Results for 'Logic Diagrams'

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  1.  32
    Logic Diagrams as Argument Maps in Eristic Dialectics.Jens Lemanski - forthcoming - Argumentation:1-21.
    This paper analyses a hitherto unknown technique of using logic diagrams to create argument maps in eristic dialectics. The method was invented in the 1810s and -20s by Arthur Schopenhauer, who is considered the originator of modern eristic. This technique of Schopenhauer could be interesting for several branches of research in the field of argumentation: Firstly, for the field of argument mapping, since here a hitherto unknown diagrammatic technique is shown in order to visualise possible situations of arguments (...)
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  2. 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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  3.  10
    Five Dogmas of Logic Diagrams and How to Escape Them.Jens Lemanski, Andrea Anna Reichenberger, Theodor Berwe, Alfred Olszok & Claudia Anger - 2022 - Language & Communication 87 (1):258-270.
    In the vein of a renewed interest in diagrammatic reasoning, this paper challenges an opposition between logic diagrams and formal languages that has traditionally been the common view in philosophy of logic and linguistics. We examine, from a philosophical point of view, what we call five dogmas of logic diagrams. These are as follows: (1) diagrams are non-linguistic; (2) diagrams are visual representations; (3) diagrams are iconic, and not symbolic; (4) diagrams (...)
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  4.  25
    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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  5. 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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  6.  33
    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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  7.  12
    Scriptural Logic: Diagrams for a Postcritical Metaphysics.Peter Ochs - 1995 - Modern Theology 11 (1):65-92.
  8.  26
    Metalogical Decorations of Logical Diagrams.Lorenz Demey & Hans 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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  9.  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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  10.  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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  11.  6
    On the Development of Logical Diagrams.Zhang Liuhua - 2002 - Modern Philosophy 2:018.
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  12.  15
    Peirce on Logical Diagrams.Eric Hammer - 1995 - Transactions of the Charles S. Peirce Society 31 (4):807 - 827.
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  13. 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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  14.  11
    Figuring It Out: Logic Diagrams[REVIEW]Amirouche Moktefi - forthcoming - History and Philosophy of Logic:1-4.
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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.  15
    A New Logical Diagram.Wm J. Newlin - 1906 - Journal of Philosophy, Psychology and Scientific Methods 3 (20):539-545.
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  17.  88
    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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  18.  2
    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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  19. 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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  20.  3
    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.  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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  22. 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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  23. 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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  24. Logic Machines, Diagrams and Boolean Algebra.Martin Gardner - 1958 - New York: Dover Publications.
  25.  4
    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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  26. Traditional Logic and the Venn Diagram; a Programed Introduction.Victor J. Cieutat - 1969 - Science Research Associates, Chicago.
  27.  27
    Traditional Logic and the Venn Diagram. [REVIEW]G. N. T. - 1972 - Review of Metaphysics 25 (3):551-552.
    This paperback is a programed text designed for teaching introductory logic, either in conjunction with a standard text based upon traditional logic or as a do-it-yourself supplement for students taking courses stressing symbolic logic. The student learns logical theory by answering a variety of short answer, objective type exercises. The correct answer is given directly below each question or exercise, and the student is required to cover the answer while working the exercise; the purpose of this immediate (...)
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  28. 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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  29.  23
    Logic Machines and Diagrams.Martin Gardner - 1958 - University of Chicago Press.
  30. Algebras, Diagrams, and Decisions in Language, Logic, and Computation.Kees Vermeulen & Ann Copestake - 2001
     
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  31. 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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  32.  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.
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  33. A Diagram Method in Propositional Logic.H. G. Hubbeling - 1965 - Logique Et Analyse 8:277-288.
     
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  34.  15
    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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  35. Traditional Logic and the Venn Diagram.V. J. CIEUTAT - 1969
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  36.  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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  37.  48
    The Logical Status of Diagrams.Sun-joo Shin - 1997 - British Journal for the Philosophy of Science 48 (2):290-291.
  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.  12
    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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  40.  15
    The Logical Status of Diagrams.Alexander Bird - 1996 - Philosophical Books 37 (1):50-51.
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  41.  2
    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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  42.  25
    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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  43.  21
    Venn Diagrams Extended: Map Logic.John Rybak & Janet Rybak - 1976 - Notre Dame Journal of Formal Logic 17 (3):469-475.
  44.  11
    Logic Machines and Diagrams.W. Mays - 1959 - Journal of Symbolic Logic 24 (1):78-79.
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  45.  18
    Venn Diagrams and Conventional Logic.Richard J. Regan - 1959 - New Scholasticism 33 (3):291-299.
  46.  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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  47.  80
    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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  48. Concept Diagrams and the Context Principle.Jens Lemanski - 2020 - In Language, Logic, and Mathematics in Schopenhauer. Cham, Schweiz: Birkhäuser (Springer nature). pp. 47-73.
    What is the primacy of logic? Concepts, judgments, or inferences? Whereas representationalists traditionally argue for a primacy of the conceptual, rationalists, referring to the context principle and the use theory of meaning, consider judgments and inferences to be primary. This dispute also seems to be applicable to logic diagrams: Whereas “Euler-type diagrams” are actually only for judgments and inferences, “concept diagrams” represent ontologies by using concepts. With reference to Schopenhauer, the paper develops a position called (...)
     
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  49.  9
    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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  50. Sun-Joo Shin, The Logical Status of Diagrams[REVIEW]Philip Peterson - 1996 - Philosophy in Review 16:208-210.
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