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: 148.5
    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: 109.5
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  3. Paul Roberts & Mike Redmayne (eds.) (2007). Innovations in Evidence and Proof: Integrating Theory, Research and Teaching. Hart.score: 105.0
  4. H. Wansing (ed.) (1996). Proof Theory of Modal Logic. Kluwer.score: 96.0
    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: 96.0
    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. A. S. Troelstra (2000). Basic Proof Theory. Cambridge University Press.score: 81.0
    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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  7. Ryo Takemura (2013). Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization. Studia Logica 101 (1):157-191.score: 81.0
    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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  8. 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: 81.0
    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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  9. Samuel R. Buss (ed.) (1998). Handbook of Proof Theory. Elsevier.score: 81.0
    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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  10. Irving H. Anellis (2012). Jean van Heijenoort's Contributions to Proof Theory and Its History. Logica Universalis 6 (3-4):411-458.score: 81.0
    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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  11. 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: 81.0
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  12. 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: 81.0
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  13. Sue Thornham (2000). Feminist Theory and Cultural Studies: Stories of Unsettled Relations. Arnold.score: 78.0
    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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  14. 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: 72.0
    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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  15. Erik Palmgren (2012). Proof-Relevance of Families of Setoids and Identity in Type Theory. Archive for Mathematical Logic 51 (1-2):35-47.score: 72.0
    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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  16. David J. Pym (2004). Reductive Logic and Proof-Search: Proof Theory, Semantics, and Control. Oxford University Press.score: 70.5
    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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  17. 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: 70.5
    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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  18. Paolo Maffezioli & Alberto Naibo (forthcoming). Proof Theory of Epistemic Logic of Programs. Logic and Logical Philosophy.score: 70.5
    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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  19. Luciano Serafini & Fausto Giunchiglia (2002). ML Systems: A Proof Theory for Contexts. [REVIEW] Journal of Logic, Language and Information 11 (4):471-518.score: 70.5
    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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  20. Stefano Baratella & Andrea Masini (2004). An Approach to Infinitary Temporal Proof Theory. Archive for Mathematical Logic 43 (8):965-990.score: 70.5
    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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  21. Shawn Hedman (2004). A First Course in Logic: An Introduction to Model Theory, Proof Theory, Computability, and Complexity. Oxford University Press.score: 69.0
    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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  22. Jeremy Avigad (2004). Forcing in Proof Theory. Bulletin of Symbolic Logic 10 (3):305-333.score: 69.0
    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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  23. A. Kino, John Myhill & Richard Eugene Vesley (eds.) (1970). Intuitionism and Proof Theory. Amsterdam,North-Holland Pub. Co..score: 69.0
    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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  24. Carlo Cellucci (1985). Proof Theory and Complexity. Synthese 62 (2):173 - 189.score: 68.5
    Different proofs may be distinguished in terms of complexity. This paper reviews the inefficiency of current logical systems.
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  25. Paolo Maffezioli, Alberto Naibo & Sara Negri (2013). The Church–Fitch Knowability Paradox in the Light of Structural Proof Theory. Synthese 190 (14):2677-2716.score: 67.5
    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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  26. Sören Stenlund (1972). Combinators, -Terms and Proof Theory. Dordrecht,D. Reidel.score: 67.5
    The main aim of Schonfinkel's paper was methodological: to reduce the primitive logical notions to as few and definite notions as possible. ...
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  27. Gerhard Jäger (1986). Theories for Admissible Sets: A Unifying Approach to Proof Theory. Bibliopolis.score: 67.5
     
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  28. Bruno Scarpellini (1971). Proof Theory and Intuitionistic Systems. New York,Springer-Verlag.score: 67.5
  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.score: 67.5
     
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  30. K. Schütte (1977). Proof Theory. Springer-Verlag.score: 67.5
     
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  31. 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.score: 67.5
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  32. Gaisi Takeuti (1987). Proof Theory. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..score: 67.5
     
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  33. Lars Hallnäs (2006). On the Proof-Theoretic Foundation of General Definition Theory. Synthese 148 (3):589 - 602.score: 64.5
    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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  34. Theophilus Mooko * (2005). The Use of Research and Theory in English Language Teaching in Botswana Secondary Schools. Educational Studies 31 (1):39-53.score: 64.0
    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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  35. 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: 63.0
    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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  36. 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: 63.0
    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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  37. Clare Hemmings (2011). Why Stories Matter: The Political Grammar of Feminist Theory. Duke University Press.score: 63.0
    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.score: 63.0
     
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  39. Jeff Edmonds (2008). How to Think About Algorithms. Cambridge University Press.score: 61.0
    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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  40. Hunter McEwan (1991). English Teaching and the Weight of Theory. Studies in Philosophy and Education 11 (2):113-121.score: 61.0
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  41. Greg Restall (2009). Truth Values and Proof Theory. Studia Logica 92 (2):241 - 264.score: 60.0
    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 (...)
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  42. Tom Børsen, Avan N. Antia & Mirjam Sophia Glessmer (2013). A Case Study of Teaching Social Responsibility to Doctoral Students in the Climate Sciences. Science and Engineering Ethics 19 (4):1491-1504.score: 60.0
    The need to make young scientists aware of their social responsibilities is widely acknowledged, although the question of how to actually do it has so far gained limited attention. A 2-day workshop entitled “Prepared for social responsibility?” attended by doctoral students from multiple disciplines in climate science, was targeted at the perceived needs of the participants and employed a format that took them through three stages of ethics education: sensitization, information and empowerment. The workshop aimed at preparing doctoral students to (...)
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  43. John Mahoney (1990). Teaching Business Ethics in the Uk, Europe, and the Usa: A Comparative Study. Athlone Press.score: 60.0
     
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  44. Sara Negri & Jan von Plato (2001). Structural Proof Theory. Cambridge University Press.score: 59.0
    A concise introduction to structural proof theory, a branch of logic studying the general structure of logical and mathematical proofs.
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  45. Morag Shiach (ed.) (1999). Feminism and Cultural Studies. Oxford University Press.score: 58.0
    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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  46. Maria Andrén (2008). Det Pedagogiska Övervägandet: En Uppmärksamhetsriktande Studie I Och Genom Humanvetenskaplig Handlingsteori. Åbo Akademis Förlag.score: 57.0
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  47. Morten Heine Sørensen (2007). Lectures on the Curry-Howard Isomorphism. Elsevier.score: 55.5
    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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  48. 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: 55.5
    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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  49. Thomas Ehrhard (ed.) (2004). Linear Logic in Computer Science. Cambridge University Press.score: 55.5
    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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  50. Helmut Pfeiffer (1989). Girard Jean-Yves. Proof Theory and Logical Complexity. Volume I. Studies in Proof Theory, No. 1. Bibliopolis, Naples 1987, Also Distributed by Humanities Press, Atlantic Highlands, NJ, 503 Pp. [REVIEW] Journal of Symbolic Logic 54 (4):1493-1494.score: 55.5
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