Logical Reasoning With Diagrams
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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.
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 Sentences
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Author : Dave Barker-Plummer
language : en
Publisher: Center for the Study of Language and Information Publica Tion
Release Date : 2017
Logical Reasoning With Diagrams Sentences written by Dave Barker-Plummer 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 2017 with LANGUAGE ARTS & DISCIPLINES categories.
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.
Figuring It Out
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Author : George Englebretsen
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-11-18
Figuring It Out written by George Englebretsen and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-18 with Philosophy categories.
The book begins with an extensive survey of the history of logic diagrams, including looking at possible diagrams from Aristotle, the development of both linear and closed figure diagrams by Leibniz, Lambert, Euler, Venn’s new system, Peirce’s Existential Graphs, and Frege’s two-dimensional notation as a kind of logic diagram system. During most of the 20th century, there was little regard for efforts to construct logic diagrams. However, since the 1980s there has been an increasing interest in such diagrams. Ever larger numbers of philosophers, logicians, mathematicians, computational scientists, and cognitive scientists have turned their attention to building, analyzing, using, or exploring in other ways systems of logic diagrams. The system offered here makes use of line segments and points and it enjoys a number of important advantages: it is simple, natural, and both expressively and inferentially powerful. It can be used to analyze syllogisms (including those involving relational terms) and arguments involving unanalyzed statements. Understanding such a system can shed valuable light on how ordinary people naturally reason.
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.
Mathematical Reasoning With Diagrams
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Author : Mateja Jamnik
language : en
Publisher: Stanford Univ Center for the Study
Release Date : 2001-01
Mathematical Reasoning With Diagrams written by Mateja Jamnik and has been published by Stanford Univ Center for the Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01 with Mathematics categories.
Mathematicians at every level use diagrams to prove theorems. Mathematical Reasoning with Diagrams investigates the possibilities of mechanizing this sort of diagrammatic reasoning in a formal computer proof system, even offering a semi-automatic formal proof system—called Diamond—which allows users to prove arithmetical theorems using diagrams.
Logical And Computational Aspects Of Model Based Reasoning
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Author : L. Magnani
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Logical And Computational Aspects Of Model Based Reasoning written by L. Magnani 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 2012-12-06 with Mathematics categories.
Information technology has been, in recent years, under increasing commercial pressure to provide devices and systems which help/ replace the human in his daily activity. This pressure requires the use of logic as the underlying foundational workhorse of the area. New logics were developed as the need arose and new foci and balance has evolved within logic itself. One aspect of these new trends in logic is the rising impor tance of model based reasoning. Logics have become more and more tailored to applications and their reasoning has become more and more application dependent. In fact, some years ago, I myself coined the phrase "direct deductive reasoning in application areas", advocating the methodology of model-based reasoning in the strongest possible terms. Certainly my discipline of Labelled Deductive Systems allows to bring "pieces" of the application areas as "labels" into the logic. I therefore heartily welcome this important book to Volume 25 of the Applied Logic Series and see it as an important contribution in our overall coverage of applied logic.
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 Inference
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Author : Peter Chapman
language : en
Publisher: Springer
Release Date : 2018-06-07
Diagrammatic Representation And Inference written by Peter Chapman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Computers categories.
This book constitutes the refereed proceedings of the 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018, held in Edinburgh, UK, in June 2018. The 26 revised full papers and 28 short papers presented together with 32 posters were carefully reviewed and selected from 124 submissions. The papers are organized in the following topical sections: generating and drawing Euler diagrams; diagrams in mathematics; diagram design, principles and classification; reasoning with diagrams; Euler and Venn diagrams; empirical studies and cognition; Peirce and existential graphs; and logic and diagrams.
Thinking With Diagrams
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Author : Alan F. Blackwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-04-30
Thinking With Diagrams written by Alan F. Blackwell 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 2001-04-30 with Art categories.
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.