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001451104 019__ $$a1350690367
001451104 020__ $$a9783031068430$$q(electronic bk.)
001451104 020__ $$a3031068432$$q(electronic bk.)
001451104 020__ $$z9783031068423
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001451104 0247_ $$a10.1007/978-3-031-06843-0$$2doi
001451104 035__ $$aSP(OCoLC)1350617448
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001451104 050_4 $$aQA9
001451104 08204 $$a510.92$$223/eng/20221117
001451104 24500 $$aV.A. Yankov on non-classical logics, history and philosophy of mathematics /$$cAlex Citkin, Ioannis Vandoulakis, editors.
001451104 264_1 $$aCham :$$bSpringer,$$c[2022]
001451104 264_4 $$c©2022
001451104 300__ $$a1 online resource (xi, 313 pages) :$$billustrations.
001451104 336__ $$atext$$btxt$$2rdacontent
001451104 337__ $$acomputer$$bc$$2rdamedia
001451104 338__ $$aonline resource$$bcr$$2rdacarrier
001451104 4901_ $$aOutstanding contributions to logic ;$$vvolume 24
001451104 500__ $$aIncludes index.
001451104 5050_ $$aIntro -- Preface -- Contents -- Contributors -- 1 Short Autobiography -- Complete Bibliography of Vadim Yankov -- Part I Non-Classical Logics -- 2 V. Yankov's Contributions to Propositional Logic -- 2.1 Introduction -- 2.2 Classes of Logics and Their Respective Algebraic Semantics -- 2.2.1 Calculi and Their Logics -- 2.2.2 Algebraic Semantics -- 2.2.3 Lattices sans serif upper D e d Subscript upper CDedC and sans serif upper L i n d Subscript left parenthesis upper C comma k right parenthesisLind(C,k) -- 2.3 Yankov's Characteristic Formulas -- 2.3.1 Formulas and Homomorphisms
001451104 5058_ $$a2.3.2 Characteristic Formulas -- 2.3.3 Splitting -- 2.3.4 Quasiorder -- 2.4 Applications of Characteristic Formulas -- 2.4.1 Antichains -- 2.5 Extensions of upper CC-Logics -- 2.5.1 Properties of Algebras bold upper A Subscript iAi -- 2.5.2 Proofs of Lemmas -- 2.6 Calculus of the Weak Law of Excluded Middle -- 2.6.1 Semantics of sans serif upper K upper CKC -- 2.6.2 sans serif upper K upper CKC from the Splitting Standpoint -- 2.6.3 Proof of Theorem2.5 -- 2.7 Some Si-Calculi -- 2.8 Realizable Formulas -- 2.9 Some Properties of Positive Logic -- 2.9.1 Infinite Sequence of Independent Formulas
001451104 5058_ $$a2.9.2 Strongly Descending Infinite Sequence of Formulas -- 2.9.3 Strongly Ascending Infinite Sequence of Formulas -- 2.10 Conclusions -- References -- 3 Dialogues and Proofs -- Yankov's Contribution to Proof Theory -- 3.1 Introduction -- 3.2 Consistency Proofs -- 3.3 Yankov's Approach -- 3.4 The Calculus -- 3.5 The Dialogue Method -- 3.6 Bar Induction -- 3.7 Proofs -- 3.8 Concluding Remarks -- References -- 4 Jankov Formulas and Axiomatization Techniques for Intermediate Logics -- 4.1 Introduction -- 4.2 Intermediate Logics and Their Semantics -- 4.2.1 Intermediate Logics
001451104 5058_ $$a4.2.2 Heyting Algebras -- 4.2.3 Kripke Frames and Esakia Spaces -- 4.3 Jankov Formulas -- 4.3.1 Jankov Lemma -- 4.3.2 Splitting Theorem -- 4.3.3 Cardinality of the Lattice of Intermediate Logics -- 4.4 Canonical Formulas -- 4.4.1 Subframe Canonical Formulas -- 4.4.2 Negation-Free Subframe Canonical Formulas -- 4.4.3 Stable Canonical Formulas -- 4.5 Canonical Formulas Dually -- 4.5.1 Subframe Canonical Formulas Dually -- 4.5.2 Stable Canonical Formulas Dually -- 4.6 Subframe and Cofinal Subframe Formulas -- 4.7 Stable Formulas -- 4.7.1 Stable Formulas -- 4.7.2 Cofinal Stable Rules and Formulas
001451104 5058_ $$a4.8 Subframization and Stabilization -- 4.8.1 Subframization -- 4.8.2 Stabilization -- References -- 5 Yankov Characteristic Formulas (An Algebraic Account) -- 5.1 Introduction -- 5.2 Background -- 5.2.1 Basic Definitions -- 5.2.2 Finitely Presentable Algebras -- 5.2.3 Splitting -- 5.3 Independent Sets of Splitting Identities -- 5.3.1 Quasi-order -- 5.3.2 Antichains -- 5.4 Independent Bases -- 5.4.1 Subvarieties Defined by Splitting Identities -- 5.4.2 Independent Bases in the Varieties Enjoying the Fsi-Spl Property -- 5.4.3 Finite Bases in the Varieties Enjoying the Fsi-Spl Property
001451104 506__ $$aAccess limited to authorized users.
001451104 520__ $$aThis book is dedicated to V.A. Yankovs seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankovs results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics. The book also contains an exposition of Yankovs revolutionary approach to constructive proof theory. The editors also include Yankovs contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.
001451104 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed November 17, 2022).
001451104 60010 $$aI͡Ankov, V. A.$$q(Vadim Anatolʹevich)
001451104 650_0 $$aProposition (Logic)
001451104 650_0 $$aMathematics$$xPhilosophy.
001451104 655_0 $$aElectronic books.
001451104 7001_ $$aCitkin, Alex,$$eeditor.
001451104 7001_ $$aVandoulakis, Ioannis,$$eeditor.
001451104 77608 $$iPrint version: $$z3031068424$$z9783031068423$$w(OCoLC)1312149405
001451104 830_0 $$aOutstanding contributions to logic ;$$vvolume 24.
001451104 852__ $$bebk
001451104 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-06843-0$$zOnline Access$$91397441.1
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001451104 980__ $$aBIB
001451104 980__ $$aEBOOK
001451104 982__ $$aEbook
001451104 983__ $$aOnline
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