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.
Thinking With Diagrams
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Author : Alan F. Blackwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
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 2013-04-18 with Computers 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.
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.
Hyperproof
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Author : Jon Barwise
language : en
Publisher: Center for the Study of Language and Information Publications
Release Date : 1995-01-01
Hyperproof written by Jon Barwise 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 1995-01-01 with Mathematics categories.
Hyperproof is a system for learning the principles of analytical reasoning and proof construction, consisting of a text and a Macintosh software program. Unlike traditional treatments of first-order logic, Hyperproof combines graphical and sentential information, presenting a set of logical rules for integrating these different forms of information. This strategy allows students to focus on the information content of proofs, rather than the syntactic structure of sentences. Using Hyperproof the student learns to construct proofs of both consequence and nonconsequence using an intuitive proof system that extends the standard set of sentential rules to incorporate information represented graphically. Hyperproof is compatible with various natural-deduction-style proof systems, including the system used in the authors' Language of First-Order Logic.
Thinking With Diagrams
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Author : Sybille Krämer
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-07-11
Thinking With Diagrams written by Sybille Krämer 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 2016-07-11 with Language Arts & Disciplines categories.
Diagrammatic reasoning is crucial for human cognition. It is hard to think of any forms of science or knowledge without the "intermediary world" of diagrams and diagrammatic representation in thought experiments and/or processes, manifested in forms as divers as notes, tables, schemata, graphs, drawings and maps. Despite their phenomenological and structural-functional differences, these forms of representation share a number of important attributes and epistemic functions. Combining aspects of linguistic and pictorial symbolism, diagrams go beyond the traditional distinction between language and image. They do not only represent, yet intervene in what is represented. Their spatiality, materiality and operativity establish a dynamic tool to exteriorize thinking, thus contributing to the idea of the extended mind. They foster imagination and problem solving, facilitate orientation in knowledge spaces and the discovery of unsuspected relationships. How can the diagrammatic nature of cognitive and knowledge practices be theorized historically as well as systematically? This is what this volume explores by investigating the semiotic dimension of diagrams as to knowledge, information and reasoning, e.g., the 'thing-ness' of diagrams in the history of art, the range of diagrammatic reasoning in logic, mathematics, philosophy and the sciences in general, including the knowledge function of maps.
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.
Visual Reasoning With Diagrams
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Author : Amirouche Moktefi
language : en
Publisher: Birkhäuser
Release Date : 2013-11-27
Visual Reasoning With Diagrams written by Amirouche Moktefi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 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.
Logic As A Tool
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Author : Valentin Goranko
language : en
Publisher: John Wiley & Sons
Release Date : 2016-10-17
Logic As A Tool written by Valentin Goranko and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-17 with Mathematics categories.
Written in a clear, precise and user-friendly style, Logic as a Tool: A Guide to Formal Logical Reasoning is intended for undergraduates in both mathematics and computer science, and will guide them to learn, understand and master the use of classical logic as a tool for doing correct reasoning. It offers a systematic and precise exposition of classical logic with many examples and exercises, and only the necessary minimum of theory. The book explains the grammar, semantics and use of classical logical languages and teaches the reader how grasp the meaning and translate them to and from natural language. It illustrates with extensive examples the use of the most popular deductive systems -- axiomatic systems, semantic tableaux, natural deduction, and resolution -- for formalising and automating logical reasoning both on propositional and on first-order level, and provides the reader with technical skills needed for practical derivations in them. Systematic guidelines are offered on how to perform logically correct and well-structured reasoning using these deductive systems and the reasoning techniques that they employ. Concise and systematic exposition, with semi-formal but rigorous treatment of the minimum necessary theory, amply illustrated with examples Emphasis both on conceptual understanding and on developing practical skills Solid and balanced coverage of syntactic, semantic, and deductive aspects of logic Includes extensive sets of exercises, many of them provided with solutions or answers Supplemented by a website including detailed slides, additional exercises and solutions For more information browse the book's website at: https://logicasatool.wordpress.com