LEADER 04147nam 22006375 450 001 9910350206303321 005 20200630140204.0 010 $a981-13-7997-1 024 7 $a10.1007/978-981-13-7997-0 035 $a(CKB)5340000000061424 035 $a(MiAaPQ)EBC5919677 035 $a(DE-He213)978-981-13-7997-0 035 $a(MiAaPQ)EBC31870647 035 $a(Au-PeEL)EBL31870647 035 $a(EXLCZ)995340000000061424 100 $a20190802d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aProof Theory and Algebra in Logic /$fby Hiroakira Ono 205 $a1st ed. 2019. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2019. 215 $a1 online resource (164 pages) 225 1 $aShort Textbooks in Logic,$x2522-5480 311 08$a981-13-7996-3 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Part I Proof Theory -- Sequent systems -- Cut elimination for sequent systems -- Proof-theoretic analysis of logical properties -- Modal and substructural logics -- Deducibility and axiomatic extensions -- Part II Algebra in Logic -- Boolean algebras and classical logic -- Many-valued algebras -- Heyting algebras and intuitionistic logic -- Logics and varieties -- Residuated structures -- Modal algebras -- References -- Index. 330 $aThis book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses. The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic. 410 0$aShort Textbooks in Logic,$x2522-5480 606 $aLogic 606 $aLogic, Symbolic and mathematical 606 $aAlgebra 606 $aOrdered algebraic structures 606 $aLogic$3https://scigraph.springernature.com/ontologies/product-market-codes/E16000 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 606 $aOrder, Lattices, Ordered Algebraic Structures$3https://scigraph.springernature.com/ontologies/product-market-codes/M11124 615 0$aLogic. 615 0$aLogic, Symbolic and mathematical. 615 0$aAlgebra. 615 0$aOrdered algebraic structures. 615 14$aLogic. 615 24$aMathematical Logic and Formal Languages. 615 24$aMathematical Logic and Foundations. 615 24$aOrder, Lattices, Ordered Algebraic Structures. 676 $a511.3 700 $aOno$b Hiroakira$4aut$4http://id.loc.gov/vocabulary/relators/aut$0990529 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910350206303321 996 $aProof Theory and Algebra in Logic$92266027 997 $aUNINA