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001 978-3-7643-9977-1
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008 100715s2010 sz | s |||| 0|eng d
020 _a9783764399771
_9978-3-7643-9977-1
024 7 _a10.1007/978-3-7643-9977-1
_2doi
050 4 _aQA8.9-QA10.3
072 7 _aUYA
_2bicssc
072 7 _aMAT018000
_2bisacsh
072 7 _aCOM051010
_2bisacsh
082 0 4 _a005.131
_223
100 1 _aLi, Wei.
_eauthor.
245 1 0 _aMathematical Logic
_h[electronic resource] :
_bFoundations for Information Science /
_cby Wei Li.
264 1 _aBasel :
_bBirkhäuser Basel,
_c2010.
300 _bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Computer Science and Applied Logic (PCS) ;
_v25
505 0 _aSyntax of First-Order Languages -- Models of First-Order Languages -- Formal Inference Systems -- Computability & Representability -- Gödel Theorems -- Sequences of Formal Theories -- Revision Calculus -- Version Sequences -- Inductive Inference -- Workflows for Scientific Discovery.
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. 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.
650 0 _aLogic, Symbolic and mathematical.
650 1 4 _aComputer Science.
650 2 4 _aMathematical Logic and Formal Languages.
650 2 4 _aMathematical Logic and Foundations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783764399764
830 0 _aProgress in Computer Science and Applied Logic (PCS) ;
_v25
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-7643-9977-1
912 _aZDB-2-SCS
999 _c112991
_d112991