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001 978-3-031-21112-6
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020 _a9783031211126
_9978-3-031-21112-6
050 4 _aQA75.5-76.95
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_2bicssc
072 7 _aCOM051000
_2bisacsh
072 7 _aUYA
_2thema
082 0 4 _a004.0151
_223
100 1 _aFarmer, William M.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSimple Type Theory
_h[electronic resource] :
_bA Practical Logic for Expressing and Reasoning About Mathematical Ideas /
_cby William M. Farmer.
250 _a1st ed. 2023.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2023.
300 _aXIV, 295 p. 10 illus., 3 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aComputer Science Foundations and Applied Logic,
_x2731-5762
500 _aAcceso multiusuario
505 0 _a1 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.
520 _aThis 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.
541 _fUABC ;
_cPerpetuidad
650 0 _aComputer science.
650 0 _aMathematical logic.
650 0 _aComputational complexity.
650 0 _aReasoning.
650 0 _aSet theory.
650 1 4 _aComputer Science Logic and Foundations of Programming.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aComputational Complexity.
650 2 4 _aFormal Reasoning.
650 2 4 _aSet Theory.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031211119
776 0 8 _iPrinted edition:
_z9783031211133
776 0 8 _iPrinted edition:
_z9783031211140
830 0 _aComputer Science Foundations and Applied Logic,
_x2731-5762
856 4 0 _zLibro electrónico
_uhttp://libcon.rec.uabc.mx:2048/login?url=https://doi.org/10.1007/978-3-031-21112-6
912 _aZDB-2-SCS
912 _aZDB-2-SXCS
942 _cLIBRO_ELEC
999 _c260850
_d260849