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.
Download or read book An Introduction to Proof Theory written by Paolo Mancosu and published by Oxford University Press. This book was released on 2021 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.
Download or read book The Legacy of Kurt Sch tte written by Reinhard Kahle and published by Springer Nature. This book was released on 2020-08-10 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on proof theory centers around the legacy of Kurt Schütte and its current impact on the subject. Schütte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schütte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound Γ0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schütte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts close to his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schütte himself that have never been published before.
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Revantha Ramanayake and published by Springer Nature. This book was released on 2023-10-15 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book constitutes the proceedings of the proceedings of the 32nd International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2023, held in Prague, Czech Republic, during September 18-21, 2023. The 20 full papers and 5 short papers included in this book together with 5 abstracts of invited talks were carefully reviewed and selected from 43 submissions. They present research on all aspects of the mechanization of reasoning with tableaux and related methods. The papers are organized in the following topical sections: tableau calculi; sequent calculi; theorem proving; non-wellfounded proofs; modal logics; linear logic and MV-algebras; separation logic; and first-order logics.
Download or read book Automated Reasoning written by Nicola Olivetti and published by Springer. This book was released on 2016-06-13 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Joint Conference on Automated Reasoning, IJCAR 2016, held in Coimbra, Portugal, in June/July 2016. IJCAR 2014 was a merger of three leading events in automated reasoning, namely CADE (International Conference on Automated Deduction), FroCoS (International Symposium on Frontiers of Combining Systems) and TABLEAUX (International Conference on Automated Reasoning with Analytic Tableaux and Related Methods). The 26 revised full research papers and 9 system descriptions presented together with 4 invited talks were carefully reviewed and selected from 79 submissions. The papers have been organized in topical sections on satisfiability of Boolean formulas, satisfiability modulo theory, rewriting, arithmetic reasoning and mechanizing mathematics, first-order logic and proof theory, first-order theorem proving, higher-order theorem proving, modal and temporal logics, non-classical logics, and verification.
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Kai Brünnler and published by Springer Science & Business Media. This book was released on 2011-06-22 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 20th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2011, held in Bern, Switzerland, in July 2011.The 16 revised research papers presented together with 2 system descriptions were carefully reviewed and selected from 34 submissions. The papers cover many topics in the wide range of applications of tableaux and related methods such as analytic tableaux for various logics, related techniques and concepts, related methods, new calculi and methods for theorem proving in classical and non-classical logics, as well as systems, tools, implementations and applications; all with a special focus on hardware and software verifications, semantic technologies, and knowledge engineering.
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Martin Giese and published by Springer. This book was released on 2009-10-20 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the research papers presented at the International C- ference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2009) held July 6-10, 2009 in Oslo, Norway. This conference was the 18th in a series of international meetings since 1992 (listed on page IX). It was collocated with FTP 2009, the Workshop on First-Order Theorem Proving. The Program Committee of TABLEAUX 2009 received 44 submissions from 24 countries. Each paper was reviewed by at least three referees, after which the reviews were sent to the authors for comment in a rebuttal phase. After a ?nal intensive discussion on the borderline papers during the online meeting of the Program Committee, 21 research papers and 1 system description were accepted based on originality, technical soundness, presentation, and relevance. Additionally,three positionpaperswereaccepted,whicharepublished asate- nical report of the University of Oslo. We wish to sincerely thank all the authors who submitted their work for consideration. And we would like to thank the Program Committee members and other referees for their great e?ort and p- fessional work in the review and selection process. Their names are listed on the following pages.
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Uwe Egly and published by Springer. This book was released on 2003-08-02 with total page 350 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 2002, held in Copenhagen, Denmark, in July/August 2002. The 20 revised full papers and two system descriptions presented together with two invited contributions 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. Among the logic calculi investigated are linear logic, temporal logic, modal logics, hybrid logic, multi-modal logics, fuzzy logics, Goedel logic, Lukasiewicz logic, intermediate logics, quantified boolean logic, and, of course, classical first-order logic.
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Roy Dyckhoff and published by Springer. This book was released on 2006-12-30 with total page 452 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 2000, held in St Andrews, Scotland, UK, in July 2000.The 23 revised full papers and 2 system descriptions presented were carefully reviewed and selected from 42 submissions. Also included are 3 invited lectures and 6 nonclassical system comparisons. All current issues surrounding the mechanization of reasoning with tableaux and similar methods are addressed - ranging from theoretical foundations to implementation, systems development, and applications, as well as covering a broad variety of logical calculi.
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Anupam Das and published by Springer Nature. This book was released on 2021-08-31 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 30th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2021, held in Birmingham, UK, in September 2021.The 23 full papers and 3 system descriptions included in the volume were carefully reviewed and selected from 46 submissions.They present research on all aspects of the mechanization of tableaux-based reasoning and related methods, including theoretical foundations, implementation techniques, systems development and applications. The papers are organized in the following topical sections: tableau calculi, sequent calculi, theorem proving, formalized proofs, non-wellfounded proofs, automated theorem provers, and intuitionistic modal logics.
Download or read book Logic Colloquium 01 written by Matthias Baaz and published by Cambridge University Press. This book was released on 2017-03-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twentieth publication in the Lecture Notes in Logic series, contains the proceedings of the 2001 European Summer Meeting of the Association for Symbolic Logic, held at the Vienna University of Technology. Two long articles present accessible expositions on resolution theorem proving and the determinacy of long games. The remaining articles cover separate research topics in many areas of mathematical logic, including applications in computer science, proof theory, set theory, model theory, computability theory, linguistics and aspects of philosophy. This collection will interest not only mathematical logicians but also philosophical logicians, historians of logic, computer scientists, formal linguists and mathematicians working in algebra, abstract analysis and topology.
Download or read book Automated Deduction CADE 18 written by Andrei Voronkov and published by Springer. This book was released on 2003-08-02 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: The First CADE in the Third Millennium This volume contains the papers presented at the Eighteenth International C- ference on Automated Deduction (CADE-18) held on July 27–30th, 2002, at the University of Copenhagen as part of the Federated Logic Conference (FLoC 2002). Despite a large number of deduction-related conferences springing into existence at the end of the last millennium, the CADE conferences continue to be the major forum for the presentation of new research in all aspects of automated deduction. CADE-18 was sponsored by the Association for Auto- ted Reasoning, CADE Inc., the Department of Computer Science at Chalmers University, the Gesellschaft fur ̈ Informatik, Safelogic AB, and the University of Koblenz-Landau. There were 70 submissions, including 60 regular papers and 10 system - scriptions. Each submission was reviewed by at least ?ve program committee members and an electronic program committee meeting was held via the Int- net. The committee decided to accept 27 regular papers and 9 system descr- tions. One paper switched its category after refereeing, thus the total number of system descriptions in this volume is 10. In addition to the refereed papers, this volume contains an extended abstract of the CADE invited talk by Ian Horrocks, the joint CADE/CAV invited talk by Sharad Malik, and the joint CADE-TABLEAUX invited talk by Matthias Baaz. One more invited lecture was given by Daniel Jackson.
Download or read book Logic for Programming Artificial Intelligence and Reasoning written by Edmund M. Clarke and published by Springer. This book was released on 2010-12-07 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 16th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2010, which took place in Dakar, Senegal, in April/May 2010. The 27 revised full papers and 9 revised short papers presented together with 1 invited talk were carefully revised and selected from 47 submissions. The papers address all current issues in automated reasoning, computational logic, programming languages and deal with logic programming, logic-based program manipulation, formal methods, and various kinds of AI logics. Subjects covered range from theoretical aspects to various applications such as automata, linear arithmetic, verification, knowledge representation, proof theory, quantified constraints, as well as modal and temporal logics.
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Marta Cialdea Mayer and published by Springer Science & Business Media. This book was released on 2003-09-03 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.
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Renate A. Schmidt and published by Springer. This book was released on 2017-09-04 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the 26th International Conference on Automated Reasoning with Analytics Tableaux and Related Methods, TABLEAUX 2017, held in Brasília, Bazil, in September 2017. The 19 contributed papers presented in this volume were carefully reviewed and selected from 27 submissions.They are organized in topical sections named: Sequent systems; tableaux; transitive closure and cyclic proofs; formalization and complexity. Also included are papers of three invited speakers.
Download or read book Logic and Its Applications written by Kamal Lodaya and published by Springer. This book was released on 2012-12-22 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 5th Indian Conference on Logic and Its Applications, ICLA 2013, held in Chennai, India, in January 2013. The 15 revised full papers presented together with 7 invited talks were carefully reviewed and selected from numerous submissions. The papers cover the topics related to pure and applied logic, foundations and philosophy of mathematics and the sciences, set theory, model theory, proof theory, areas of theoretical computer science, artificial intelligence and other disciplines which are of direct interest to mathematical and philosophical logic.
Download or read book Typed Lambda Calculi and Applications written by Simona Ronchi Della Rocca and published by Springer. This book was released on 2007-07-11 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Conference on Typed Lambda Calculi and Applications, TLCA 2007, held in Paris, France in June 2007 in conjunction with RTA 2007, the 18th International Conference on Rewriting Techniques and Applications as part of RDP 2007, the 4th International Conference on Rewriting, Deduction, and Programming. The 25 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 52 submissions. The papers present original research results that are broadly relevant to the theory and applications of typed calculi and address a wide variety of topics such as proof-theory, semantics, implementation, types, and programming.
