The Logical Status of Diagrams

The Logical Status of Diagrams
Author: Sun-Joo Shin
Publisher: Cambridge University Press
Total Pages: 211
Release: 1994
Genre: Mathematics
ISBN: 052146157X

The validity of the transformation rules ensures that the correct application of the rules will not lead to fallacies. The book concludes with a discussion of some fundamental differences between graphical systems and linguistic systems.

Logical Reasoning with Diagrams

Logical Reasoning with Diagrams
Author: Gerard Allwein
Publisher: Oxford University Press, USA
Total Pages: 287
Release: 1996
Genre: Knowledge representation (Information theory).
ISBN: 0195104277

Information technology has lead to an increasing need to present information visually. This volume addresses the logical aspects of the visualization of information. Properties of diagrams, charts and maps are explored and their use in problem solving and

Visual Reasoning with Diagrams

Visual Reasoning with Diagrams
Author: Amirouche Moktefi
Publisher: Springer Science & Business Media
Total Pages: 210
Release: 2013-07-08
Genre: Mathematics
ISBN: 3034806000

Logic, the discipline that explores valid reasoning, does not need to be limited to a specific form of representation but should include any form as long as it allows us to draw sound conclusions from given information. The use of diagrams has a long but unequal history in logic: The golden age of diagrammatic logic of the 19th century thanks to Euler and Venn diagrams was followed by the early 20th century's symbolization of modern logic by Frege and Russell. Recently, we have been witnessing a revival of interest in diagrams from various disciplines - mathematics, logic, philosophy, cognitive science, and computer science. This book aims to provide a space for this newly debated topic - the logical status of diagrams - in order to advance the goal of universal logic by exploring common and/or unique features of visual reasoning.

The Iconic Logic of Peirce's Graphs

The Iconic Logic of Peirce's Graphs
Author: Sun-Joo Shin
Publisher: MIT Press
Total Pages: 228
Release: 2002
Genre: Mathematics
ISBN: 9780262194709

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 Existential Graphs. At the dawn of modern logic, Charles S. Peirce invented two types of logical systems, one symbolic and the other graphical. In this book Sun-Joo Shin explores the philosophical roots of the birth of Peirce's Existential Graphs in his theory of representation and logical notation. Shin demonstrates that Peirce is the first philosopher to lay a solid philosophical foundation for multimodal representation systems. Shin analyzes Peirce's well-known, but much-criticized nonsymbolic representation system. She presents a new approach to his graphical system based on her discovery of its unique nature and on a reconstruction of Peirce's theory of representation. By seeking to understand graphical systems on their own terms, she uncovers the reasons why graphical systems, and Existential Graphs in particular, have been underappreciated among logicians. Drawing on perspectives from the philosophy of mind, cognitive science, logic, and computer science, Shin provides evidence for a genuinely interdisciplinary project on multimodal reasoning.

Cogwheels of the Mind

Cogwheels of the Mind
Author: A. W. F. Edwards
Publisher: JHU Press
Total Pages: 134
Release: 2004-05-10
Genre: Mathematics
ISBN: 9780801874345

For anyone interested in mathematics or its history, Cogwheels of the Mind is invaluable and compelling reading.

Logical Reasoning with Diagrams & Sentences

Logical Reasoning with Diagrams & Sentences
Author: Dave Barker-Plummer
Publisher: Center for the Study of Language and Information Publica Tion
Total Pages: 0
Release: 2017
Genre: LANGUAGE ARTS & DISCIPLINES
ISBN: 9781575869513

The Logical Reasoning with Diagrams and Sentences courseware package teaches the principles of analytical reasoning and proof construction using a carefully crafted combination of textbook, desktop, and online materials. This package is sure to be an essential resource in a range of courses incorporating logical reasoning, including formal linguistics, philosophy, mathematics, and computer science. Unlike traditional formal treatments of reasoning, this package uses both graphical and sentential representations to reflect common situations in everyday reasoning where information is expressed in many forms, such as finding your way to a location using a map and an address. It also teaches students how to construct and check the logical validity of a variety of proofs--of consequence and non-consequence, consistency and inconsistency, and independence--using an intuitive proof system which extends standard proof treatments with sentential, graphical, and heterogeneous inference rules, allowing students to focus on proof content rather than syntactic structure. Building upon the widely used Tarski's World and Language, Proof and Logic courseware packages, Logical Reasoning with Diagrams and Sentences contains more than three hundred exercises, most of which can be assessed by the Grade Grinder online assessment service; is supported by an extensive website through which students and instructors can access online video lectures by the authors; and allows instructors to create their own exercises and assess their students' work. Logical Reasoning with Diagrams and Sentences is an expanded revision of the Hyperproof courseware package.

The Concept of Relevance and the Logic Diagram Tradition

The Concept of Relevance and the Logic Diagram Tradition
Author: Jan Dejnožka
Publisher:
Total Pages: 0
Release: 2012
Genre: Logic, Modern
ISBN: 9781475071092

PRAISE FOR THE BOOK:"Dejnozka's erudition continues to astound me." - Nicholas Griffin.As Canada Research Chair and Director of the Bertrand Russell Research Centre at McMaster University, Professor Griffin directs the editing of the ongoing editions of The Collected Papers of Bertrand Russell, currently at 16 volumes. He also edited The Cambridge Companion to Bertrand Russell, and has written several books and articles."Dejnozka challenges the reader to open his mind for a new interpretation of Russell's work, in particular that relevance notions have a greater place in his philosophy of logic than has been stressed before. Dejnozka's work is full of material which stimulates one to rethink Russell's philosophy of logic, and it is greatly to the author's credit that he brings to light such a wealth of crucial issues in the history and philosophy of logic." - Shahid Rahman.Professor Rahman teaches at the Université de Lille (France). He has served as dean and supervised many dissertations. He is the author of several books and the editor of several anthologies in logic and the philosophy of logic. He recently edited a book on Hugh MacColl. He has also written many articles and reviews, and read papers at various congresses.PUBLISHED REVIEW:"Dejnozka's defense of his view is well articulated and strongly supported by citing thinkers of the caliber of Quine, Russell and Wittgenstein, among others. Moreover, the defense is presented in a clear and explicit way, making evident the role played by relevance logic and diagrams.... Finally, a very positive aspect is the presence of many explanatory notes, placed at the end of the book, that shed light on the discussion in the text." Edgar L. B. Almeida, Logic and Logical Philosophy (2013).PUBLISHED REVIEW:"The main argument of the book is interesting for suggesting that truth ground containment, i.e. the classical notion of consequence, embodies a meaningful notion of a connection between the assumptions and the conclusion of a valid argument.... I do think that the book's main claims hold.... Yes, classical validity can be seen as involving a...notion of containment - containment of truth grounds. Yes, this notion can be found in the writings of outstanding modern classical logicians such as Wittgenstein or Russell. Yes, the relevantist's notion of relevance...can be seen as a species of a broader genus. Perhaps the greatest merit of the present book is that it emphasizes these points explicitly." Igor Sedlár, Organon F (2014).BOOK DESCRIPTION:In the first volume of their monumental work, Entailment, Alan Ross Anderson and Nuel D. 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. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and Quine are implicit relevantists on the deepest level. In showing this, I reunite two fields of logic which have become basically separated from each other: relevance logic and diagram logic. I argue that there are two main concepts of relevance, intensional and extensional. The first is that of the relevantists. The second is the concept of truth-ground containment as following from in Wittgenstein's Tractatus. I show that this second concept belongs to the diagram tradition of showing that the premisses contain the conclusion by the fact that the conclusion is diagrammed in the very act of diagramming the premisses. I argue that the extensional concept is primary, with at least five usable modern classical filters or constraints, and indefinitely many secondary intensional filters or constraints. In this way, I argue for a major reunion of purpose in logic between relevantists and modern classical logicians.

Thinking with Diagrams

Thinking with Diagrams
Author: Alan F. Blackwell
Publisher: Springer Science & Business Media
Total Pages: 170
Release: 2013-04-18
Genre: Computers
ISBN: 9401735247

This book provides an introductory overview of the rapid growth in interdisciplinary research into Thinking with Diagrams. Diagrammatic representations are becoming more common in everyday human experience, yet they offer unique challenges to cognitive science research. Neither linguistic nor perceptual theories are sufficient to completely explain their advantages and applications. These research challenges may be part of the reason why so many diagrams are badly designed or badly used. This is ironic when the user interfaces of computer software and the worldwide web are becoming so completely dominated by graphical and diagrammatic representations. This book includes chapters commissioned from leading researchers in the major disciplines involved in diagrams research. They review the philosophical status of diagrams, the cognitive processes involved in their application, and a range of specialist fields in which diagrams are central, including education, architectural design and visual programming languages. The result is immediately relevant to researchers in cognitive science and artificial intelligence, as well as in applied technology areas such as human-computer interaction and information design.

Logic Machines and Diagrams

Logic Machines and Diagrams
Author: Martin Gardner
Publisher:
Total Pages: 165
Release: 1982
Genre: Philosophy
ISBN: 9780226282442

Traces the development of logic machines from diagrams of logical statements to modern computers and discusses the fundamentals of mathematical logic