LEADER 03411nam 2200577 450 001 9910484070503321 005 20220318002222.0 010 $a3-030-56554-8 024 7 $a10.1007/978-3-030-56554-1 035 $a(CKB)4100000011515530 035 $a(DE-He213)978-3-030-56554-1 035 $a(MiAaPQ)EBC6380775 035 $a(MiAaPQ)EBC6647476 035 $a(Au-PeEL)EBL6380775 035 $a(OCoLC)1225937380 035 $a(Au-PeEL)EBL6647476 035 $a(PPN)269144951 035 $a(EXLCZ)994100000011515530 100 $a20220318d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDecidability of logical theories and their combination /$fJoa?o Rasga, Cristina Sernadas 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cBirkha?user,$d[2020] 210 4$dİ2020 215 $a1 online resource (XIII, 178 p. 70 illus., 1 illus. in color.) 225 1 $aStudies in Universal Logic,$x2297-0282 311 $a3-030-56553-X 320 $aIncludes bibliographical references and index. 327 $aChapter 1: First Order Logic -- Chapter 2: Reasoning with Theories -- Chapter 3: Decidability Results on Theories -- Chapter 4: Quantifier Elimination -- Chapter 5: Combination of Theories -- Appendix: Basics of Computability -- Bibliography -- Table of Symbols -- Subject Index. 330 $aThis textbook provides a self-contained introduction to decidability of first-order theories and their combination. The technical material is presented in a systematic and universal way and illustrated with plenty of examples and a range of proposed exercises. After an overview of basic first-order logic concepts, the authors discuss some model-theoretic notions like embeddings, diagrams, and elementary substructures. The text then goes on to explore an applicable way to deduce logical consequences from a given theory and presents sufficient conditions for a theory to be decidable. The chapters that follow focus on quantifier elimination, decidability of the combination of first-order theories and the basics of computability theory. The inclusion of a chapter on Gentzen calculus, cut elimination, and Craig interpolation, as well as a chapter on combination of theories and preservation of decidability, help to set this volume apart from similar books in the field. Decidability of Logical Theories and their Combination is ideal for graduate students of Mathematics and is equally suitable for Computer Science, Philosophy and Physics students who are interested in gaining a deeper understanding of the subject. The book is also directed to researchers that intend to get acquainted with first-order theories and their combination. 410 0$aStudies in Universal Logic,$x2297-0282 606 $aLogic, Symbolic and mathematical 606 $aFirst-order logic 606 $aMathematics$xPhilosophy 615 0$aLogic, Symbolic and mathematical. 615 0$aFirst-order logic. 615 0$aMathematics$xPhilosophy. 676 $a511.3 700 $aRasga$b Joa?o$0845263 702 $aSernadas$b Cristina 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484070503321 996 $aDecidability of Logical Theories and Their Combination$91886075 997 $aUNINA