Search results for 'Proof theory Study and teaching' (try it on Scholar)

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  1.  16
    Despina A. Stylianou, Maria L. Blanton & Eric J. Knuth (eds.) (2009). Teaching and Learning Proof Across the Grades: A K-16 Perspective. Routledge.
    Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help ...
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  2. Paul Roberts & Mike Redmayne (eds.) (2007). Innovations in Evidence and Proof: Integrating Theory, Research and Teaching. Hart.
     
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  3. Maurice Joseph Burke (ed.) (2008). Navigating Through Reasoning and Proof in Grades 9-12. National Council of Teachers of Mathematics.
     
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  4.  4
    Wendell V. Harris (1987). Beyond Deconstruction: The Uses and Abuses of Literary Theory_, And: _Interpretive Conventions: The Reader in the Study of American Fiction_, And: _Textual Power: Literary Theory and the Teaching of English (Review). Philosophy and Literature 11 (2):317-329.
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  5. Housheng Duan (2011). Zheng Ming Ping Jia Yuan Li: Jian Ji Dui Min Shi Su Song Fang Fa Lun de Tan Tao = the Theory of Proof Evaluation: With Some Study of the Civil Procedure Methodology. Fa Lü Chu Ban She.
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  6.  3
    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 (...)
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  7.  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.
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  8.  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 (...)
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  9. 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. (...)
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  10.  10
    H. Kushida & M. Okada (2007). A Proof–Theoretic Study of the Correspondence of Hybrid Logic and Classical Logic. Journal of Logic, Language and Information 16 (1):35-61.
    In this paper, we show the equivalence between the provability of a proof system of basic hybrid logic and that of translated formulas of the classical predicate logic with equality and explicit substitution by a purely proof–theoretic method. Then we show the equivalence of two groups of proof systems of hybrid logic: the group of labelled deduction systems and the group of modal logic-based systems.
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  11.  9
    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; ...
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  12. Shawn Hedman (2004). A First Course in Logic: An Introduction to Model Theory, Proof Theory, Computability, and Complexity. Oxford University Press.
    The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, (...)
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  13. Shawn Hedman (2004). A First Course in Logic: An Introduction to Model Theory, Proof Theory, Computability, and Complexity. Oxford University Press Uk.
    The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, (...)
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  14. David J. Pym & Eike Ritter (2004). Reductive Logic and Proof-Search: Proof Theory, Semantics, and Control. Oxford University Press Uk.
    This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes 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. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, (...)
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  15.  18
    Lars Hallnäs (2006). On the Proof-Theoretic Foundation of General Definition Theory. Synthese 148 (3):589 - 602.
    A general definition theory should serve as a foundation for the mathematical study of definitional structures. The central notion of such a theory is a precise explication of the intuitively given notion of a definitional structure. The purpose of this paper is to discuss the proof theory of partial inductive definitions as a foundation for this kind of a more general definition theory. Among the examples discussed is a suggestion for a more abstract definition (...)
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  16.  7
    S. Parsons, P. J. Barker & A. E. Armstrong (2001). The Teaching of Health Care Ethics to Students of Nursing in the UK: A Pilot Study. Nursing Ethics 8 (1):45-56.
    Senior lecturers/lecturers in mental health nursing (11 in round one, nine in round two, and eight in the final round) participated in a three-round Delphi study into the teaching of health care ethics (HCE) to students of nursing. The participants were drawn from six (round one) and four (round three) UK universities. Information was gathered on the organization, methods used and content of HCE modules. Questionnaire responses were transcribed and the content analysed for patterns of interest and areas (...)
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  17.  15
    Richard Scheines, Matt Easterday & David Danks (2007). Teaching the Normative Theory of Causal Reasoning. In Alison Gopnik & Laura Schulz (eds.), Causal Learning: Psychology, Philosophy, and Computation. Oxford University Press 119--38.
    There is now substantial agreement about the representational component of a normative theory of causal reasoning: Causal Bayes Nets. There is less agreement about a normative theory of causal discovery from data, either computationally or cognitively, and almost no work investigating how teaching the Causal Bayes Nets representational apparatus might help individuals faced with a causal learning task. Psychologists working to describe how naïve participants represent and learn causal structure from data have focused primarily on learning from (...)
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  18.  5
    Theophilus Mooko * (2005). The Use of Research and Theory in English Language Teaching in Botswana Secondary Schools. Educational Studies 31 (1):39-53.
    The purpose of this study was to establish the usage of research and theory in the teaching of English language in secondary schools in Botswana. Altogether 100 questionnaires were administered in 19 secondary schools. The results of this study indicate that teachers rarely ever refer to language research in their teaching. Less value was also placed on the theoretical information acquired during training. The respondents indicated that their teaching is essentially based on utilizing their (...)
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  19. Theophilus Mooko* (2005). The Use of Research and Theory in English Language Teaching in Botswana Secondary Schools. Educational Studies 31 (1):39-53.
    The purpose of this study was to establish the usage of research and theory in the teaching of English language in secondary schools in Botswana. Altogether 100 questionnaires were administered in 19 secondary schools. The results of this study indicate that teachers rarely ever refer to language research in their teaching. Less value was also placed on the theoretical information acquired during training. The respondents indicated that their teaching is essentially based on utilizing their (...)
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  20.  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 (...)
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  21.  39
    Arnon Avron (1988). The Semantics and Proof Theory of Linear Logic. Theoretical Computer Science 57:161-184.
    Linear logic is a new logic which was recently developed by Girard in order to provide a logical basis for the study of parallelism. It is described and investigated in Gi]. Girard's presentation of his logic is not so standard. In this paper we shall provide more standard proof systems and semantics. We shall also extend part of Girard's results by investigating the consequence relations associated with Linear Logic and by proving corresponding str ong completeness theorems. Finally, we (...)
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  22.  34
    Thomas Studer (2008). On the Proof Theory of the Modal Mu-Calculus. Studia Logica 89 (3):343 - 363.
    We study the proof-theoretic relationship between two deductive systems for the modal mu-calculus. First we recall an infinitary system which contains an omega rule allowing to derive the truth of a greatest fixed point from the truth of each of its (infinitely many) approximations. Then we recall a second infinitary calculus which is based on non-well-founded trees. In this system proofs are finitely branching but may contain infinite branches as long as some greatest fixed point is unfolded infinitely (...)
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  23.  8
    G. Thomas Goodnight (2008). Strategic Maneuvering in Direct to Consumer Drug Advertising: A Study in Argumentation Theory and New Institutional Theory. [REVIEW] Argumentation 22 (3):359-371.
    New Institutional Theory is used to explain the context for argumentation in modern practice. The illustration of Direct to Consumer Drug advertising is deployed to show how communicative argument between a doctor and patient is influenced by force exogenous to the practice of medicine. The essay shows how strategic maneuvering shifts the burden of proof within institutional relations.
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  24.  11
    Barbara Applebaum (2002). Teaching Applied Ethics, Critical Theory, and “Having to Brush One's Teeth”. Teaching Philosophy 25 (1):27-40.
    This paper argues that to study and teach ethics without due attention to feminism and other relevant aspects of critical theory is to be ethically handicapped. In arguing for this point, the author explains the key components of critical theory, how critical theory augments critical thinking insofar as the former points out certain limitations of exclusive abstract analysis, and how a consideration of critical theory can aid teachers to achieve their learning objectives. In illustrating these (...)
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  25.  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 (...)
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  26.  26
    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 (...)
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  27.  6
    Jinhua Jia (2015). Redefining the Ideal Character: A Comparative Study Between the Concept of Detachment in the Aṣṭasāhasrikā and Guo Xiang’s Theory of Eremitism at Court. Dao: A Journal of Comparative Philosophy 14 (4):545-565.
    The Aṣṭasāhasrikā Prajñāpāramitā Sūtra criticizes the traditional practice of dwelling in an isolated place for self-cultivation and advocates returning to the human realm with a liberated mind and compassionate engagement. This new theory of detachment aims at defining the Bodhisattva, a new ideal character, for the rising Mahāyāna movement. In his theory of eremitism at court, Guo Xiang 郭象 describes a sage image of governing the empire with a detached mind. This image is invested with the concept of (...)
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  28. Sue Thornham (2000). Feminist Theory and Cultural Studies: Stories of Unsettled Relations. Arnold.
    Feminist theory is a central strand of cultural studies. This book explores the history of feminist cultural studies from the early work of Mary Wollstonecraft, Charlotte Perkins Gilman, Virginia Woolf, Simone de Beauvoir, through the 1970s Women's Liberation Movement. It also provides a comprehensive introduction to the contemporary key approaches, theories and debates of feminist theory within cultural studies, offering a major re-mapping of the field. It will be an essential text for students taking courses within both cultural (...)
     
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  29.  4
    G. Thomas Goodnight (2008). Strategic Maneuvering in Direct to Consumer Drug Advertising: A Study in Argumentation Theory and New Institutional Theory. Argumentation 22 (3):359-371.
    New Institutional Theory is used to explain the context for argumentation in modern practice. The illustration of Direct to Consumer Drug advertising is deployed to show how communicative argument between a doctor and patient is influenced by force exogenous to the practice of medicine. The essay shows how strategic maneuvering shifts the burden of proof within institutional relations.
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  30.  16
    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.
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  31.  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.
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  32.  6
    George R. Exner (1997). An Accompaniment to Higher Mathematics. Springer.
    This text prepares undergraduate mathematics students to meet two challenges in the study of mathematics, namely, to read mathematics independently and to understand and write proofs. The book begins by teaching how to read mathematics actively, constructing examples, extreme cases, and non-examples to aid in understanding an unfamiliar theorem or definition (a technique famililar to any mathematician, but rarely taught); it provides practice by indicating explicitly where work with pencil and paper must interrupt reading. The book then turns (...)
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  33. 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 (...)
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  34. Arnon Avron, The Method of Hypersequents in the Proof Theory of Propositional Non-Classical Logics.
    Until not too many years ago, all logics except classical logic (and, perhaps, intuitionistic logic too) were considered to be things esoteric. Today this state of a airs seems to have completely been changed. There is a growing interest in many types of nonclassical logics: modal and temporal logics, substructural logics, paraconsistent logics, non-monotonic logics { the list is long. The diversity of systems that have been proposed and studied is so great that a need is felt by many researchers (...)
     
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  35. Gaisi Takeuti (1987). Proof Theory. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
     
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  36.  51
    Jeffrey P. Schloss (2006). 'Evolutionary Theory and Religious Belief. In Philip Clayton & Zachory Simpson (ed.), The Oxford Handbook of Religion and Science. Oxford University Press 198.
    Accession Number: ATLA0001712127; Hosting Book Page Citation: p 187-206.; Physical Description: table ; Language(s): English; General Note: Bibliography: p 204-206.; Issued by ATLA: 20130825; Publication Type: Essay.
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  37. Clare Hemmings (2011). Why Stories Matter: The Political Grammar of Feminist Theory. Duke University Press.
    Progress -- Loss -- Return -- Amenability -- Citation tactics -- Affective subjects.
     
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  38. Richard C. Whitfield (ed.) (1976). Theory of Knowledge Course: Syllabus and Teachers' Notes. Department of Education, University of Aston in Birmingham [for] the International Baccalaureate Office.
     
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  39. K. Schütte (1977). Proof Theory. Springer-Verlag.
     
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  40.  8
    Philip N. Johnson-Laird (1997). Rules and Illusions: A Critical Study of Rips's the Psychology of Proof. [REVIEW] Minds and Machines 7 (3):387-407.
  41.  1
    Daniel Vázquez (2014). Reflections on Tutoring Ancient Greek Philosophy: A Case Study of Teaching First-Year Undergraduates in the UK. Studying Teacher Education 10 (2):117-129.
    This is a case study of my reflections on teaching a first-year undergraduate tutorial on Ancient Greek Philosophy in the UK. This study draws upon the notion of reflective practice as an essential feature of teaching, in this case applied to Higher Education. My aim is to show how a critical engagement with my teaching practices and the overall learning experience modified, developed, or strengthened my practices, attitudes, and teaching philosophy during the course of (...)
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  42.  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 (...)
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  43.  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.
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  44.  18
    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 (...)
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  45.  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 (...)
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  46. J. Y. Girard (1991). Proof Theory and Logical Complexity. Annals of Pure and Applied Logic 53 (4):197.
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  47.  65
    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 ${A \supset \diamondsuit \mathcal{K} A}$ (KP). The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$ (OP). A Gentzen-style reconstruction of the Church–Fitch (...)
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  48.  15
    Yanping Liu (2015). Skopos Theory and Legal Translation: A Case Study of Examples From the Criminal Law of the P.R.C. International Journal for the Semiotics of Law - Revue Internationale de Sémiotique Juridique 28 (1):125-133.
    Legal translation has become a principal means to unfold Chinese laws to the world in the global era and the study of it has proved to be of practical significance. Since the proper theory guidance is the key to the quality of LT translation, this paper focuses on the Skopos theory and the strategies applied in the practice of LT. A case study of LT examples from the Criminal Law of the P.R.C. has been made while (...)
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  49.  13
    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. (...)
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  50. Gerhard Jäger (1986). Theories for Admissible Sets: A Unifying Approach to Proof Theory. Bibliopolis.
     
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