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Author: Sun-Joo Shin
Publisher: Cambridge University Press
ISBN: 052146157X
Category : Mathematics
Languages : en
Pages : 211
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Book Description
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.
Author: Sun-Joo Shin
Publisher: Cambridge University Press
ISBN: 052146157X
Category : Mathematics
Languages : en
Pages : 211
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Book Description
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.
Author: Amirouche Moktefi
Publisher: Springer Science & Business Media
ISBN: 3034806000
Category : Mathematics
Languages : en
Pages : 210
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Book Description
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.
Author: Gerard Allwein
Publisher: Oxford University Press, USA
ISBN: 0195104277
Category : Knowledge representation (Information theory).
Languages : en
Pages : 287
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Book Description
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
Author: Sun-Joo Shin
Publisher: MIT Press
ISBN: 9780262194709
Category : Mathematics
Languages : en
Pages : 228
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Book Description
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.
Author: A. W. F. Edwards
Publisher: JHU Press
ISBN: 9780801874345
Category : Mathematics
Languages : en
Pages : 134
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Book Description
For anyone interested in mathematics or its history, Cogwheels of the Mind is invaluable and compelling reading.
Author: Marcus Giaquinto
Publisher: Oxford University Press
ISBN: 0199285942
Category : Mathematics
Languages : en
Pages : 298
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Book Description
Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis.
Author: Alan F. Blackwell
Publisher: Springer Science & Business Media
ISBN: 9401735247
Category : Computers
Languages : en
Pages : 170
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Book Description
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.
Author: Markus Knauff
Publisher: MIT Press
ISBN: 0262045079
Category : Psychology
Languages : en
Pages : 879
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Book Description
The first reference on rationality that integrates accounts from psychology and philosophy, covering descriptive and normative theories from both disciplines. Both analytic philosophy and cognitive psychology have made dramatic advances in understanding rationality, but there has been little interaction between the disciplines. This volume offers the first integrated overview of the state of the art in the psychology and philosophy of rationality. Written by leading experts from both disciplines, The Handbook of Rationality covers the main normative and descriptive theories of rationality—how people ought to think, how they actually think, and why we often deviate from what we can call rational. It also offers insights from other fields such as artificial intelligence, economics, the social sciences, and cognitive neuroscience. The Handbook proposes a novel classification system for researchers in human rationality, and it creates new connections between rationality research in philosophy, psychology, and other disciplines. Following the basic distinction between theoretical and practical rationality, the book first considers the theoretical side, including normative and descriptive theories of logical, probabilistic, causal, and defeasible reasoning. It then turns to the practical side, discussing topics such as decision making, bounded rationality, game theory, deontic and legal reasoning, and the relation between rationality and morality. Finally, it covers topics that arise in both theoretical and practical rationality, including visual and spatial thinking, scientific rationality, how children learn to reason rationally, and the connection between intelligence and rationality.
Author: Dave Barker-Plummer
Publisher: Center for the Study of Language and Information Publica Tion
ISBN: 9781575869513
Category : LANGUAGE ARTS & DISCIPLINES
Languages : en
Pages : 0
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Book Description
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.
Author: Sybille Krämer
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 1501503758
Category : Language Arts & Disciplines
Languages : en
Pages : 254
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Book Description
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.
