Science
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Topics In Logic Philosophy And Foundations Of Mathematics And Computer Science
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Author : Stanisław Krajewski
language : en
Publisher: IOS Press
Release Date : 2007
Topics In Logic Philosophy And Foundations Of Mathematics And Computer Science written by Stanisław Krajewski and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume honors Professor Andrzej Grzegorczyk, the nestor of Polish logicians, on his 85th anniversary. The editors would like to express the respect and sympathy they have for him. His textbook The Outline of Mathematical Logic has been published in many editions and translated into several languages. It was this textbook that introduced many of us into the world of mathematical logic. Professor Grzegorczyk has made fundamental contributions to logic and to philosophy. His results, mainly on hierarchy of primitive recursive functions, known as the Grzegorczyk hierarchy, are of fundamental importance to theoretical computer science. In particular, they were precursory for the computational complexity theory. The editors would like to stress that this special publication celebrates a scientist who is still actively pursuing genuinely innovative directions of research. Quite recently, Andrzej Grzegorczyk gave a new proof of undecidability of the first order functional calculus. His proof does not use the arithmetization of Kurt Gödel. In recognition of his merits, the University of Clermont-Ferrand conferred to Professor Andrzej Grzegorczyk the Doctorat Honoris Causa. The work and life of Professor Andrzej Grzegorczyk is presented in the article by Professors Stanislaw Krajewski and Jan Wolenski. The papers in this collection have been submitted on invitational basis.
Philosophical And Mathematical Logic
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Author : Harrie de Swart
language : en
Publisher: Springer
Release Date : 2018-11-28
Philosophical And Mathematical Logic written by Harrie de Swart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Philosophy categories.
This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. The reader will not only be provided with an introduction to classical logic, but to philosophical (modal, epistemic, deontic, temporal) and intuitionistic logic as well. The first chapter is an easy to read non-technical Introduction to the topics in the book. The next chapters are consecutively about Propositional Logic, Sets (finite and infinite), Predicate Logic, Arithmetic and Gödel’s Incompleteness Theorems, Modal Logic, Philosophy of Language, Intuitionism and Intuitionistic Logic, Applications (Prolog; Relational Databases and SQL; Social Choice Theory, in particular Majority Judgment) and finally, Fallacies and Unfair Discussion Methods. Throughout the text, the author provides some impressions of the historical development of logic: Stoic and Aristotelian logic, logic in the Middle Ages and Frege's Begriffsschrift, together with the works of George Boole (1815-1864) and August De Morgan (1806-1871), the origin of modern logic. Since "if ..., then ..." can be considered to be the heart of logic, throughout this book much attention is paid to conditionals: material, strict and relevant implication, entailment, counterfactuals and conversational implicature are treated and many references for further reading are given. Each chapter is concluded with answers to the exercises. Philosophical and Mathematical Logic is a very recent book (2018), but with every aspect of a classic. What a wonderful book! Work written with all the necessary rigor, with immense depth, but without giving up clarity and good taste. Philosophy and mathematics go hand in hand with the most diverse themes of logic. An introductory text, but not only that. It goes much further. It's worth diving into the pages of this book, dear reader! Paulo Sérgio Argolo
Mathematics Logic And Their Philosophies
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Author : Mojtaba Mojtahedi
language : en
Publisher: Springer Nature
Release Date : 2021-02-09
Mathematics Logic And Their Philosophies written by Mojtaba Mojtahedi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-09 with Philosophy categories.
This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.
Three Views Of Logic
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Author : Donald W. Loveland
language : en
Publisher: Princeton University Press
Release Date : 2014-01-26
Three Views Of Logic written by Donald W. Loveland and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-26 with Mathematics categories.
The first interdisciplinary textbook to introduce students to three critical areas in applied logic Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses
The History And Philosophy Of Polish Logic
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Author : K. Mulligan
language : en
Publisher: Springer
Release Date : 2016-01-26
The History And Philosophy Of Polish Logic written by K. Mulligan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-26 with Philosophy categories.
The book presents the state of the art of research into the legacy of interwar Polish analytic philosophy and exemplifies different approaches to the history of philosophy. It contains discussions and reconstructions of aspects of Polish philosophy and logic as well as reactions to and developments of this tradition.
Mathematical Logic And Computation
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Author : Jeremy Avigad
language : en
Publisher: Cambridge University Press
Release Date : 2022-11-24
Mathematical Logic And Computation written by Jeremy Avigad 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 2022-11-24 with Computers categories.
A thorough introduction to the fundamental methods and results in mathematical logic, and its foundational role in computer science.
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.
Logicism Intuitionism And Formalism
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Author : Sten Lindström
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-25
Logicism Intuitionism And Formalism written by Sten Lindström 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 2008-11-25 with Mathematics categories.
This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.
Logic For Mathematics And Computer Science
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Author : Stanley Burris
language : en
Publisher: Upper Saddle River, N.J. : Prentice Hall
Release Date : 1998
Logic For Mathematics And Computer Science written by Stanley Burris and has been published by Upper Saddle River, N.J. : Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Computers categories.
This text is intended for one semester courses in Logic, it can also be applied to a two semester course, in either Computer Science or Mathematics Departments. Unlike other texts on mathematical logic that are either too advanced, too sparse in examples or exercises, too traditional in coverage, or too philosophical in approach, this text provides an elementary "hands-on" presentation of important mathematical logic topics, new and old, that is readily accessible and relevant to all students of the mathematical sciences -- not just those in traditional pure mathematics.
Logic And Metalogic
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Author :
language : en
Publisher: PediaPress
Release Date :
Logic And Metalogic written by and has been published by PediaPress this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.