Visual Reasoning With Diagrams
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Visual Reasoning With Diagrams
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Author : Amirouche Moktefi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-08
Visual Reasoning With Diagrams written by Amirouche Moktefi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-08 with Mathematics categories.
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.
Logical Reasoning With Diagrams
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Author : Gerard Allwein
language : en
Publisher: Oxford University Press
Release Date : 1996-06-13
Logical Reasoning With Diagrams written by Gerard Allwein and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-13 with Computers categories.
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 the properties of diagrams, charts, and maps, and their use in problem solving and teaching basic reasoning skills. As computers make visual representations more commonplace, it is important for professionals, researchers and students in computer science, philosophy, and logic to develop an understanding of these tools; this book can clarify the relationship between visuals and information.
After Euclid
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Author : Jesse Norman
language : en
Publisher: Center for the Study of Language and Information Publica Tion
Release Date : 2006
After Euclid written by Jesse Norman and has been published by Center for the Study of Language and Information Publica Tion this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
What does it mean to have visual intuition? Can we gain geometrical knowledge by using visual reasoning? And if we can, is it because we have a faculty of intuition? In After Euclid, Jesse Norman reexamines the ancient and long-disregarded concept of visual reasoning and reasserts its potential as a formidable tool in our ability to grasp various kinds of geometrical knowledge. The first detailed philosophical case study of its kind, this text is essential reading for scholars in the fields of mathematics and philosophy.
Diagrammatic Reasoning
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Author : B. Chandrasekaran
language : en
Publisher: Menlo Park, Calif. : AAAI Press
Release Date : 1995
Diagrammatic Reasoning written by B. Chandrasekaran and has been published by Menlo Park, Calif. : AAAI Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Computers categories.
foreword by Herbert Simon Diagrammatic reasoning -- the understanding of concepts and ideas by the use of diagrams and imagery, as opposed to linguistic or algebraic representations -- not only allows us to gain insight into the way we think, but is a potential base for constructing representations of diagrammatic information that can be stored and processed by computers.Diagrammatic Reasoning brings together recent investigations into the cognitive, the logical, and particularly the computational characteristics of diagrammatic representations and the reasoning that can be done with them. Following a foreword by Herbert Simon and an introduction by the editors, twenty-seven chapters provide an overview of the recent history of the subject, survey and extend the underlying theory of diagrammatic representation, and provide numerous examples of diagrammatic reasoning (human and mechanical) that illustrate both its powers and its limitations.Each of the book's four sections (Historical and Philosophical Background, Theoretical Foundations, Cognitive and Computational Models, and Problem Solving with Diagrams) begins with an introduction by an eminent researcher. These introductions provide interesting personal perspectives as well as place the work in the proper context.Distributed for AAAI Press
Visual And Spatial Analysis
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Author : Boris Kovalerchuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-06
Visual And Spatial Analysis written by Boris Kovalerchuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-06 with Computers categories.
Advanced visual analysis and problem solving has been conducted successfully for millennia. The Pythagorean Theorem was proven using visual means more than 2000 years ago. In the 19th century, John Snow stopped a cholera epidemic in London by proposing that a specific water pump be shut down. He discovered that pump by visually correlating data on a city map. The goal of this book is to present the current trends in visual and spatial analysis for data mining, reasoning, problem solving and decision-making. This is the first book to focus on visual decision making and problem solving in general with specific applications in the geospatial domain - combining theory with real-world practice. The book is unique in its integration of modern symbolic and visual approaches to decision making and problem solving. As such, it ties together much of the monograph and textbook literature in these emerging areas. This book contains 21 chapters that have been grouped into five parts: (1) visual problem solving and decision making, (2) visual and heterogeneous reasoning, (3) visual correlation, (4) visual and spatial data mining, and (5) visual and spatial problem solving in geospatial domains. Each chapter ends with a summary and exercises. The book is intended for professionals and graduate students in computer science, applied mathematics, imaging science and Geospatial Information Systems (GIS). In addition to being a state-of-the-art research compilation, this book can be used a text for advanced courses on the subjects such as modeling, computer graphics, visualization, image processing, data mining, GIS, and algorithm analysis.
Logic And Visual Information
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Author : Eric Hammer
language : en
Publisher: Center for the Study of Language and Information Publications
Release Date : 1995-10-27
Logic And Visual Information written by Eric Hammer and has been published by Center for the Study of Language and Information Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-27 with Mathematics categories.
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 computation. 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, Peirce diagrams, and a system having both diagrams and sentences among its well-formed representations. Syntax, semantics, rules of inference, and soundness and completeness results are provided for each of the systems. In addition to developing the logic of diagrams, key questions about the status of visual information are discussed, such as the relationship between language and visually-presented information.
Diagrammatic Representation And Reasoning
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Author : Michael Anderson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27
Diagrammatic Representation And Reasoning written by Michael Anderson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-27 with Mathematics categories.
The rise in computing and multimedia technology has spawned an increasing interest in the role of diagrams and sketches, not only for the purpose of conveying information but also for creative thinking and problem-solving. This book attempts to characterise the nature of "a science of diagrams" in a wide-ranging, multidisciplinary study that contains accounts of the most recent research results in computer science and psychology. Key topics include: cognitive aspects, formal aspects, and applications. It is a well-written and indispensable survey for researchers and students in the fields of cognitive science, artificial intelligence, human-computer interaction, and graphics and visualisation.
The Logical Status Of Diagrams
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Author : Sun-Joo Shin
language : en
Publisher: Cambridge University Press
Release Date : 1994
The Logical Status Of Diagrams written by Sun-Joo Shin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
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.
Diagrams Visual Imagination And Continuity In Peirce S Philosophy Of Mathematics
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Author : Vitaly Kiryushchenko
language : en
Publisher: Springer Nature
Release Date : 2023-05-12
Diagrams Visual Imagination And Continuity In Peirce S Philosophy Of Mathematics written by Vitaly Kiryushchenko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-12 with Mathematics categories.
This book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce’s mathematical philosophy. It presents mathematics as a science that presupposes a special imaginative connection between our responsiveness to reasons and our most fundamental perceptual intuitions about space and time. Central to this view on the nature of mathematics is Peirce’s idea of diagrammatic reasoning. In practicing this kind of reasoning, one treats diagrams not simply as external auxiliary tools, but rather as immediate visualizations of the very process of the reasoning itself. Thus conceived, one's capacity to diagram their thought reveals a set of characteristics common to ordinary language, visual perception, and necessary mathematical reasoning. The book offers an original synthetic approach that allows tracing the roots of Peirce’s conception of a diagram in certain patterns of interrelation between his semiotics, his pragmaticist philosophy, his logical and mathematical ideas, bits and pieces of his biography, his personal intellectual predispositions, and his scientific practice as an applied mathematician.
Data Representations Transformations And Statistics For Visual Reasoning
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Author : Ross Maciejewski
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Data Representations Transformations And Statistics For Visual Reasoning written by Ross Maciejewski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Mathematics categories.
Analytical reasoning techniques are methods by which users explore their data to obtain insight and knowledge that can directly support situational awareness and decision making. Recently, the analytical reasoning process has been augmented through the use of interactive visual representations and tools which utilize cognitive, design and perceptual principles. These tools are commonly referred to as visual analytics tools, and the underlying methods and principles have roots in a variety of disciplines. This chapter provides an introduction to young researchers as an overview of common visual representations and statistical analysis methods utilized in a variety of visual analytics systems. The application and design of visualization and analytical algorithms are subject to design decisions, parameter choices, and many conflicting requirements. As such, this chapter attempts to provide an initial set of guidelines for the creation of the visual representation, including pitfalls and areas where the graphics can be enhanced through interactive exploration. Basic analytical methods are explored as a means of enhancing the visual analysis process, moving from visual analysis to visual analytics. Table of Contents: Data Types / Color Schemes / Data Preconditioning / Visual Representations and Analysis / Summary