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000913401 019__ $$a1111771522$$a1117304069$$a1117702254
000913401 020__ $$a9789811379970$$q(electronic book)
000913401 020__ $$a9811379971$$q(electronic book)
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000913401 0247_ $$a10.1007/978-981-13-7997-0$$2doi
000913401 0247_ $$a10.1007/978-981-13-7
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000913401 1001_ $$aOno, Hiroakira,$$eauthor.
000913401 24510 $$aProof theory and algebra in logic /$$cHiroakira Ono.
000913401 264_1 $$aSingapore :$$bSpringer,$$c[2019]
000913401 264_4 $$c©2019
000913401 300__ $$a1 online resource :$$billustrations.
000913401 336__ $$atext$$btxt$$2rdacontent
000913401 337__ $$acomputer$$bc$$2rdamedia
000913401 338__ $$aonline resource$$bcr$$2rdacarrier
000913401 4901_ $$aShort textbooks in logic,$$x2522-5480
000913401 504__ $$aIncludes bibliographical references and index.
000913401 5050_ $$aIntroduction -- Part I Proof Theory -- Sequent systems -- Cut elimination for sequent systems -- Proof-theoretic analysis of logical properties -- Modal and substructural logics -- Deducibility and axiomatic extensions -- Part II Algebra in Logic -- Boolean algebras and classical logic -- Many-valued algebras -- Heyting algebras and intuitionistic logic -- Logics and varieties -- Residuated structures -- Modal algebras -- References -- Index.
000913401 506__ $$aAccess limited to authorized users.
000913401 520__ $$aThis book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses. The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic.
000913401 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed August 28, 2019).
000913401 650_0 $$aProof theory.
000913401 650_0 $$aAlgebraic logic.
000913401 77608 $$iPrint version: $$z9811379963$$z9789811379963$$w(OCoLC)1091008618
000913401 830_0 $$aShort textbooks in logic.
000913401 852__ $$bebk
000913401 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-981-13-7997-0$$zOnline Access$$91397441.1
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