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Simple Type Theory : A Practical Logic for Expressing and Reasoning About Mathematical Ideas / by William M. Farmer
(Computer Science Foundations and Applied Logic. ISSN:27315762)

データ種別	電子ブック
版	1st ed. 2023.
出版者	(Cham : Springer International Publishing : Imprint: Birkhäuser)
出版年	2023
大きさ	XIV, 295 p. 10 illus., 3 illus. in color : online resource
著者標目	*Farmer, William M author SpringerLink (Online service)

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URL	巻　次	配架場所	請求記号	登録番号	コメント	刷　年	状　態	利用注記	ISBN	予約	請求メモ
URL		射水-電子	007	EB0001902	Computer Scinece R0 2005-6,2022-3				9783031211126

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一般注記	1 Introduction -- 2 Answers to Readers’ Questions -- 3 Preliminary Concepts -- 4 Syntax -- 5 Semantics -- 6 Additional Notation -- 7 Beta-reduction and Substitution -- 8 Proof Systems -- 9 Theories -- 10 Sequences -- 11 Developments -- 12 Real Number Mathematics -- 13 Morphisms 14 Alonzo Variants -- 15 Software Support 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 HTTP:URL=https://doi.org/10.1007/978-3-031-21112-6
件　名	LCSH:Computer science LCSH:Mathematical logic LCSH:Computational complexity LCSH:Reasoning LCSH:Set theory FREE:Computer Science Logic and Foundations of Programming FREE:Mathematical Logic and Foundations FREE:Computational Complexity FREE:Formal Reasoning FREE:Set Theory
分　類	LCC:QA75.5-76.95 DC23:004.0151
書誌ID	EB00001290
ISBN	9783031211126