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  1. Aristotle's syllogistic from the standpoint of modern formal logic.Jan Łukasiewicz - 1957 - New York: Garland.
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  • The existential graphs of Charles S. Peirce.Don D. Roberts - 1973 - The Hague,: Mouton.
    1 INTRODUCTION Above the other titles he might justly have claimed, Charles S. Peirce prized the title 'logician'. He expressed in several places his ...
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  • Formal Logic (1847).Augustus De Morgan - 2018 - Franklin Classics.
    This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...)
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  • What is a syllogism?Timothy J. Smiley - 1973 - Journal of Philosophical Logic 2 (1):136 - 154.
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  • Completeness of an ancient logic.John Corcoran - 1972 - Journal of Symbolic Logic 37 (4):696-702.
    In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...)
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  • Aristotle's natural deduction system.John Corcoran - 1974 - In Ancient logic and its modern interpretations. Boston,: Reidel. pp. 85--131.
    This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".
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  • Linear Logic.Jean-Yves Girard - 1987 - Theoretical Computer Science 50:1–102.
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  • Logical reasoning with diagrams.Gerard Allwein & Jon Barwise (eds.) - 1996 - New York: 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 explore (...)
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  • The iconic logic of Peirce's graphs.Sun-Joo Shin - 2002 - Cambridge: MIT Press.
    A case study of multimodal systems and a new interpretation of Charles S. Peirce's theory of reasoning and signs based on an analysis of his system of ...
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  • (1 other version)Logic machines and diagrams.Martin Gardner - 1982 - Chicago: University of Chicago Press.
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  • Logic and Visual Information.Eric Hammer - 1995 - CSLI Publications.
    This book examines the logical foundations of visual information: information presented in the form of diagrams, graphs, charts, tables, and maps. The importance of visual information is clear from its frequent presence in everyday reasoning and communication, and also in compution. Chapters of the book develop the logics of familiar systems of diagrams such as Venn diagrams and Euler circles. Other chapters develop the logic of higraphs, Pierce diagrams, and a system having both diagrams and sentences among its well-formed representations. (...)
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  • On the Diagrammatic and Mechanical Representation of Propositions and Reasonings.John Venn - 1880 - Philosophical Magazine 9 (59):1-18.
    Schemes of diagrammatic representation have been so familiarly introduced into logical treatises during the last century or so, that many readers, even of those who have made no professional study of logic, may be supposed to be acquainted with the general nature and object of such devices. Of these schemes one only, viz. that commonly called "Eulerian circles," has met with any general acceptance. A variety of others indeed have been proposed by ingenious and celebrated logicians, several of which would (...)
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  • The structure of multiplicatives.Vincent Danos & Laurent Regnier - 1989 - Archive for Mathematical Logic 28 (3):181-203.
    Investigating Girard's new propositionnal calculus which aims at a large scale study of computation, we stumble quickly on that question: What is a multiplicative connective? We give here a detailed answer together with our motivations and expectations.
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  • The Iconic Logic of Peirce's Graphs.Sun-joo Shin - 2003 - Transactions of the Charles S. Peirce Society 39 (1):127-133.
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  • Linear logic: its syntax and semantics.Jean-Yves Girard - 1995 - In Jean-Yves Girard, Yves Lafont & Laurent Regnier (eds.), Advances in linear logic. New York, NY, USA: Cambridge University Press. pp. 222--1.
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  • The Iconic Logic of Peirce's Graphs.Jesse Norman - 2004 - Mind 113 (452):783-787.
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  • Euler’s visual logic.Eric Hammer & Sun-Joo Shin - 1998 - History and Philosophy of Logic 19 (1):1-29.
    The evolution of Euler diagrams is examined from Euler's original system through the modifications made by Venn and Peirce. It is shown that these modifications were motivated by an attempt to increase the expressivity of the diagrams, but that a side effect of these modifications was a loss of the visual clarity of Euler's original system. Euler's original system is reconstructed from a modern, logical point of view. Formal semantics and rules of inference are provided for this reconstruction of Euler's (...)
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  • Reasoning with Sentences and Diagrams.Eric Hammer - 1994 - Notre Dame Journal of Formal Logic 35 (1):73-87.
    A formal system is studied having both sentences and diagrams as well-formed representations. Proofs in the system allow inference back and forth between sentences and diagrams, as well as between diagrams and diagrams, and between sentences and sentences. This sort of heterogeneous system is of interest because external representations other than linguistic ones occur commonly in actual reasoning in conjunction with language. Syntax, semantics, and rules of inference for the system are given and it is shown to be sound and (...)
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  • A Diagrammatic Inference System with Euler Circles.Koji Mineshima, Mitsuhiro Okada & Ryo Takemura - 2012 - Journal of Logic, Language and Information 21 (3):365-391.
    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 regions as in (...)
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  • On the Insufficiency of Linear Diagrams for Syllogisms.Oliver Lemon & Ian Pratt - 1998 - Notre Dame Journal of Formal Logic 39 (4):573-580.
    In Volume 33:1 of the Notre Dame Journal of Formal Logic, a system for diagramming syllogistic inferences using straight line segments is presented by Englebretsen. In light of recent research on the representational power of diagrammatic representation systems by the authors, we point out some problems with the proposal, and indeed, with any proposal for representing logically possible situations diagrammatically. We shall first outline the proposed linear diagrammatic system of Englebretsen, and then show by means of counterexamples that it is (...)
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  • Linear diagrams for syllogisms (with relationals).George Englebretsen - 1991 - Notre Dame Journal of Formal Logic 33 (1):37-69.
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  • (1 other version)A Diagrammatic Calculus of Syllogisms.Ruggero Pagnan - 2012 - Journal of Logic, Language and Information 21 (3):347-364.
    A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid if and only if it is provable in the calculus.
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  • Situation-theoretic account of valid reasoning with Venn diagrams.Sun-Joo Shin - 1996 - In Gerard Allwein & Jon Barwise (eds.), Logical reasoning with diagrams. New York: Oxford University Press.
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  • Towards a model theory of diagrams.Hammer Eric & Danner Norman - 1996 - Journal of Philosophical Logic 25 (5):463 - 482.
    A logical system is studied whose well-formed representations consist of diagrams rather than formulas. The system, due to Shin [2, 3], is shown to be complete by an argument concerning maximally consistent sets of diagrams. The argument is complicated by the lack of a straight forward counterpart of atomic formulas for diagrams, and by the lack of a counterpart of negation for most diagrams.
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  • A diagrammatic treatment of syllogistic.M. B. Smyth - 1971 - Notre Dame Journal of Formal Logic 12 (4):483-488.
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  • Review of Sun-Joo Shin: The Logical Status of Diagrams[REVIEW]Sun-joo Shin - 1997 - British Journal for the Philosophy of Science 48 (2):290-291.
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  • Struktura poprawnych trybów sylogizmun-terminowego.Krystyna Głazowska - 1958 - Studia Logica 8 (1):249 - 257.
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  • The structure of validn-term syllogisms.K. Głazowska - 1958 - Studia Logica 8 (1):257-257.
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  • A case study of the design and implementation of heterogeneous reasoning systems.Nik Swoboda & Gerard Allwein - 2002 - In L. Magnani, N. J. Nersessian & C. Pizzi (eds.), Logical and Computational Aspects of Model-Based Reasoning. Kluwer Academic Publishers. pp. 3--20.
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