Results for 'Logic Diagrams'

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  1.  22
    Logic Diagrams, Sacred Geometry and Neural Networks.Jens Lemanski - 2019 - Logica Universalis 13 (4):495-513.
    In early modernity, one can find many spatial logic diagrams whose geometric forms share a family resemblance with religious art and symbols. The family resemblance these diagrams bear in form is often based on a vesica piscis or on a cross: Both logic diagrams and spiritual symbols focus on the intersection or conjunction of two or more entities, e.g. subject and predicate, on the one hand, or god and man, on the other. This paper deals (...)
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  2. What is a Logical Diagram?Catherine Legg - 2013 - In Sun-Joo Shin & Amirouche Moktefi (eds.), Visual Reasoning with Diagrams. Springer. pp. 1-18.
    Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a (...)
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  3.  26
    Metalogical Decorations of Logical Diagrams.Lorenz6 Demey & Hans5 Smessaert - 2016 - Logica Universalis 10 (2-3):233-292.
    In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations (...)
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  4.  32
    Logic Diagrams in the Weigel and Weise Circles.Jens Lemanski - 2018 - History and Philosophy of Logic 39 (1):3-28.
    From the mid-1600s to the beginning of the eighteenth century, there were two main circles of German scholars which focused extensively on diagrammatic reasoning and representation in logic. The first circle was formed around Erhard Weigel in Jena and consists primarily of Johann Christoph Sturm and Gottfried Wilhelm Leibniz; the second circle developed around Christian Weise in Zittau, with the support of his students, particularly Samuel Grosser and Johann Christian Lange. Each of these scholars developed an original form of (...)
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  5. Peirce, Logic Diagrams, and the Elementary Operations of Reasoning.P. N. Johnson-Laird - 2002 - Thinking and Reasoning 8 (1):69 – 95.
    This paper describes Peirce's systems of logic diagrams, focusing on the so-called ''existential'' graphs, which are equivalent to the first-order predicate calculus. It analyses their implications for the nature of mental representations, particularly mental models with which they have many characteristics in common. The graphs are intended to be iconic, i.e., to have a structure analogous to the structure of what they represent. They have emergent logical consequences and a single graph can capture all the different ways in (...)
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  6.  1
    Figuring It Out: Logic Diagrams.George Englebretsen - 2019 - De Gruyter.
    Many systems of logic diagrams have been offered both historically and more recently. Each of them has clear limitations. An original alternative system is offered here. It is simpler, more natural, and more expressively and inferentially powerful. It can be used to analyze not only syllogisms but arguments involving relational terms and unanalyzed statement terms.
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  7.  9
    Figuring It Out: Logic Diagrams.Amirouche Moktefi - forthcoming - History and Philosophy of Logic:1-4.
    Linear diagrams have an old history. Their past supporters include distinguished logicians such as Leibniz, Lambert and Keynes. Although circular diagrams...
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  8.  12
    Scriptural Logic: Diagrams for a Postcritical Metaphysics.Peter Ochs - 1995 - Modern Theology 11 (1):65-92.
  9. Means or End? On the Valuation of Logic Diagrams.Jens Lemanski - 2016 - Logic-Philosophical Studies 14:98-122.
    From the beginning of the 16th century to the end of the 18th century, there were not less than ten philosophers who focused extensively on Venn’s ostensible analytical diagrams, as noted by modern historians of logic (Venn, Gardner, Baron, Coumet et al.). But what was the reason for early modern philosophers to use logic or analytical diagrams? Among modern historians of logic one can find two theses which are closely connected to each other: M. Gardner (...)
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  10.  43
    On Frege's Logical Diagrams.Iulian D. Toader - 2004 - In Diagrammatic Representation and Inference. Springer: Lecture Notes in Computer Science, vol. 2980,. pp. 22-25.
    This paper argues that a particular point raised by Schröder – that Frege's logical notation fails to be modelled on arithmetical notation – is based on a misunderstanding, for the modelling was meant as conceptual, rather than notational.
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  11.  6
    On the Development of Logical Diagrams.Zhang Liuhua - 2002 - Modern Philosophy 2:018.
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  12.  15
    A New Logical Diagram.Wm J. Newlin - 1906 - Journal of Philosophy, Psychology and Scientific Methods 3 (20):539-545.
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  13. Logical Reasoning with Diagrams.Gerard Allwein & Jon Barwise (eds.) - 1996 - Oxford, England: Oxford University Press.
    One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers (...)
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  14.  15
    Peirce on Logical Diagrams.Eric Hammer - 1995 - Transactions of the Charles S. Peirce Society 31 (4):807 - 827.
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  15.  3
    A New Logical Diagram.J. Newlin - 1906 - Journal of Philosophy, Psychology and Scientific Methods 3 (20):539.
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  16.  87
    The Concept of Relevance and the Logic Diagram Tradition.Jan Dejnožka - 2010 - Logica Universalis 4 (1):67-135.
    What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and (...)
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  17.  21
    Logic Machines and Diagrams.Martin Gardner - 1958 - University of Chicago Press.
  18.  46
    The Logical Status of Diagrams.Sun-joo Shin - 1997 - British Journal for the Philosophy of Science 48 (2):290-291.
  19. Algebras, Diagrams, and Decisions in Language, Logic, and Computation.Kees Vermeulen & Ann Copestake - 2001
     
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  20.  1
    A Correctness Proof for Al-Barakāt’s Logical Diagrams.Wilfrid Hodges - forthcoming - Review of Symbolic Logic:1-16.
    In Baghdad in the mid twelfth century Abū al-Barakāt proposes a radical new procedure for finding the conclusions of premise-pairs in syllogistic logic, and for identifying those premise-pairs that have no conclusions. The procedure makes no use of features of the standard Aristotelian apparatus, such as conversions or syllogistic figures. In place of these al-Barakāt writes out pages of diagrams consisting of labelled horizontal lines. He gives no instructions and no proof that the procedure will yield correct results. (...)
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  21. Rehearsal for a Different Reading+ Response to Article by Ludwig, Kh on Gunther, Gotthard Theory of Non-Aristotelian Logic-Diagram of a Reconstruction of Gunther Theory of Negative Languages.J. Ditterich & R. Kaehr - 1979 - Philosophisches Jahrbuch 86 (2):385-408.
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  22.  15
    Jan Dejnožka, The Concept of Relevance and the Logic Diagram Tradition : Ann Arbor, Michigan: CreateSpace, 2012, Pp. 154; Reprinted in 2015 with Minor Corrections. ISBN 9781475071092. $13.99.Francesco Bellucci - 2019 - Studia Logica 107 (4):853-857.
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  23.  1
    Geometric and Cognitive Differences Between Logical Diagrams for the Boolean Algebra B_4.Lorenz6 Demey & Hans5 Smessaert - 2018 - Annals of Mathematics and Artificial Intelligence 83 (2):185-208.
    © 2018, Springer International Publishing AG, part of Springer Nature. Aristotelian diagrams are used extensively in contemporary research in artificial intelligence. The present paper investigates the geometric and cognitive differences between two types of Aristotelian diagrams for the Boolean algebra B4. Within the class of 3D visualizations, the main geometric distinction is that between the cube-based diagrams and the tetrahedron-based diagrams. Geometric properties such as collinearity, central symmetry and distance are examined from a cognitive perspective, focusing (...)
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  24. Argument Diagramming in Logic, Artificial Intelligence, and Law.Chris Reed, Douglas Walton & Fabrizio Macagno - 2007 - Artificial Intelligence, and Law 22 (1):87-109.
    In this paper, we present a survey of the development of the technique of argument diagramming covering not only the fields in which it originated - informal logic, argumentation theory, evidence law and legal reasoning – but also more recent work in applying and developing it in computer science and artificial intelligence. Beginning with a simple example of an everyday argument, we present an analysis of it visualised as an argument diagram constructed using a software tool. In the context (...)
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  25.  15
    Venn Diagram with Names of Individuals and Their Absence: A Non-Classical Diagram Logic.Reetu Bhattacharjee, Mihir Kr Chakraborty & Lopamudra Choudhury - 2018 - Logica Universalis 12 (1-2):141-206.
    Venn diagram system has been extended by introducing names of individuals and their absence. Absence gives a kind of negation of singular propositions. We have offered here a non-classical interpretation of this negation. Soundness and completeness of the present diagram system have been established with respect to this interpretation.
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  26. Logic Machines, Diagrams and Boolean Algebra.Martin Gardner - 1958 - New York: Dover Publications.
  27.  28
    Diagrams and the Concept of Logical System.Jon Barwise & Eric Hammer - 1996 - In Gerard Allwein & Jon Barwise (eds.), Logical Reasoning with Diagrams. Oxford University Press.
  28.  11
    Logic Machines and Diagrams.W. Mays - 1959 - Journal of Symbolic Logic 24 (1):78-79.
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  29.  10
    The Interaction Between Logic and Geometry in Aristotelian Diagrams.Lorenz6 Demey & Hans5 Smessaert - 2016 - Diagrammatic Representation and Inference, Diagrams 9781:67 - 82.
    © Springer International Publishing Switzerland 2016. We develop a systematic approach for dealing with informationally equivalent Aristotelian diagrams, based on the interaction between the logical properties of the visualized information and the geometrical properties of the concrete polygon/polyhedron. To illustrate the account’s fruitfulness, we apply it to all Aristotelian families of 4-formula fragments that are closed under negation and to all Aristotelian families of 6-formula fragments that are closed under negation.
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  30. Enhancing the Diagramming Method in Informal Logic.Dale Jacquette - 2011 - Argument: Biannual Philosophical Journal 1 (2):327-360.
    The argument diagramming method developed by Monroe C. Beardsley in his (1950) book Practical Logic, which has since become the gold standard for diagramming arguments in informal logic, makes it possible to map the relation between premises and conclusions of a chain of reasoning in relatively complex ways. The method has since been adapted and developed in a number of directions by many contemporary informal logicians and argumentation theorists. It has proved useful in practical applications and especially pedagogically (...)
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  31.  5
    Schopenhauer’s Partition Diagrams and Logical Geometry.Jens Lemanski & Lorenz Demey - 2021 - In A. Basu, G. Stapleton, S. Linker, C. Legg, E. Manalo & P. Viana (eds.), Diagrams 2021: Diagrammatic Representation and Inference. 93413 Cham, Deutschland: pp. 149-165.
    The paper examines Schopenhauer’s complex diagrams from the Berlin Lectures of the 1820 s, which show certain partitions of classes. Drawing upon ideas and techniques from logical geometry, we show that Schopenhauer’s partition diagrams systematically give rise to a special type of Aristotelian diagrams, viz. (strong) α -structures.
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  32.  23
    Schopenhauer Diagrams for Conceptual Analysis.Michał Dobrzański & Jens Lemanski - 2020 - In Ahti Veikko Pietarinen, P. Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter & Sven Linker (eds.), Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science, vol 12169. Cham, Schweiz: pp. 281-288.
    In his Berlin Lectures of the 1820s, the German philosopher Arthur Schopenhauer (1788–1860) used spatial logic diagrams for philosophy of language. These logic diagrams were applied to many areas of semantics and pragmatics, such as theories of concept formation, concept development, translation theory, clarification of conceptual disputes, etc. In this paper we first introduce the basic principles of Schopenhauer’s philosophy of language and his diagrammatic method. Since Schopenhauer often gives little information about how the individual (...) are to be understood, we then make the attempt to reconstruct, specify and further develop one diagram type for the field of conceptual analysis. (shrink)
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  33.  14
    Truth Diagrams Versus Extant Notations for Propositional Logic.Peter C.-H. Cheng - 2020 - Journal of Logic, Language and Information 29 (2):121-161.
    Truth diagrams are introduced as a novel graphical representation for propositional logic. To demonstrate their epistemic efficacy a set of 28 concepts are proposed that any comprehensive representation for PL should encompass. TDs address all the criteria whereas seven other existing representations for PL only provide partial coverage. These existing representations are: the linear formula notation, truth tables, a PL specific interpretation of Venn Diagrams, Frege’s conceptual notation, diagrams from Wittgenstein’s Tractatus, Pierce’s alpha graphs and Gardner’s (...)
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  34. Line Diagrams for Logic: Drawing Conclusions.George Englebretsen - 1998 - Lewiston, NY, USA: Mellen Press.
    This text presents a number of reasons for the reinstatement of a traditional terminist logic, contributing to the ongoing debate concerning the proper connections between formal logic, natural language, artificial reasoning, and mathematics.
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  35. Traditional Logic and the Venn Diagram; a Programed Introduction.Victor J. Cieutat - 1969 - Science Research Associates, Chicago.
  36.  3
    Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation.Lorenz6 Demey & Hans5 Smessaert - 2017 - Symmetry 9 (10).
    © 2017 by the authors. Aristotelian diagrams visualize the logical relations among a finite set of objects. These diagrams originated in philosophy, but recently, they have also been used extensively in artificial intelligence, in order to study various knowledge representation formalisms. In this paper, we develop the idea that Aristotelian diagrams can be fruitfully studied as geometrical entities. In particular, we focus on four polyhedral Aristotelian diagrams for the Boolean algebra B4, viz. the rhombic dodecahedron, the (...)
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  37.  79
    Peirce and the Logical Status of Diagrams.Sun-Joo Shin - 1994 - History and Philosophy of Logic 15 (1):45-68.
    In this paper, I aim to identify Peirce?s great contribution to logical diagrams and its limit.Peirce is the first person who believed that the same logical status can be given to diagrams as to symbolic systems.Even though this belief led him to invent his own graphical system, Existential Graphs, the success or failure of this system does not determine the value of Peirce?s general insights about logical diagrams.In order to make this point clear, I will show that (...)
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  38.  26
    Logical Reasoning with Diagrams, Gerard Allwein and Jon Barwise, Eds.Maarten de Rijke - 1999 - Journal of Logic, Language and Information 8 (3):387-390.
  39. A Diagram Method in Propositional Logic.H. G. Hubbeling - 1965 - Logique Et Analyse 8:277-288.
     
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  40.  18
    Venn Diagrams and Conventional Logic.Richard J. Regan - 1959 - New Scholasticism 33 (3):291-299.
  41.  15
    The Logical Status of Diagrams.Alexander Bird - 1996 - Philosophical Books 37 (1):50-51.
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  42. Traditional Logic and the Venn Diagram.V. J. CIEUTAT - 1969
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  43.  21
    Venn Diagrams Extended: Map Logic.John Rybak & Janet Rybak - 1976 - Notre Dame Journal of Formal Logic 17 (3):469-475.
  44.  4
    Euclid and His Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry.Nathaniel Miller - 2007 - Center for the Study of Language and Inf.
    Twentieth-century developments in logic and mathematics have led many people to view Euclid’s proofs as inherently informal, especially due to the use of diagrams in proofs. In _Euclid and His Twentieth-Century Rivals_, Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest (...)
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  45.  28
    Formalization of Reliability Block Diagrams in Higher-Order Logic.Waqar Ahmed, Osman Hasan & Sofiène Tahar - 2016 - Journal of Applied Logic 18:19-41.
  46.  1
    Schopenhauer Diagrams for Conceptual Analysis.Michał Dobrzański & Jens Lemanski - 2020 - In Diagrammatic Representation and Inference 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings. Basel: Springer. pp. 281-288.
    In his Berlin Lectures of the 1820s, the German philosopher Arthur Schopenhauer (1788–1860) used spatial logic diagrams for philosophy of language. These logic diagrams were applied to many areas of semantics and pragmatics, such as theories of concept formation, concept development, translation theory, clarification of conceptual disputes, etc. In this paper we first introduce the basic principles of Schopenhauer’s philosophy of language and his diagrammatic method. Since Schopenhauer often gives little information about how the individual (...) are to be understood, we then make the attempt to reconstruct, specify and further develop one diagram type for the field of conceptual analysis. (shrink)
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  47.  7
    Proof theory for heterogeneous logic combining formulas and diagrams: proof normalization.Ryo Takemura - 2021 - Archive for Mathematical Logic 60 (7):783-813.
    We extend natural deduction for first-order logic by introducing diagrams as components of formal proofs. From the viewpoint of FOL, we regard a diagram as a deductively closed conjunction of certain FOL formulas. On the basis of this observation, we first investigate basic heterogeneous logic wherein heterogeneous inference rules are defined in the styles of conjunction introduction and elimination rules of FOL. By examining what is a detour in our heterogeneous proofs, we discuss that an elimination-introduction pair (...)
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  48.  44
    How Diagrams Can Support Syllogistic Reasoning: An Experimental Study.Yuri Sato & Koji Mineshima - 2015 - Journal of Logic, Language and Information 24 (4):409-455.
    This paper explores the question of what makes diagrammatic representations effective for human logical reasoning, focusing on how Euler diagrams support syllogistic reasoning. It is widely held that diagrammatic representations aid intuitive understanding of logical reasoning. In the psychological literature, however, it is still controversial whether and how Euler diagrams can aid untrained people to successfully conduct logical reasoning such as set-theoretic and syllogistic reasoning. To challenge the negative view, we build on the findings of modern diagrammatic (...) and introduce an Euler-style diagrammatic representation system that is designed to avoid problems inherent to a traditional version of Euler diagrams. It is hypothesized that Euler diagrams are effective not only in interpreting sentential premises but also in reasoning about semantic structures implicit in given sentences. To test the hypothesis, we compared Euler diagrams with other types of diagrams having different syntactic or semantic properties. Experiment compared the difference in performance between syllogistic reasoning with Euler diagrams and Venn diagrams. Additional analysis examined the case of a linear variant of Euler diagrams, in which set-relationships are represented by one-dimensional lines. The experimental results provide evidence supporting our hypothesis. It is argued that the efficacy of diagrams in supporting syllogistic reasoning crucially depends on the way they represent the relational information contained in categorical sentences. (shrink)
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  49. Diagram-Based Geometric Practice.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 65--79.
    This chapter provides a survey of issues about diagrams in traditional geometrical reasoning. After briefly refuting several common philosophical objections, and giving a sketch of diagram-based reasoning practice in Euclidean plane geometry, discussion focuses first on problems of diagram sensitivity, and then on the relationship between uniform treatment and geometrical generality. Here, one finds a balance between representationally enforced unresponsiveness (to differences among diagrams) and the intellectual agent's contribution to such unresponsiveness that is somewhat different from what one (...)
     
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  50.  8
    Categorical Abstract Algebraic Logic: The Diagram and the Reduction Operator Lemmas.George Voutsadakis - 2007 - Mathematical Logic Quarterly 53 (2):147-161.
    The study of structure systems, an abstraction of the concept of first-order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first-order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality-free first-order structures are provided in the framework of structure systems. (© 2007 WILEY-VCH (...)
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