Simple Type Theory: A Practical Logic for Expressing and Reasoning About Mathematical Ideas

Farmer, William M.

ISBN 10: 3031211146 ISBN 13: 9783031211140

Editorial: Birkh?user, 2024

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2024. Paperback. . . . . . N� de ref. del art�culo V9783031211140

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Sinopsis:

This unique textbook, in contrast to a standard logic text, provides the reader with a logic that actually can be used in practice to express and reason about mathematical ideas.

The book is an introduction to simple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic called Alonzo that is based on Alonzo Church's formulation of simple type theory known as Church's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The book illustrates, using Alonzo, how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge.

Topics and features:

Offers the first book-length introduction to simple type theory as a predicate logic
Provides the reader with a logic that is close to mathematical practice
Presents the tools needed to build libraries of mathematical knowledge
Employs two semantics, one for mathematics and one for logic
Emphasizes the model-theoretic view of predicate logic
Includes several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooks

Aimed at students of computing and mathematics at the graduate or upper-undergraduate level, this book is also well-suited for mathematicians, computing professionals, engineers, and scientists who need a practical logic for expressing and reasoning about mathematical ideas.

William M. Farmer is a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada.

Acerca del autor: William M. Farmer has over 35 years of experience working in industry and academia in computing and mathematics. He received a B.A. in mathematics from the University of Notre Dame in 1978 and an M.A. in mathematics in 1980, an M.S. in computer sciences in 1983, and a Ph.D. in mathematics in 1984 from the University of Wisconsin-Madison. He is currently a Professor in the Department of Computing and Software at McMaster University. Before joining McMaster in 1999, he conducted research in computer science for twelve years at The MITRE Corporation in Bedford, Massachusetts, USA and taught computer programming and networking courses for two years at St. Cloud State University.
Dr. Farmer's research interests are logic, mechanized mathematics, mathematical knowledge management, and formal methods. One of his most significant achievements is the design and implementation of the IMPS proof assistant, which was done at MITRE in partnership with Dr. JoshuaGuttman and Dr. Javier Thayer. His work on IMPS has lead to research on developing practice-oriented logics and set theories and on organizing mathematical knowledge as a network of interconnected axiomatic theories. He and Dr. Jacques Carette are currently leading the MathScheme project at McMaster with the aim of developing a framework for integrating axiomatic and algorithmic mathematics. On this project Dr. Farmer has focused on how to reason about the interplay of syntax and semantics, as exhibited in syntax-based mathematical algorithms like symbolic differentiation, within a logic equipped with global quotation and evaluation operators. Dr. Farmer has had a career-long interest in using simple type theory as a practical logic for expressing and reasoning about mathematical ideas. He is the author of "The Seven Virtues of Simple Type Theory", Journal of Applied Logic, 6:267-286, 2008, one of the leading references on simple type theory.

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T�tulo: Simple Type Theory: A Practical Logic for ...
Editorial: Birkh?user
A�o de publicaci�n: 2024
Encuadernaci�n: Encuadernaci�n de tapa blanda
Condici�n: New

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Simple Type Theory

Farmer, William M.

Publicado por Springer, Berlin|Springer International Publishing|Birkh�user, 2024

ISBN 10: 3031211146 ISBN 13: 9783031211140

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Simple Type Theory | A Practical Logic for Expressing and Reasoning About Mathematical Ideas

William M. Farmer

Publicado por Springer International Publishing, 2024

ISBN 10: 3031211146 ISBN 13: 9783031211140

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Simple Type Theory : A Practical Logic for Expressing and Reasoning About Mathematical Ideas

William M. Farmer

Publicado por Springer International Publishing, 2024

ISBN 10: 3031211146 ISBN 13: 9783031211140

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Taschenbuch. Condici�n: Neu. Druck auf Anfrage Neuware - Printed after ordering - This unique textbook, in contrast to a standard logic text, provides the reader with a logic that actually can beusedin practice to express and reason about mathematical ideas.The book is an introduction tosimple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic calledAlonzothat is based on Alonzo Church's formulation of simple type theory known asChurch's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The book illustrates, using Alonzo, how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge.Topics and features:Offers the first book-length introduction to simple type theory as a predicate logicProvides the reader with a logic that is close to mathematical practicePresents the tools needed to build libraries of mathematical knowledgeEmploys two semantics, one for mathematics and one for logicEmphasizes the model-theoretic view of predicate logicIncludes several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooksAimed at students of computing and mathematics at the graduate or upper-undergraduate level, this book is also well-suited for mathematicians, computing professionals, engineers, and scientists who need apracticallogic for expressing and reasoning about mathematical ideas.William M. Farmeris a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada. N� de ref. del art�culo: 9783031211140

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Simple Type Theory

William M. Farmer

Publicado por Berlin Springer International Publishing Springer, 2024

ISBN 10: 3031211146 ISBN 13: 9783031211140

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Taschenbuch. Condici�n: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This unique textbook, in contrast to a standard logic text, provides the reader with a logic that actually can beusedin practice to express and reason about mathematical ideas.The book is an introduction tosimple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic calledAlonzothat is based on Alonzo Church's formulation of simple type theory known asChurch's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The book illustrates, using Alonzo, how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge.Topics and features:Offers the first book-length introduction to simple type theory as a predicate logicProvides the reader with a logic that is close to mathematical practicePresents the tools needed to build libraries of mathematical knowledgeEmploys two semantics, one for mathematics and one for logicEmphasizes the model-theoretic view of predicate logicIncludes several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooksAimed at students of computing and mathematics at the graduate or upper-undergraduate level, this book is also well-suited for mathematicians, computing professionals, engineers, and scientists who need apracticallogic for expressing and reasoning about mathematical ideas.William M. Farmeris a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada. 295 pp. Englisch. N� de ref. del art�culo: 9783031211140

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Simple Type Theory

William M. Farmer

Publicado por Springer International Publishing, Springer International Publishing Jan 2024, 2024

ISBN 10: 3031211146 ISBN 13: 9783031211140

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Librería: buchversandmimpf2000, Emtmannsberg, BAYE, Alemania

Calificaci�n del vendedor: 5 de 5 estrellas

Taschenbuch. Condici�n: Neu. Neuware -This unique textbook, in contrast to a standard logic text, provides the reader with a logic that actually can be used in practice to express and reason about mathematical ideas.The book is an introduction to simple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic called Alonzo that is based on Alonzo Church's formulation of simple type theory known as Church's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The book illustrates, using Alonzo, how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge.Topics and features:Offers the first book-length introduction to simple type theory as a predicate logicProvides the reader with a logic that is close to mathematical practicePresents the tools needed to build libraries of mathematical knowledgeEmploys two semantics, one for mathematics and one for logicEmphasizes the model-theoretic view of predicate logicIncludes several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooksAimed at students of computing and mathematics at the graduate or upper-undergraduate level, this book is also well-suited for mathematicians, computing professionals, engineers, and scientists who need a practical logic for expressing and reasoning about mathematical ideas.William M. Farmer is a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 312 pp. Englisch. N� de ref. del art�culo: 9783031211140

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