Mathematical Logic And Formal Systems
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Mathematical Logic And Formal Systems
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Author : Alcantara
language : en
Publisher: CRC Press
Release Date : 1985-04-25
Mathematical Logic And Formal Systems written by Alcantara and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-04-25 with Mathematics categories.
This unique collection of research papers provides an important contribution to the area of Mathematical Logic and Formal Systems. Exploring interesting practical applications as well as problems for further investigation, this single-source reference discusses the interpretations of the concept of probability and their relationship to statistical methods ... illustrates the problem of set theoretical foundations and category theory ... treats the various aspects of the theory of large cardinals including combinatorial properties of some sets naturally related to them ... resolves an open problem in the theory of relations ... and characterizes interpretations of elementary theories as functors between categories whose objects are structures. Written by world-renowned authorities in their fields, Mathematical Logic and Formal Systems is important reading for logicians, pure and applied mathematicians, and graduate students in logic courses. Book jacket.
Mathematical Logic
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Author :
language : en
Publisher:
Release Date :
Mathematical Logic written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Introduction To Mathematical Logic
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Author : Agustin Willmott
language : en
Publisher: Larsen and Keller Education
Release Date : 2019-06-20
Introduction To Mathematical Logic written by Agustin Willmott and has been published by Larsen and Keller Education this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-20 with categories.
Mathematical logic is a subfield of mathematics that is concerned with the application of formal logic to mathematics. It is closely associated with the foundations of mathematics, metamathematics and theoretical computer science. The study of the deductive power of formal proof systems and the expressive power of formal systems are the unifying themes in mathematical logic. Set theory, recursion theory, proof theory and model theory are the primary subfields in mathematical logic. Each of these fields has a distinct focus. The systems of propositional logic and first-order logic are widely explored for application in the foundations of mathematics. The classical logic systems such as second-order logic or infinitary logic and nonclassical logic systems such as intuitionistic logic are also studied in this field. This book provides comprehensive insights into the field of mathematical logic. It presents the complex subject of mathematical logic in the most comprehensible and easy to understand language. In this book, constant effort has been made to make the understanding of the difficult concepts as easy and informative as possible, for the readers.
Fundamentals Of Mathematical Logic
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Author : Samuel Parkers
language : en
Publisher:
Release Date : 2022-09-20
Fundamentals Of Mathematical Logic written by Samuel Parkers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-20 with categories.
The sub-field of mathematics that focuses on identifying the applications of formal logic to mathematics is known as mathematical logic. It is also known as symbolic logic or formal logic. It is concerned with the study of expressive and deductive power of formal systems. Some of the formal logical systems are first-order logic, nonclassical and modal logic, algebraic logic and other classical logics. The discipline is divided into four areas. These are model theory, proof theory, set theory and recursion theory. The field is closely related to theoretical computer science and foundations of mathematics. The field finds its applications in other disciplines such as physics, biology, economics, metaphysics, law and morals, and psychology. This book explores all the important aspects of related to this discipline in the present day scenario. Different approaches, evaluations, methodologies and studies on mathematical logic have been included herein. As this field is emerging at a rapid pace, the contents of this book will help the readers understand the modern concepts and applications of the subject.
Mathematical Logic Formal Systems
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Author : Open University Course Team
language : en
Publisher:
Release Date : 2008-12-06
Mathematical Logic Formal Systems written by Open University Course Team and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-06 with categories.
In this and units ML05 up to ML08, we develop a formal proof system capable of deriving results about number theory, leading up to Godel's Incompleteness Theorems, setting limits to what such formal systems can achieve. In unit ML01, we look at a formal language for expressing statements about number theory and how such statements can be true or false, depending on the interpretation of the symbols used. We look at tautologies, which are some of the statements always true because of their shape, and at what it means for one statement to be a consequence of others, to give a yardstick for what we expect from theformal proof system.To order all 8 units in the Mathematical Logic series please see product M381/PP01
A Beginner S Further Guide To Mathematical Logic
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Author : Raymond M Smullyan
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-11-11
A Beginner S Further Guide To Mathematical Logic written by Raymond M Smullyan 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 2016-11-11 with Mathematics categories.
'A wealth of examples to which solutions are given permeate the text so the reader will certainly be active.'The Mathematical GazetteThis is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan.This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results.The present volume begins with a bit more on propositional and first-order logic, followed by what I would call a 'fein' chapter, which simultaneously generalizes some results from recursion theory, first-order arithmetic systems, and what I dub a 'decision machine.' Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic.This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics.
An Introduction To Formal Logic
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Author : Peter Smith
language : en
Publisher: Cambridge University Press
Release Date : 2003-11-06
An Introduction To Formal Logic written by Peter Smith 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 2003-11-06 with Mathematics categories.
Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
Popular Lectures On Mathematical Logic
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Author : Hao Wang
language : en
Publisher: Courier Corporation
Release Date : 2014-09-22
Popular Lectures On Mathematical Logic written by Hao Wang and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-22 with Mathematics categories.
Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.
Number Theory And Mathematical Logic
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Author : Open University Course Team
language : en
Publisher:
Release Date : 2004-01
Number Theory And Mathematical Logic written by Open University Course Team and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01 with categories.
In this and units ML05 up to ML08, we develop a formal proof system capable of deriving results about number theory, leading up to Gödel's Incompleteness Theorems, setting limits to what such formal systems can achieve. In unit ML01, we look at a formal language for expressing statements about number theory and how such statements can be true or false, depending on the interpretation of the symbols used. We look at tautologies, which are some of the statements always true because of their shape, and at what it means for one statement to be a consequence of others, to give a yardstick for what we expect from the formal proof system.
Logic Works
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Author : Lorne Falkenstein
language : en
Publisher: Routledge
Release Date : 2021-11-30
Logic Works written by Lorne Falkenstein and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-30 with Philosophy categories.
Logic Works is a critical and extensive introduction to logic. It asks questions about why systems of logic are as they are, how they relate to ordinary language and ordinary reasoning, and what alternatives there might be to classical logical doctrines. The book covers classical first-order logic and alternatives, including intuitionistic, free, and many-valued logic. It also considers how logical analysis can be applied to carefully represent the reasoning employed in academic and scientific work, better understand that reasoning, and identify its hidden premises. Aiming to be as much a reference work and handbook for further, independent study as a course text, it covers more material than is typically covered in an introductory course. It also covers this material at greater length and in more depth with the purpose of making it accessible to those with no prior training in logic or formal systems. Online support material includes a detailed student solutions manual with a running commentary on all starred exercises, and a set of editable slide presentations for course lectures. Key Features Introduces an unusually broad range of topics, allowing instructors to craft courses to meet a range of various objectives Adopts a critical attitude to certain classical doctrines, exposing students to alternative ways to answer philosophical questions about logic Carefully considers the ways natural language both resists and lends itself to formalization Makes objectual semantics for quantified logic easy, with an incremental, rule-governed approach assisted by numerous simple exercises Makes important metatheoretical results accessible to introductory students through a discursive presentation of those results and by using simple case studies