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

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  1. Despina A. Stylianou, Maria L. Blanton & Eric J. Knuth (eds.) (2009). Teaching and Learning Proof Across the Grades: A K-16 Perspective. Routledge.score: 594.0
    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. Maurice Joseph Burke (ed.) (2008). Navigating Through Reasoning and Proof in Grades 9-12. National Council of Teachers of Mathematics.score: 438.0
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  3. Paul Roberts & Mike Redmayne (eds.) (2007). Innovations in Evidence and Proof: Integrating Theory, Research and Teaching. Hart.score: 420.0
  4. H. Wansing (ed.) (1996). Proof Theory of Modal Logic. Kluwer.score: 288.0
    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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  5. Dov M. Gabbay (2000). Goal-Directed Proof Theory. Kluwer Academic.score: 288.0
    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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  6. 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.score: 243.0
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  7. 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.score: 243.0
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  8. Sue Thornham (2000). Feminist Theory and Cultural Studies: Stories of Unsettled Relations. Arnold.score: 234.0
    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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  9. George R. Exner (1997). An Accompaniment to Higher Mathematics. Springer.score: 216.0
    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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  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.score: 211.5
    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. Shawn Hedman (2004). A First Course in Logic: An Introduction to Model Theory, Proof Theory, Computability, and Complexity. Oxford University Press.score: 207.0
    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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  12. Jeremy Avigad (2004). Forcing in Proof Theory. Bulletin of Symbolic Logic 10 (3):305-333.score: 207.0
    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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  13. A. Kino, John Myhill & Richard Eugene Vesley (eds.) (1970). Intuitionism and Proof Theory. Amsterdam,North-Holland Pub. Co..score: 207.0
    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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  14. Jeff Edmonds (2008). How to Think About Algorithms. Cambridge University Press.score: 206.0
    There are many algorithm texts that provide lots of well-polished code and proofs of correctness. Instead, this book presents insights, notations, and analogies to help the novice describe and think about algorithms like an expert. By looking at both the big picture and easy step-by-step methods for developing algorithms, the author helps students avoid the common pitfalls. He stresses paradigms such as loop invariants and recursion to unify a huge range of algorithms into a few meta-algorithms. Part of the goal (...)
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  15. Lars Hallnäs (2006). On the Proof-Theoretic Foundation of General Definition Theory. Synthese 148 (3):589 - 602.score: 193.5
    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. Theophilus Mooko * (2005). The Use of Research and Theory in English Language Teaching in Botswana Secondary Schools. Educational Studies 31 (1):39-53.score: 192.0
    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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  17. 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.score: 189.0
    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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  18. 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.score: 189.0
    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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  19. Clare Hemmings (2011). Why Stories Matter: The Political Grammar of Feminist Theory. Duke University Press.score: 189.0
    Progress -- Loss -- Return -- Amenability -- Citation tactics -- Affective subjects.
     
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  20. 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.score: 189.0
     
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  21. Morag Shiach (ed.) (1999). Feminism and Cultural Studies. Oxford University Press.score: 174.0
    This latest volume in the Oxford Readings in Feminism series consists of an exciting collection of articles addressing key questions for feminism and cultural studies. Encompassing both classic articles and challenging new work, Feminism and Cultural Studies is organized thematically and addresses commodification, women and labor, mass culture, fantasy and ideas of home.
     
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  22. Maria Andrén (2008). Det Pedagogiska Övervägandet: En Uppmärksamhetsriktande Studie I Och Genom Humanvetenskaplig Handlingsteori. Åbo Akademis Förlag.score: 171.0
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  23. Morten Heine Sørensen (2007). Lectures on the Curry-Howard Isomorphism. Elsevier.score: 166.5
    The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, (...) normalization corresponds to term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transforms proofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq). This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features - The Curry-Howard Isomorphism treated as common theme - Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics - Thorough study of the connection between calculi and logics - Elaborate study of classical logics and control operators - Account of dialogue games for classical and intuitionistic logic - Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme. · Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics. · Elaborate study of classical logics and control operators. · Account of dialogue games for classical and intuitionistic logic. · Theoretical foundations of computer-assisted reasoning. (shrink)
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  24. Koji Mineshima, Mitsuhiro Okada & Ryo Takemura (2012). A Diagrammatic Inference System with Euler Circles. Journal of Logic, Language and Information 21 (3):365-391.score: 166.5
    Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the eighteenth century. But it is quite recent (more precisely, in the 1990s) that logicians started to study them from a formal logical viewpoint. We propose a novel approach to the formalization of Euler diagrammatic reasoning, in which diagrams are defined not in terms of (...)
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  25. Thomas Ehrhard (ed.) (2004). Linear Logic in Computer Science. Cambridge University Press.score: 166.5
    Linear Logic is a branch of proof theory which provides refined tools for the study of the computational aspects of proofs. These tools include a duality-based categorical semantics, an intrinsic graphical representation of proofs, the introduction of well-behaved non-commutative logical connectives, and the concepts of polarity and focalisation. These various aspects are illustrated here through introductory tutorials as well as more specialised contributions, with a particular emphasis on applications to computer science: denotational semantics, lambda-calculus, logic programming and (...)
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  26. George Boolos (1979). The Unprovability of Consistency: An Essay in Modal Logic. Cambridge University Press.score: 166.5
    The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate (...)
     
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  27. A. S. Troelstra (2000). Basic Proof Theory. Cambridge University Press.score: 162.0
    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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  28. Ryo Takemura (2013). Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization. Studia Logica 101 (1):157-191.score: 162.0
    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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  29. 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.score: 162.0
    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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  30. Samuel R. Buss (ed.) (1998). Handbook of Proof Theory. Elsevier.score: 162.0
    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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  31. Irving H. Anellis (2012). Jean van Heijenoort's Contributions to Proof Theory and Its History. Logica Universalis 6 (3-4):411-458.score: 162.0
    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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  32. Stanley Hauerwas (2007). The State of the University: Academic Knowledges and the Knowledge of God. Blackwell Pub..score: 162.0
    In this book, controversial and world-renowned theologian, Stanley Hauerwas, tackles the issue of theology being sidelined as a necessary discipline in the modern university. It is an attempt to reclaim the knowledge of God as just that – knowledge. Questions why theology is no longer considered a necessary subject in the modern university, and explores the role it should play in the development of our “knowledge” Considers how theology is often excluded from the knowledges of the modern university because these (...)
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  33. Josefina Figueira-McDonough, Ann Nichols-Casebolt & F. Ellen Netting (eds.) (1998). The Role of Gender in Practice Knowledge: Claiming Half the Human Experience. Garland Pub..score: 162.0
    Feminist critiques of the social sciences are based on the assumption that because the social sciences were developed for the most part by white, middle-class, Western men, the perspectives of women were ignored. This book offers an approach for integrating gender-related content into the social work curriculum. The distinguished contributors discuss the shortcoming of dominant knowledge, address the pressing need for a gender-integrated curriculum, consider the pedagogies consistent with the implementation of an integrate curriculum, address specific areas in social work (...)
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  34. 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.score: 162.0
    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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  35. Ronald Barnett (1997). Higher Education: A Critical Business. Open University Press.score: 162.0
     
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  36. Michel Foucault (2011). The Courage of the Truth (the Government of Self and Others Ii): Lectures at the Collège de France, 1983-1984. Palgrave Macmillan.score: 162.0
  37. Rita Russo (2009). Epistemologia Ed Insegnamento Delle Scienze. Pensa.score: 162.0
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  38. Anneli Sarvimäki (1988). Knowledge in Interactive Practice Disciplines: An Analysis of Knowledge in Education and Health Care. Dept. Of Education, University of Helsinki.score: 162.0
  39. Arnon Avron, The Semantics and Proof Theory of Linear Logic.score: 157.5
    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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  40. Thomas Studer (2008). On the Proof Theory of the Modal Mu-Calculus. Studia Logica 89 (3):343 - 363.score: 157.5
    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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  41. Jorge Alexis Arevalo (2010). Critical Reflective Organizations: An Empirical Observation of Global Active Citizenship and Green Politics. [REVIEW] Journal of Business Ethics 96 (2):299 - 316.score: 153.0
    Relationships between the environmental and economic dimensions of sustainability have been solidly specified, but relatively little attention has been given to the social sphere. The current study attempts to fill this gap by integrating corporate environmentalism more fully with concepts of corporate sustainability. This investigation draws specifically from neo-Habermasian critical environmental theory research and brings three concepts together for closer empirical examination: the public sphere, the communicative rationality, and discursive design with the goal of capturing whether critical and (...)
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  42. Aarne Ranta (1998). Syntactic Calculus with Dependent Types. Journal of Logic, Language and Information 7 (4):413-431.score: 153.0
    The aim of this study is to look at the the syntactic calculus of Bar-Hillel and Lambek, including semantic interpretation, from the point of view of constructive type theory. The syntactic calculus is given a formalization that makes it possible to implement it in a type-theoretical proof editor. Such an implementation combines formal syntax and formal semantics, and makes the type-theoretical tools of automatic and interactive reasoning available in grammar.In the formalization, the use of the dependent types (...)
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  43. May Britt Postholm (2011). Developing Teaching in the "University Classroom": The Teacher as Researcher When Initiating and Researching Innovations. Outlines. Critical Practice Studies 13 (1):1-18.score: 153.0
    The teacher’s role in the university classroom has traditionally been to present the syllabus to listening students. In Norway new rules have been introduced for the activity in this classroom. The overarching goal for the teaching is to organize a learning situation that makes the students active learners. The article deals with the teacher as a researcher, and focuses on how innovative actions can be implemented by the teacher and studied from a researcher point of view. The text presents (...)
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  44. M. F. Peschl, G. Bottaro, M. Hartner-Tiefenthaler & K. Rötzer (2014). Authors' Response: Challenges in Studying and Teaching Innovation: Between Theory and Practice. Constructivist Foundations 9 (3):440-446.score: 145.0
    Upshot: This response focuses on the following issues, which summarize the points made by the commentaries: (i) further reflection on and details of the methodological framework that was applied to studying the proposed design of our innovation course, (ii) the issue of generalizability of the findings for teaching innovation (in this context the question of generic or transferable skills will become central), and (iii) finally, more precise explanation of what we mean by “learning from the future as it emerges.”.
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  45. Yanping Liu (forthcoming). 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:1-9.score: 144.0
    Legal translation (shortened as LT) 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 (...)
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  46. Erik Palmgren (2012). Proof-Relevance of Families of Setoids and Identity in Type Theory. Archive for Mathematical Logic 51 (1-2):35-47.score: 144.0
    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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  47. Burkard Polster (2004). Q.E.D.: Beauty in Mathematical Proof. Walker & Co..score: 144.0
    Q.E.D. presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras’s theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes’ method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino (...)
     
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  48. Hunter McEwan (1991). English Teaching and the Weight of Theory. Studies in Philosophy and Education 11 (2):113-121.score: 143.0
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  49. David J. Pym (2004). Reductive Logic and Proof-Search: Proof Theory, Semantics, and Control. Oxford University Press.score: 141.0
    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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  50. Paolo Maffezioli & Alberto Naibo (forthcoming). Proof Theory of Epistemic Logic of Programs. Logic and Logical Philosophy.score: 141.0
    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 (...)
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