Search results for 'Proof theory Popular works' (try it on Scholar)

1000+ found
Order:
  1.  27
    Donald C. Benson (1999). The Moment of Proof: Mathematical Epiphanies. Oxford University Press.
    When Archimedes, while bathing, suddenly hit upon the principle of buoyancy, he ran wildly through the streets of Syracuse, stark naked, crying "eureka!" In The Moment of Proof, Donald Benson attempts to convey to general readers the feeling of eureka--the joy of discovery--that mathematicians feel when they first encounter an elegant proof. This is not an introduction to mathematics so much as an introduction to the pleasures of mathematical thinking. And indeed the delights of this book are many (...)
    Direct download  
     
    Export citation  
     
    My bibliography  
  2.  53
    William W. Tait (2006). Gödel's Correspondence on Proof Theory and Constructive Mathematics Kurt Gödel. Collected Works. Volume IV: Selected Correspondence A–G; Volume V: Selected Correspondence H–Z. Solomon Feferman, John W. Dawson, Warren Goldfarb, Charles Parsons, and Wilfried Sieg, Eds. Oxford: Oxford University Press, 2002. Pp. Xi+ 662; Xxiii+ 664. ISBN 0-19-850073-4; 0-19-850075-0. [REVIEW] Philosophia Mathematica 14 (1):76-111.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  3.  46
    A. S. Troelstra (2000). Basic Proof Theory. Cambridge University Press.
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   52 citations  
  4.  5
    J. P. McEvoy (1997). Introducing Quantum Theory. Totem Books Ltd..
    Quantum theory is one of science's most thrilling, challenging and even mysterious areas. Scientists such as Planck, Einstein, Bohr, Heisenberg and Schrödinger uncovered bizarre paradoxes in the early 20th century that seemed to destroy the fundamental assumptions of 'classical physics' - the basic laws we are taught in school. Notoriously difficult, quantum theory is nonetheless an amazing and inspiring intellectual adventure, explained here with patience, wit and clarity.
    Direct download  
     
    Export citation  
     
    My bibliography  
  5.  23
    Samuel R. Buss (ed.) (1998). Handbook of Proof Theory. 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  
     
    My bibliography   14 citations  
  6.  27
    Ryo Takemura (2013). Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization. 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 (7 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  7.  4
    Dov M. Gabbay (2000). Goal-Directed Proof Theory. Kluwer Academic.
    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  
     
    Export citation  
     
    My bibliography   5 citations  
  8.  24
    H. Wansing (ed.) (1996). Proof Theory of Modal Logic. Kluwer.
    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  
     
    My bibliography   4 citations  
  9.  17
    Irving H. Anellis (2012). Jean van Heijenoort's Contributions to Proof Theory and Its History. 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  
     
    My bibliography  
  10.  15
    Peter Aczel, Harold Simmons & S. S. Wainer (eds.) (1992). Proof Theory: A Selection of Papers From the Leeds Proof Theory Programme, 1990. 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  
     
    My bibliography  
  11. David Steiner & Thomas Strahm (2006). On the Proof Theory of Type Two Functionals Based on Primitive Recursive Operations. Mathematical Logic Quarterly 52 (3):237-252.
    This paper is a companion to work of Feferman, Jäger, Glaß, and Strahm on the proof theory of the type two functionals μ and E1 in the context of Feferman-style applicative theories. In contrast to the previous work, we analyze these two functionals in the context of Schlüter's weakened applicative basis PRON which allows for an interpretation in the primitive recursive indices. The proof-theoretic strength of PRON augmented by μ and E1 is measured in terms of the (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  12.  38
    John Corcoran (1971). Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value. Journal of Structural Learning 3 (2):1-16.
    1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  13. Gaisi Takeuti (1987). Proof Theory. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
     
    Export citation  
     
    My bibliography   77 citations  
  14.  29
    Philip Clayton (2010). Freedom, Consciousness, and Science: An Emergentist Response to the Challenge. In Science and Religion in Dialogue. Wiley-Blackwell 985--998.
    This chapter contains sections titled: * A Neuroscientific Theory of Cognition: The Global Workspace Model * The Burden of Proof and the Loss of Innocence * The Harshest Attack on Freedom and Consciousness: Daniel Dennett * A More Radical Entailment? * Consciousness as an Emergent Property * Conclusion * Notes.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  15. K. Schütte (1977). Proof Theory. Springer-Verlag.
     
    Export citation  
     
    My bibliography   55 citations  
  16.  2
    Stefano Baratella & Andrea Masini (2004). An Approach to Infinitary Temporal Proof Theory. Archive for Mathematical Logic 43 (8):965-990.
    Aim of this work is to investigate from a proof-theoretic viewpoint a propositional and a predicate sequent calculus with an ω–type schema of inference that naturally interpret the propositional and the predicate until–free fragments of Linear Time Logic LTL respectively. The two calculi are based on a natural extension of ordinary sequents and of standard modal rules. We examine the pure propositional case (no extralogical axioms), the propositional and the first order predicate cases (both with a possibly infinite set (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  17.  19
    Paolo Maffezioli & Alberto Naibo (2013). Proof Theory of Epistemic Logic of Programs. Logic and Logical Philosophy.
    A combination of epistemic logic and dynamic logic of programs is presented. Although rich enough to formalize some simple game-theoretic scenarios, its axiomatization is problematic as it leads to the paradoxical conclusion that agents are omniscient. A cut-free labelled Gentzen-style proof system is then introduced where knowledge and action, as well as their combinations, are formulated as rules of inference, rather than axioms. This provides a logical framework for reasoning about games in a modular and systematic way, and to (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography  
  18.  13
    David J. Pym (2004). Reductive Logic and Proof-Search: Proof Theory, Semantics, and Control. Oxford University Press.
    This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search including proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences.
    Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  19.  12
    Luciano Serafini & Fausto Giunchiglia (2002). ML Systems: A Proof Theory for Contexts. [REVIEW] Journal of Logic, Language and Information 11 (4):471-518.
    In the last decade the concept of context has been extensivelyexploited in many research areas, e.g., distributed artificialintelligence, multi agent systems, distributed databases, informationintegration, cognitive science, and epistemology. Three alternative approaches to the formalization of the notion ofcontext have been proposed: Giunchiglia and Serafini's Multi LanguageSystems (ML systems), McCarthy's modal logics of contexts, andGabbay's Labelled Deductive Systems.Previous papers have argued in favor of ML systems with respect to theother approaches. Our aim in this paper is to support these arguments froma (...)
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography  
  20.  69
    Paolo Maffezioli, Alberto Naibo & Sara Negri (2013). The Church–Fitch Knowability Paradox in the Light of Structural Proof Theory. Synthese 190 (14):2677-2716.
    Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  21.  14
    Erik Palmgren (2012). Proof-Relevance of Families of Setoids and Identity in Type Theory. Archive for Mathematical Logic 51 (1-2):35-47.
    Families of types are fundamental objects in Martin-Löf type theory. When extending the notion of setoid (type with an equivalence relation) to families of setoids, a choice between proof-relevant or proof-irrelevant indexing appears. It is shown that a family of types may be canonically extended to a proof-relevant family of setoids via the identity types, but that such a family is in general proof-irrelevant if, and only if, the proof-objects of identity types are unique. (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  22.  8
    Tzvetan Todorov & Loulou Mack (1986). Race," Writing, and Culture". Critical Inquiry 13 (1):171-181.
    “Racism” is the name given to a type of behavior which consists in the display of contempt or aggressiveness toward other people on account of physical differences between them and oneself. It should be noted that this definition does not contain the word “race,” and this observation leads us to the first surprise in this area which contains many: whereas racism is a well-attested social phenomenon, “race” itself does not exist! Or, to put it more clearly: there are a great (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  23. J. Y. Girard (1991). Proof Theory and Logical Complexity. Annals of Pure and Applied Logic 53 (4):197.
    Direct download  
     
    Export citation  
     
    My bibliography   24 citations  
  24. Gerhard Jäger (1986). Theories for Admissible Sets: A Unifying Approach to Proof Theory. Bibliopolis.
     
    Export citation  
     
    My bibliography   13 citations  
  25.  52
    Carlo Cellucci (1985). Proof Theory and Complexity. Synthese 62 (2):173-189.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  26.  6
    Sören Stenlund (1972). Combinators, -Terms and Proof Theory. Dordrecht,D. Reidel.
    The main aim of Schonfinkel's paper was methodological: to reduce the primitive logical notions to as few and definite notions as possible. ...
    Direct download  
     
    Export citation  
     
    My bibliography   3 citations  
  27. Bruno Scarpellini (1971). Proof Theory and Intuitionistic Systems. New York,Springer-Verlag.
  28.  2
    S. J. Maslov, G. E. Mints & V. P. Orevkov (1971). Mechanical Proof-Search and the Theory of Logical Deduction in the Ussr. Revue Internationale de Philosophie 25 (4=98):575-584.
    A survey of works on automatic theorem-proving in the ussr 1964-1970. the philosophical problems are not touched.
    Direct download  
     
    Export citation  
     
    My bibliography  
  29. K. Schütte, Justus Diller & G. H. Müller (eds.) (1975). 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. Springer-Verlag.
     
    Export citation  
     
    My bibliography  
  30. Sanjida O'Connell (1998). Mindreading: An Investigation Into How We Learn to Love and Lie. Doubleday.
    "I know what you're thinking," we say, but how do we know what others are thinking or feeling? Because evolution has granted us what has come to be known as "Theory of Mind," the ability not only to be self-aware but aware of others' consciousness. Theory of Mind develops slowly-and in some cases, such as autism, develops little or not at all. Theory of Mind allows us to interact socially, to care about others, to manage our behavior (...)
     
    Export citation  
     
    My bibliography  
  31.  60
    Greg Restall (2009). Truth Values and Proof Theory. Studia Logica 92 (2):241 - 264.
    I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  32.  12
    Sara Negri & Jan von Plato (2001). Structural Proof Theory. Cambridge University Press.
    A concise introduction to structural proof theory, a branch of logic studying the general structure of logical and mathematical proofs.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   32 citations  
  33. Jeremy Avigad (2004). Forcing in Proof Theory. Bulletin of Symbolic Logic 10 (3):305-333.
    Paul Cohen’s method of forcing, together with Saul Kripke’s related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I (...)
    Direct download (14 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  34. Sara Negri, Jan von Plato & Aarne Ranta (2010). Structural Proof Theory. Cambridge University Press.
    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 (...)
     
    Export citation  
     
    My bibliography   3 citations  
  35.  5
    Michele Abrusci & Pasquali (2016). Quantification in Ordinary Language and Proof Theory. Philosophia Scientiæ 20:185-205.
    This paper gives an overview of the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this usual general framework represents a departure from empirical linguistic data. We briefly sketch a different idea for proof theory which is closer to the language itself than standard approaches in many aspects. We stress the importance of Hilbert’s operators—the epsilon-operator for existential and tau-operator for universal quantifications. Indeed, these operators are helpful in (...)
    No categories
    Direct download  
     
    Export citation  
     
    My bibliography  
  36.  1
    Toshiyasu Arai (2003). Proof Theory for Theories of Ordinals—I: Recursively Mahlo Ordinals. 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 (3 more)  
     
    Export citation  
     
    My bibliography   7 citations  
  37.  3
    Toshiyasu Arai (2004). Proof Theory for Theories of Ordinals II: Π3-Reflection. Annals of Pure and Applied Logic 129 (1-3):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 (2 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  38. Andrew Arana (2010). Proof Theory in Philosophy of Mathematics. Philosophy Compass 5 (4):336-347.
    A variety of projects in proof theory of relevance to the philosophy of mathematics are surveyed, including Gödel's incompleteness theorems, conservation results, independence results, ordinal analysis, predicativity, reverse mathematics, speed-up results, and provability logics.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  39. Sara Negri, Jan von Plato & Aarne Ranta (2011). Structural Proof Theory. Cambridge University Press.
    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 (...)
     
    Export citation  
     
    My bibliography   1 citation  
  40.  49
    Gaisi Takeuti (1985). Proof Theory and Set Theory. 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 (6 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  41.  74
    Solomon Feferman, The Proof Theory of Classical and Constructive Inductive Definitions. A 40 Year Saga, 1968-2008.
    1. Pohlers and The Problem. I first met Wolfram Pohlers at a workshop on proof theory organized by Walter Felscher that was held in Tübingen in early April, 1973. Among others at that workshop relevant to the work surveyed here were Kurt Schütte, Wolfram’s teacher in Munich, and Wolfram’s fellow student Wilfried Buchholz. This is not meant to slight in the least the many other fine logicians who participated there.2 In Tübingen I gave a couple of survey lectures (...)
    Direct download  
     
    Export citation  
     
    My bibliography  
  42.  18
    Solomon Feferman (2000). Does Reductive Proof Theory Have a Viable Rationale? Erkenntnis 53 (1-2):63-96.
    The goals of reduction andreductionism in the natural sciences are mainly explanatoryin character, while those inmathematics are primarily foundational.In contrast to global reductionistprograms which aim to reduce all ofmathematics to one supposedly ``universal'' system or foundational scheme, reductive proof theory pursues local reductions of one formal system to another which is more justified in some sense. In this direction, two specific rationales have been proposed as aims for reductive proof theory, the constructive consistency-proof rationale and (...)
    Direct download (9 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  43.  26
    Christian G. Fermüller & George Metcalfe (2009). Giles's Game and the Proof Theory of Łukasiewicz Logic. Studia Logica 92 (1):27 - 61.
    In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in Łukasiewicz logic. In this paper, it is shown that ‘disjunctive strategies’ for Giles’s game, combining ordinary strategies for all instances of the game played on the same formula, may be interpreted as derivations in a corresponding proof system. (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  44.  10
    A. Kino, John Myhill & Richard Eugene Vesley (eds.) (1970). Intuitionism and Proof Theory. Amsterdam,North-Holland Pub. Co..
    Our first aim is to make the study of informal notions of proof plausible. Put differently, since the raison d'étre of anything like existing proof theory seems to rest on such notions, the aim is nothing else but to make a case for proof theory; ...
    Direct download  
     
    Export citation  
     
    My bibliography   5 citations  
  45.  57
    Jeremy Avigad, “Clarifying the Nature of the Infinite”: The Development of Metamathematics and Proof Theory.
    We discuss the development of metamathematics in the Hilbert school, and Hilbert’s proof-theoretic program in particular. We place this program in a broader historical and philosophical context, especially with respect to nineteenth century developments in mathematics and logic. Finally, we show how these considerations help frame our understanding of metamathematics and proof theory today.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  46.  31
    Grigori Mints (1991). Proof Theory in the USSR 1925-1969. 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 (6 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  47.  37
    Jeremy Avigad, Proof Theory.
    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  
     
    My bibliography  
  48.  4
    Andrea Masini (1992). 2-Sequent Calculus: A Proof Theory of Modalities. Annals of Pure and Applied Logic 58 (3):229-246.
    Masini, A., 2-Sequent calculus: a proof theory of modalities, Annals of Pure and Applied Logic 58 229–246. In this work we propose an extension of the Getzen sequent calculus in order to deal with modalities. We extend the notion of a sequent obtaining what we call a 2-sequent. For the obtained calculus we prove a cut elimination theorem.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  49.  35
    George Tourlakis (2010). On the Proof-Theory of Two Formalisations of Modal First-Order Logic. Studia Logica 96 (3):349-373.
    We introduce a Gentzen-style modal predicate logic and prove the cut-elimination theorem for it. This sequent calculus of cut-free proofs is chosen as a proxy to develop the proof-theory of the logics introduced in [14, 15, 4]. We present syntactic proofs for all the metatheoretical results that were proved model-theoretically in loc. cit. and moreover prove that the form of weak reflection proved in these papers is as strong as possible.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  50.  12
    Harold Schellinx (1996). A Linear Approach to Modal Proof Theory. In H. Wansing (ed.), Proof Theory of Modal Logic. Kluwer 33.
1 — 50 / 1000