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Author : J.Y. Girard
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (473 download)
Download or read book Three-valued Logic and Cut-elimination: The Actual Meaning Og Takeuti's Conjecture written by J.Y. Girard and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. Y. Girard
Publisher :
ISBN 13 :
Total Pages : 54 pages
Book Rating : 4.F/5 ( download)
Download or read book Three-valued Logic and Cut-elimination written by J. Y. Girard and published by . This book was released on 1976 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. Y. Girard
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (11 download)
Download or read book Three-valued Logic and Cut-elimination: the Actual Meanig of Takeuti's Conjecture written by J. Y. Girard and published by . This book was released on 1976 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wei Li
Publisher : Springer Nature
ISBN 13 : 9811942706
Total Pages : 284 pages
Book Rating : 4.8/5 (119 download)
Download or read book R-Calculus, III: Post Three-Valued Logic written by Wei Li and published by Springer Nature. This book was released on 2022-11-19 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of the book series shows R-calculus is a Gentzen-typed deduction system which is non-monotonic, and is a concrete belief revision operator which is proved to satisfy the AGM postulates and the DP postulates. In this book, R-calculus is taken as Tableau-based/sequent-based/multisequent-based to preserve the satisfiability of the Theory/sequent/multisequent to revise, or sequent-based, to preserve the satisfiability of the sequent to revise. The R-calculi for Post and three-valued logic is given. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic.
Author : Melvin Fitting
Publisher : Physica
ISBN 13 : 3790817694
Total Pages : 374 pages
Book Rating : 4.7/5 (98 download)
Download or read book Beyond Two: Theory and Applications of Multiple-Valued Logic written by Melvin Fitting and published by Physica. This book was released on 2013-06-05 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.
Author : Brigitte Pientka
Publisher : Springer Nature
ISBN 13 : 3031384997
Total Pages : 614 pages
Book Rating : 4.0/5 (313 download)
Download or read book Automated Deduction – CADE 29 written by Brigitte Pientka and published by Springer Nature. This book was released on 2023-10-04 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book constitutes the proceedings of the 29th International Conference on Automated Deduction, CADE 29, which took place in Rome, Italy, during July 2023. The 28 full papers and 5 short papers presented were carefully reviewed and selected from 77 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions.
Author : Yaroslav Shramko
Publisher : Springer Science & Business Media
ISBN 13 : 9400709072
Total Pages : 254 pages
Book Rating : 4.4/5 (7 download)
Download or read book Truth and Falsehood written by Yaroslav Shramko and published by Springer Science & Business Media. This book was released on 2011-09-15 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of (basic) truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi.
Author : Matthias Baaz
Publisher : Springer Science & Business Media
ISBN 13 : 9400703201
Total Pages : 286 pages
Book Rating : 4.4/5 (7 download)
Download or read book Methods of Cut-Elimination written by Matthias Baaz and published by Springer Science & Business Media. This book was released on 2011-01-07 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on cut-elimination in first-order predicate logic from an algorithmic point of view. Instead of just proving the existence of cut-free proofs, it focuses on the algorithmic methods transforming proofs with arbitrary cuts to proofs with only atomic cuts (atomic cut normal forms, so-called ACNFs). The first part investigates traditional reductive methods from the point of view of proof rewriting. Within this general framework, generalizations of Gentzen's and Sch\”utte-Tait's cut-elimination methods are defined and shown terminating with ACNFs of the original proof. Moreover, a complexity theoretic comparison of Gentzen's and Tait's methods is given. The core of the book centers around the cut-elimination method CERES (cut elimination by resolution) developed by the authors. CERES is based on the resolution calculus and radically differs from the reductive cut-elimination methods. The book shows that CERES asymptotically outperforms all reductive methods based on Gentzen's cut-reduction rules. It obtains this result by heavy use of subsumption theorems in clause logic. Moreover, several applications of CERES are given (to interpolation, complexity analysis of cut-elimination, generalization of proofs, and to the analysis of real mathematical proofs). Lastly, the book demonstrates that CERES can be extended to nonclassical logics, in particular to finitely-valued logics and to G\"odel logic.
Author : Jean-Yves Girard
Publisher :
ISBN 13 :
Total Pages : 516 pages
Book Rating : 4.3/5 (91 download)
Download or read book Proof Theory and Logical Complexity written by Jean-Yves Girard and published by . This book was released on 1987 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This long awaited book ... fills essential gaps in monographic literature on proof theory and prepares readers for volume 2 (to be published soon) containing an exposition of the author's new approach to proof theory for higher order logic. Even in traditional topics, like Gödel's completeness and incompleteness theorems, and cut elemination, accents are different compared to books by Kleene, Schütte, or Takeuti, which are strongly influenced by Hilbert's aim: to make mathematical theories (number theory, analysis etc.) more reliable by transformations of formalized proofs. The author is much closer to the approach of G. Kreisel (to whom this book is dedicated): Hilbert's program needs drastic rethinking and one of the main tasks is in finding mathematical applications of the results obtained in proof theory. Possibly, it is not a pure chance that the system of second order functionals developed by the author in his normalization proof for second order logic (was rediscovered and) became a tool in computer science. The book under review presents not only this material, but also other results by the author which became a part of modern proof theory including analysis of cut-free provability in terms of 3-valued logic. The material which was not previously covered (at least in such detail) in proof-theoretic monographs includes strong normalizability proofs (after Tait and Gandy), applications of reflection principles, recursive ordinals, operations on local correct (but not necessarily well-founded) omega-derivations, no-counterexample interpretation, using proof theory to extract combinatory estimates with a detailed treatment of van der Waerden's theorem. This is a difficult, but rewarding postgraduate-level textbook. The author does not avoid philosophical questions, and such discussion supported by theorems is certainly fruitful, although the reviewer would not agree with all author's conclusions"-- description of volume 1.
Author : J. Diller
Publisher : Springer
ISBN 13 : 3540380205
Total Pages : 393 pages
Book Rating : 4.5/5 (43 download)
Download or read book ISILC - Proof Theory Symposion written by J. Diller and published by Springer. This book was released on 2006-11-14 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: a
Author : A. S. Troelstra
Publisher : Cambridge University Press
ISBN 13 : 9780521779111
Total Pages : 436 pages
Book Rating : 4.7/5 (791 download)
Download or read book Basic Proof Theory written by A. S. Troelstra and published by Cambridge University Press. This book was released on 2000-07-27 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.
Author : Marta Cialdea Mayer
Publisher : Springer
ISBN 13 : 3540452060
Total Pages : 283 pages
Book Rating : 4.5/5 (44 download)
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Marta Cialdea Mayer and published by Springer. This book was released on 2003-10-24 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2003, held in Rome, Italy in September 2003. The 20 revised full papers presented were carefully reviewed and selected for inclusion in the book. All current issues surrounding the mechanization of logical reasoning with tableaux and similar methods are addressed in the context of a broad variety of logic calculi.
Author : Jose L. Fiadeiro
Publisher : Springer Science & Business Media
ISBN 13 : 3540662464
Total Pages : 356 pages
Book Rating : 4.5/5 (46 download)
Download or read book Recent Trends in Algebraic Development Techniques written by Jose L. Fiadeiro and published by Springer Science & Business Media. This book was released on 1999-07-28 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The European conference situationin the general area of software science has longbeen considered unsatisfactory. A fairlylarge number of small and medi- sized conferences and workshops take place on an irregular basis, competing for high-quality contributions and for enough attendees to make them ?nancially viable. Discussions aiming at a consolidation have been underway since at least 1992, with concrete planning beginning in summer 1994 and culminating in a public meeting at TAPSOFT’95 in Aarhus. On the basis of a broad consensus, it was decided to establish a single annual federated spring conference in the slot that was then occupied by TAPSOFT and CAAP/ESOP/CC, comprising a number of existing and new conferences and covering a spectrum from theory to practice. ETAPS’98, the ?rst instance of the European Joint Conferences on Theory and Practice of Software, is taking place this year in Lisbon. It comprises ?ve conferences (FoSSaCS, FASE, ESOP, CC, TACAS), four workshops (ACoS, VISUAL, WADT, CMCS), seven invited lectures, and nine tutorials.
Author : Heinz-Dieter Ebbinghaus
Publisher : Springer Science & Business Media
ISBN 13 : 3662090589
Total Pages : 653 pages
Book Rating : 4.6/5 (62 download)
Download or read book Ω-Bibliography of Mathematical Logic written by Heinz-Dieter Ebbinghaus and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gert H. Müller The growth of the number of publications in almost all scientific areas, as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg 11. Non-classical Logics W. Rautenberg 111. Model Theory H.-D. Ebbinghaus IV. Recursion Theory P.G. Hinman V. Set Theory A.R. Blass VI. ProofTheory; Constructive Mathematics J.E. Kister; D. van Dalen & A.S. Troelstra.
Author : Lloyd Humberstone
Publisher : MIT Press
ISBN 13 : 0262016540
Total Pages : 1511 pages
Book Rating : 4.2/5 (62 download)
Download or read book The Connectives written by Lloyd Humberstone and published by MIT Press. This book was released on 2011 with total page 1511 pages. Available in PDF, EPUB and Kindle. Book excerpt: In The Connectives, Lloyd Humberstone examines the semantics and pragmatics of natural language sentence connectives (and, or, if, not), giving special attention to their formal behavior according to proposed logical systems and the degree to which such treatments capture their intuitive meanings. It will be an essential resource for philosophers, mathematicians, computer scientists, linguists, or any scholar who finds connectives, and the conceptual issues surrounding them, to be a source of interest.
Author : Erich Grädel
Publisher : Springer Science & Business Media
ISBN 13 : 3642040268
Total Pages : 577 pages
Book Rating : 4.6/5 (42 download)
Download or read book Computer Science Logic written by Erich Grädel and published by Springer Science & Business Media. This book was released on 2009-08-28 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 23rd International Workshop on Computer Science Logic, CSL 2009, held in Coimbra, Portugal, in September 2009. The 34 papers presented together with 5 invited talks were carefully reviewed and selected from 89 full paper submissions. All current aspects of logic in computer science are addressed, ranging from foundational and methodological issues to application issues of practical relevance. The book concludes with a presentation of this year's Ackermann award, the EACSL Outstanding Dissertation Award for Logic in Computer Science.
Author : Sergei Artemov
Publisher : Springer
ISBN 13 : 3540926879
Total Pages : 478 pages
Book Rating : 4.5/5 (49 download)
Download or read book Logical Foundations of Computer Science written by Sergei Artemov and published by Springer. This book was released on 2009-02-11 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2009, held in Deerfield Beach, Florida, USA in January 2008. The volume presents 31 revised refereed papers carefully selected by the program committee. All current aspects of logic in computer science are addressed, including constructive mathematics and type theory, logical foundations of programming, logical aspects of computational complexity, logic programming and constraints, automated deduction and interactive theorem proving, logical methods in protocol and program verification and in program specification and extraction, domain theory logics, logical foundations of database theory, equational logic and term rewriting, lambda and combinatory calculi, categorical logic and topological semantics, linear logic, epistemic and temporal logics, intelligent and multiple agent system logics, logics of proof and justification, nonmonotonic reasoning, logic in game theory and social software, logic of hybrid systems, distributed system logics, system design logics, as well as other logics in computer science.
