Methods Of Cut Elimination PDF Download
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Author | : Matthias Baaz |
Publisher | : Springer Science & Business Media |
Total Pages | : 286 |
Release | : 2011-01-07 |
Genre | : Mathematics |
ISBN | : 9400703201 |
Download Methods of Cut-Elimination Book in PDF, ePub and Kindle
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 | : Paolo Mancosu |
Publisher | : Oxford University Press |
Total Pages | : 431 |
Release | : 2021 |
Genre | : Philosophy |
ISBN | : 0192895931 |
Download An Introduction to Proof Theory Book in PDF, ePub and Kindle
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.
Author | : Maria Luisa Dalla Chiara |
Publisher | : Springer Science & Business Media |
Total Pages | : 528 |
Release | : 2013-06-29 |
Genre | : Science |
ISBN | : 9401704872 |
Download Logic and Scientific Methods Book in PDF, ePub and Kindle
This is the first of two volumes comprising the papers submitted for publication by the invited participants to the Tenth International Congress of Logic, Methodology and Philosophy of Science, held in Florence, August 1995. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science. The invited lectures published in the two volumes demonstrate much of what goes on in the fields of the Congress and give the state of the art of current research. The two volumes cover the traditional subdisciplines of mathematical logic and philosophical logic, as well as their interfaces with computer science, linguistics and philosophy. Philosophy of science is broadly represented, too, including general issues of natural sciences, social sciences and humanities. The papers in Volume One are concerned with logic, mathematical logic, the philosophy of logic and mathematics, and computer science.
Author | : Syraya Chin-Mu Yang |
Publisher | : Springer |
Total Pages | : 308 |
Release | : 2017-11-25 |
Genre | : Philosophy |
ISBN | : 9811063559 |
Download Philosophical Logic: Current Trends in Asia Book in PDF, ePub and Kindle
This volume brings together a group of logic-minded philosophers and philosophically oriented logicians, mainly from Asia, to address a variety of logical and philosophical topics of current interest, offering a representative cross-section of the philosophical logic landscape in early 21st-century Asia. It surveys a variety of fields, including modal logic, epistemic logic, formal semantics, decidability and mereology. The book proposes new approaches and constructs more powerful frameworks, such as cover theory, an algebraic approach to cut-elimination, and a Boolean approach to causal discovery, to name but a few. Readers may find a wide range of applications of these original works in current research of philosophical logic, especially in the structural and conceptual analysis of some significant semantic properties and formal systems. The variety of topics and issues discussed here will appeal to readers from a broad spectrum of disciplines, ranging from mathematical/philosophical logic, computing science, cognitive science and artificial intelligence, to linguistics, game theory and beyond.
Author | : Martin Giese |
Publisher | : Springer Science & Business Media |
Total Pages | : 352 |
Release | : 2009-06-24 |
Genre | : Computers |
ISBN | : 3642027156 |
Download Automated Reasoning with Analytic Tableaux and Related Methods Book in PDF, ePub and Kindle
This book constitutes the refereed proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2009, held in Oslo, Norway, in July 2009. The 21 revised research papers presented together with 1 system description and 2 invited talks were carefully reviewed and selected from 44 submissions. The papers cover many topics in the wide range of applications of tableaux and related methods in areas such as hardware and software verfications, semantic technologies, and knowledge engineering.
Author | : Matthias Baaz |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2017-03-30 |
Genre | : Mathematics |
ISBN | : 1108695442 |
Download Logic Colloquium '01 Book in PDF, ePub and Kindle
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.
Author | : Edmund M. Clarke |
Publisher | : Springer Science & Business Media |
Total Pages | : 526 |
Release | : 2011-01-04 |
Genre | : Computers |
ISBN | : 3642175104 |
Download Logic for Programming, Artificial Intelligence, and Reasoning Book in PDF, ePub and Kindle
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.
Author | : Didier Galmiche |
Publisher | : Springer |
Total Pages | : 297 |
Release | : 2013-09-11 |
Genre | : Computers |
ISBN | : 3642405371 |
Download Automated Reasoning with Analytic Tableaux and Related Methods Book in PDF, ePub and Kindle
This book constitutes the refereed proceedings of the 22th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2013, held in Nancy, France, in September 2013. The 20 revised research papers presented together with 4 system descriptions were carefully reviewed and selected from 38 submissions. The papers cover many topics as proof-theory in classical and non-classical logics, analytic tableaux for various logics, related techniques and concepts, e.g., model checking and BDDs, related methods (model elimination, sequent calculi, resolution, and connection method), new calculi and methods for theorem proving and verification in classical and non-classical logics, systems, tools, implementations and applications as well as automated deduction and formal methods applied to logic, mathematics, software development, protocol verification, and security.
Author | : Kai Brünnler |
Publisher | : Springer Science & Business Media |
Total Pages | : 288 |
Release | : 2011-06-22 |
Genre | : Computers |
ISBN | : 3642221181 |
Download Automated Reasoning with Analytic Tableaux and Related Methods Book in PDF, ePub and Kindle
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.
Author | : S. Barry Cooper |
Publisher | : Springer Science & Business Media |
Total Pages | : 842 |
Release | : 2007-06-11 |
Genre | : Computers |
ISBN | : 3540730001 |
Download Computation and Logic in the Real World Book in PDF, ePub and Kindle
This book constitutes the refereed proceedings of the Third International Conference on Computability in Europe, CiE 2007, held in Sienna, Italy, in June 2007. The 50 revised full papers presented together with 36 invited papers were carefully reviewed and selected from 167 submissions.