LEADER 04653nam 22006255 450 001 9910768186603321 005 20200629194544.0 010 $a3-0348-0862-3 024 7 $a10.1007/978-3-0348-0862-0 035 $a(CKB)3710000000306087 035 $a(SSID)ssj0001386598 035 $a(PQKBManifestationID)11764674 035 $a(PQKBTitleCode)TC0001386598 035 $a(PQKBWorkID)11374700 035 $a(PQKB)11062641 035 $a(DE-He213)978-3-0348-0862-0 035 $a(MiAaPQ)EBC6310553 035 $a(MiAaPQ)EBC5576337 035 $a(Au-PeEL)EBL5576337 035 $a(OCoLC)1066178831 035 $a(PPN)183096592 035 $a(EXLCZ)993710000000306087 100 $a20141107d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical Logic $eFoundations for Information Science /$fby Wei Li 205 $a2nd ed. 2014. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (XIV, 301 p. 13 illus.) 225 1 $aProgress in Computer Science and Applied Logic,$x2297-0576 ;$v25 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-0348-0861-5 320 $aIncludes bibliographical references and index. 327 $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. 330 $aMathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel?s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines. 410 0$aProgress in Computer Science and Applied Logic,$x2297-0576 ;$v25 606 $aMathematical logic 606 $aMathematical Logic and Formal Languages$3https://scigraph.springernature.com/ontologies/product-market-codes/I16048 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 615 0$aMathematical logic. 615 14$aMathematical Logic and Formal Languages. 615 24$aMathematical Logic and Foundations. 676 $a511.3 676 $a511.3 700 $aLi$b Wei$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721674 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910768186603321 996 $aMathematical logic$91410153 997 $aUNINA