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020 _a9783034808620
_9978-3-0348-0862-0
024 7 _a10.1007/978-3-0348-0862-0
_2doi
035 _ato000541821
040 _aSpringer
_cSpringer
_dRU-ToGU
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072 7 _aCOM051010
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082 0 4 _a005.131
_223
100 1 _aLi, Wei.
_eauthor.
_9320382
245 1 0 _aMathematical Logic
_helectronic resource
_bFoundations for Information Science /
_cby Wei Li.
250 _a2nd ed. 2014.
260 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2014.
300 _aXIV, 301 p. 13 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aProgress in Computer Science and Applied Logic,
_x2297-0576 ;
_v25
505 0 _aPreface -- Preface to the Second Edition -- I Elements of Mathematical Logic -- 1 Syntax of First-Order Languages -- 2 Models of First-Order Languages -- 3 Formal Inference Systems -- 4 Computability & Representability -- 5 Gödel Theorems -- II Logical Framework of Scientific Discovery -- 6 Sequences of Formal Theories -- 7 Revision Calculus -- 8 Version Sequences -- 9 Inductive Inference -- 10 Meta-Language Environments -- Appendix 1 Sets and Maps -- Appendix 2 Proof of the Representability Theorem -- Bibliography -- Index.
520 _aMathematical 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. The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging. 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.
650 0 _aComputer Science.
_9155490
650 0 _aLogic, Symbolic and mathematical.
_9293145
650 1 4 _aComputer Science.
_9155490
650 2 4 _aMathematical Logic and Formal Languages.
_9303363
650 2 4 _aMathematical Logic and Foundations.
_9306112
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
830 0 _aProgress in Computer Science and Applied Logic,
_9447212
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0862-0
912 _aZDB-2-SMA
999 _c399484