Results for 'Proof theory'

958 found
Order:
See also
  1.  39
    Proof theory: a selection of papers from the Leeds Proof Theory Programme, 1990.Peter Aczel, Harold Simmons & Stanley S. Wainer (eds.) - 1992 - New York: Cambridge University Press.
    This work is derived from the SERC "Logic for IT" Summer School Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles which form an invaluable introduction to proof theory aimed at both mathematicians and computer scientists.
    Direct download  
     
    Export citation  
     
    Bookmark  
  2. Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - New York: Cambridge University Press. Edited by Jan Von Plato.
    Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions (...)
    Direct download  
     
    Export citation  
     
    Bookmark   125 citations  
  3.  17
    (1 other version)Proof theory.Gaisi Takeuti - 1987 - New York, N.Y., U.S.A.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co..
    This comprehensive monograph is a cornerstone in the area of mathematical logic and related fields. Focusing on Gentzen-type proof theory, the book presents a detailed overview of creative works by the author and other 20th-century logicians that includes applications of proof theory to logic as well as other areas of mathematics. 1975 edition.
    Direct download  
     
    Export citation  
     
    Bookmark   128 citations  
  4.  50
    A Proof Theory for the Logic of Provability in True Arithmetic.Hirohiko Kushida - 2020 - Studia Logica 108 (4):857-875.
    In a classical 1976 paper, Solovay proved the arithmetical completeness of the modal logic GL; provability of a formula in GL coincides with provability of its arithmetical interpretations of it in Peano Arithmetic. In that paper, he also provided an axiomatic system GLS and proved arithmetical completeness for GLS; provability of a formula in GLS coincides with truth of its arithmetical interpretations in the standard model of arithmetic. Proof theory for GL has been studied intensively up to the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  5. (1 other version)Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
     
    Export citation  
     
    Bookmark   5 citations  
  6.  15
    ISILC Proof Theory Symposion: dedicated to Kurt Schütte on the occasion of his 65th birthday: proceedings of the International Summer Institute and Logic Colloquium, Kiel, 1974.K. Schütte, Justus Diller & G. H. Müller (eds.) - 1975 - New York: Springer Verlag.
  7.  89
    Mathematical proof theory in the light of ordinal analysis.Reinhard Kahle - 2002 - Synthese 133 (1/2):237 - 255.
    We give an overview of recent results in ordinal analysis. Therefore, we discuss the different frameworks used in mathematical proof-theory, namely "subsystem of analysis" including "reverse mathematics", "Kripke-Platek set theory", "explicit mathematics", "theories of inductive definitions", "constructive set theory", and "Martin-Löf's type theory".
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  8.  13
    Proof Theory: History and Philosophical Significance.Vincent F. Hendricks, Stig Andur Pedersen & Klaus Frovin Jørgensen (eds.) - 2000 - Dordrecht and Boston: Kluwer Academic Publishers.
    hiS volume in the Synthese Library Series is the result of a conference T held at the University of Roskilde, Denmark, October 31st-November 1st, 1997. The aim was to provide a forum within which philosophers, math ematicians, logicians and historians of mathematics could exchange ideas pertaining to the historical and philosophical development of proof theory. Hence the conference was called Proof Theory: History and Philosophical Significance. To quote from the conference abstract: Proof theory was (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  9.  18
    Proof theory: sequent calculi and related formalisms.Katalin Bimbó - 2015 - Boca Raton: CRC Press, Taylor & Francis Group.
    Sequent calculi constitute an interesting and important category of proof systems. They are much less known than axiomatic systems or natural deduction systems are, and they are much less known than they should be. Sequent calculi were designed as a theoretical framework for investigations of logical consequence, and they live up to the expectations completely as an abundant source of meta-logical results. The goal of this book is to provide a fairly comprehensive view of sequent calculi -- including a (...)
    Direct download  
     
    Export citation  
     
    Bookmark   10 citations  
  10.  14
    Proof Theory.Jeremy Avigad - 2012 - In Sven Ove Hansson & Vincent F. Hendricks, Introduction to Formal Philosophy. Cham: Springer. pp. 177-190.
    Proof theory began in the 1920s as a part of Hilbert’s program, which aimed to secure the foundations of mathematics by modeling infinitary mathematics with formal axiomatic systems and proving those systems consistent using restricted, finitary means. The program thus viewed mathematics as a system of reasoning with precise linguistic norms, governed by rules that can be described and studied in concrete terms. Today such a viewpoint has applications in mathematics, computer science, and the philosophy of mathematics.
    Direct download  
     
    Export citation  
     
    Bookmark  
  11. Proof Theory For Finitely Valid Sentences.J. Degen - 2001 - Reports on Mathematical Logic:47-59.
    We investigate infinitary sequent calculi which generate the finitely valid sentences of first-order logic, of simple type theory and of transitive closure logic, respectively.
     
    Export citation  
     
    Bookmark  
  12.  78
    Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization.Ryo Takemura - 2013 - Studia Logica 101 (1):157-191.
    Proof-theoretical notions and techniques, developed on the basis of sentential/symbolic representations of formal proofs, are applied to Euler diagrams. A translation of an Euler diagrammatic system into a natural deduction system is given, and the soundness and faithfulness of the translation are proved. Some consequences of the translation are discussed in view of the notion of free ride, which is mainly discussed in the literature of cognitive science as an account of inferential efficacy of diagrams. The translation enables us (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  13.  50
    Why does the proof-theory of hybrid logic work so well?Torben Braüner - 2007 - Journal of Applied Non-Classical Logics 17 (4):521-543.
    This is primarily a conceptual paper. The goal of the paper is to put into perspective the proof-theory of hybrid logic and in particular, try to give an answer to the following question: Why does the proof-theory of hybrid logic work so well compared to the proof-theory of ordinary modal logic?Roughly, there are two different kinds of proof systems for modal logic: Systems where the formulas involved in the rules are formulas of the (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  14. Proof Theory of Finite-valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   18 citations  
  15.  15
    Proof theory.K. Schütte - 1977 - New York: Springer Verlag.
  16.  44
    Proof theory of modal logic.Heinrich Wansing (ed.) - 1996 - Boston: Kluwer Academic Publishers.
    Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.
    Direct download  
     
    Export citation  
     
    Bookmark   5 citations  
  17. Proof theory for fuzzy logics. Applied Logic Series, vol. 36.G. Metcalfe, N. Olivetti & D. Gabbay - 2010 - Bulletin of Symbolic Logic 16 (3):415-419.
     
    Export citation  
     
    Bookmark   1 citation  
  18. An Introduction to Proof Theory: Normalization, Cut-Elimination, and Consistency Proofs.Paolo Mancosu, Sergio Galvan & Richard Zach - 2021 - Oxford: Oxford University Press. Edited by Sergio Galvan & Richard Zach.
    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, natural deduction and the normalization theorems, the sequent calculus, including cut-elimination and mid-sequent theorems, (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  19.  8
    Proof theory. Gödel and the metamathematical tradition.Jeremy Avigad - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson, Kurt Gödel: essays for his centennial. Ithaca, NY: Association for Symbolic Logic.
    At the turn of the nineteenth century, mathematics exhibited a style of argumentation that was more explicitly computational than is common today. Over the course of the century, the introduction of abstract algebraic methods helped unify developments in analysis, number theory, geometry, and the theory of equations; and work by mathematicians like Dedekind, Cantor, and Hilbert towards the end of the century introduced set-theoretic language and infinitary methods that served to downplay or suppress computational content. This shift in (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  20.  17
    (1 other version)The Proof Theory of Classical and Constructive Inductive Definitions. A Forty Year Saga, 1968 – 2008.Solomon Feferman - 2010 - In Ralf Schindler, Ways of Proof Theory. De Gruyter. pp. 7-30.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  21. Proof Theory and Semantics for a Theory of Definite Descriptions.Nils Kürbis - 2021 - In Anupam Das & Sara Negri, TABLEAUX 2021, LNAI 12842.
    This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown to (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  22. Proof theories for superpositions of adaptive logics.Christian Straßer & Frederik van de Putte - 2016 - Logique Et Analyse 58 (230):307--346.
     
    Export citation  
     
    Bookmark  
  23.  31
    Proof Theory as an Analysis of Impredicativity( New Developments in Logic: Proof-Theoretic Ordinals and Set-Theoretic Ordinals).Ryota Akiyoshi - 2012 - Journal of the Japan Association for Philosophy of Science 39 (2):93-107.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  24.  13
    Proof Theory.J. N. Crossley - 1982 - Journal of Symbolic Logic 47 (1):218-220.
  25.  40
    Proof Theory of First Order Abduction: Sequent Calculus and Structural Rules.Seyed Ahmad Mirsanei - 2021 - Eighth Annual Conference of Iranian Association for Logic (Ial).
    The logical formalism of abductive reasoning is still an open discussion and various theories have been presented about it. Abduction is a type of non-monotonic and defeasible reasonings, and the logic containing such a reasoning is one of the types of non-nonmonotonic and defeasible logics, such as inductive logic. Abduction is a kind of natural reasoning and it is a solution to the problems having this form "the phenomenon of φ cannot be explained by the theory of Θ" and (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  26. Proof theory and meaning.Göran Sundholm - 1986 - In D. Gabbay & F. Guenther, Handbook of Philosophical Logic, Vol. Iii. D. Reidel Publishing Co.. pp. 471–506.
  27. Topics in the Proof Theory of Non-classical Logics. Philosophy and Applications.Fabio De Martin Polo - 2023 - Dissertation, Ruhr-Universität Bochum
    Chapter 1 constitutes an introduction to Gentzen calculi from two perspectives, logical and philosophical. It introduces the notion of generalisations of Gentzen sequent calculus and the discussion on properties that characterize good inferential systems. Among the variety of Gentzen-style sequent calculi, I divide them in two groups: syntactic and semantic generalisations. In the context of such a discussion, the inferentialist philosophy of the meaning of logical constants is introduced, and some potential objections – mainly concerning the choice of working with (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  28.  62
    Handbook of proof theory.Samuel R. Buss (ed.) - 1998 - New York: Elsevier.
    This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that (...)
    Direct download  
     
    Export citation  
     
    Bookmark   34 citations  
  29.  25
    Reciprocal Influences Between Proof Theory and Logic Programming.Dale Miller - 2019 - Philosophy and Technology 34 (1):75-104.
    The topics of structural proof theory and logic programming have influenced each other for more than three decades. Proof theory has contributed the notion of sequent calculus, linear logic, and higher-order quantification. Logic programming has introduced new normal forms of proofs and forced the examination of logic-based approaches to the treatment of bindings. As a result, proof theory has responded by developing an approach to proof search based on focused proof systems in (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  30.  64
    Basic proof theory, A.S. Troelstra and H. Schwichtenberg.Harold Schellinx - 1998 - Journal of Logic, Language and Information 7 (2):221-223.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  31.  66
    Proof theory in the abstract.J. M. E. Hyland - 2002 - Annals of Pure and Applied Logic 114 (1-3):43-78.
    Categorical proof theory is an approach to understanding the structure of proofs. We illustrate the idea first by analyzing G0̈del's Dialectica interpretation and the Diller-Nahm variant in categorical terms. Then we consider the problematic question of the structure of classical proofs. We show how double negation translations apply in the case of the Dialectica interpretations. Finally we formulate a proposal as to how to give a more faithful analysis of proofs in the sequent calculus.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  32. Stoic Sequent Logic and Proof Theory.Susanne Bobzien - 2019 - History and Philosophy of Logic 40 (3):234-265.
    This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  33.  61
    General Proof Theory: Introduction.Thomas Piecha & Peter Schroeder-Heister - 2019 - Studia Logica 107 (1):1-5.
    This special issue on general proof theory collects papers resulting from the conference on general proof theory held in November 2015 in Tübingen.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  34.  58
    Proof Theory.Wilfried Sieg - unknown
  35.  46
    Proof Theory of Paraconsistent Weak Kleene Logic.Francesco Paoli & Michele Pra Baldi - 2020 - Studia Logica 108 (4):779-802.
    Paraconsistent Weak Kleene Logic is the 3-valued propositional logic defined on the weak Kleene tables and with two designated values. Most of the existing proof systems for PWK are characterised by the presence of linguistic restrictions on some of their rules. This feature can be seen as a shortcoming. We provide a cut-free calculus for PWK that is devoid of such provisos. Moreover, we introduce a Priest-style tableaux calculus for PWK.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  36.  43
    Proof theory for theories of ordinals—I: recursively Mahlo ordinals.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 122 (1-3):1-85.
    This paper deals with a proof theory for a theory T22 of recursively Mahlo ordinals in the form of Π2-reflecting on Π2-reflecting ordinals using a subsystem Od of the system O of ordinal diagrams in Arai 353). This paper is the first published one in which a proof-theoretic analysis à la Gentzen–Takeuti of recursively large ordinals is expounded.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  37.  58
    Proof theory for theories of ordinals II: Π3-reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1):39-92.
    This paper deals with a proof theory for a theory T3 of Π3-reflecting ordinals using the system O of ordinal diagrams in Arai 1375). This is a sequel to the previous one 1) in which a theory for recursively Mahlo ordinals is analyzed proof-theoretically.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  38.  63
    Proof theory of reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.
    The paper contains proof-theoretic investigation on extensions of Kripke-Platek set theory, KP, which accommodate first-order reflection. Ordinal analyses for such theories are obtained by devising cut elimination procedures for infinitary calculi of ramified set theory with Пn reflection rules. This leads to consistency proofs for the theories KP+Пn reflection using a small amount of arithmetic and the well-foundedness of a certain ordinal system with respect to primitive decending sequences. Regarding future work, we intend to avail ourselves of (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   38 citations  
  39.  36
    Proof theory for heterogeneous logic combining formulas and diagrams: proof normalization.Ryo Takemura - 2021 - Archive for Mathematical Logic 60 (7):783-813.
    We extend natural deduction for first-order logic (FOL) by introducing diagrams as components of formal proofs. From the viewpoint of FOL, we regard a diagram as a deductively closed conjunction of certain FOL formulas. On the basis of this observation, we first investigate basic heterogeneous logic (HL) wherein heterogeneous inference rules are defined in the styles of conjunction introduction and elimination rules of FOL. By examining what is a detour in our heterogeneous proofs, we discuss that an elimination-introduction pair of (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  40. Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
     
    Export citation  
     
    Bookmark   166 citations  
  41.  25
    Goal-directed proof theory.Dov M. Gabbay - 2000 - Boston: Kluwer Academic. Edited by Nicola Olivetti.
    Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of non-classical systems, covering intuitionistic, intermediate, modal and substructural (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  42.  11
    Universal proof theory: Feasible admissibility in intuitionistic modal logics.Amirhossein Akbar Tabatabai & Raheleh Jalali - 2025 - Annals of Pure and Applied Logic 176 (2):103526.
  43. Pure proof theory aims, methods and results.Wolfram Pohlers - 1996 - Bulletin of Symbolic Logic 2 (2):159-188.
    Apologies. The purpose of the following talk is to give an overview of the present state of aims, methods and results in Pure Proof Theory. Shortage of time forces me to concentrate on my very personal views. This entails that I will emphasize the work which I know best, i.e., work that has been done in the triangle Stanford, Munich and Münster. I am of course well aware that there are as important results coming from outside this triangle (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  44.  31
    Proof Theory for Fuzzy Logics.George Metcalfe, Nicola Olivetti & Dov M. Gabbay - 2008 - Dordrecht, Netherland: Springer.
    Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by (...)
  45. Proof theory and set theory.Gaisi Takeuti - 1985 - Synthese 62 (2):255 - 263.
    The foundations of mathematics are divided into proof theory and set theory. Proof theory tries to justify the world of infinite mind from the standpoint of finite mind. Set theory tries to know more and more of the world of the infinite mind. The development of two subjects are discussed including a new proof of the accessibility of ordinal diagrams. Finally the world of large cardinals appears when we go slightly beyond girard's categorical (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  46.  64
    Proof Theory for Functional Modal Logic.Shawn Standefer - 2018 - Studia Logica 106 (1):49-84.
    We present some proof-theoretic results for the normal modal logic whose characteristic axiom is \. We present a sequent system for this logic and a hypersequent system for its first-order form and show that these are equivalent to Hilbert-style axiomatizations. We show that the question of validity for these logics reduces to that of classical tautologyhood and first-order logical truth, respectively. We close by proving equivalences with a Fitch-style proof system for revision theory.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  47.  16
    Proof theory and intuitionistic systems.Bruno Scarpellini - 1971 - New York,: Springer Verlag.
  48. Proof theory in the USSR 1925–1969.Grigori Mints - 1991 - Journal of Symbolic Logic 56 (2):385-424.
    We present a survey of proof theory in the USSR beginning with the paper by Kolmogorov [1925] and ending (mostly) in 1969; the last two sections deal with work done by A. A. Markov and N. A. Shanin in the early seventies, providing a kind of effective interpretation of negative arithmetic formulas. The material is arranged in chronological order and subdivided according to topics of investigation. The exposition is more detailed when the work is little known in the (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  49.  58
    Jean van Heijenoort’s Contributions to Proof Theory and Its History.Irving H. Anellis - 2012 - Logica Universalis 6 (3-4):411-458.
    Jean van Heijenoort was best known for his editorial work in the history of mathematical logic. I survey his contributions to model-theoretic proof theory, and in particular to the falsifiability tree method. This work of van Heijenoort’s is not widely known, and much of it remains unpublished. A complete list of van Heijenoort’s unpublished writings on tableaux methods and related work in proof theory is appended.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  50. Proof Theory and Complexity.Carlo Cellucci - 1985 - Synthese 62 (2):173-189.
1 — 50 / 958