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Logical Reasoning with Diagrams

Logical Reasoning with Diagrams
Author: Gerard Allwein
Publisher: Oxford University Press
Total Pages: 287
Release: 1996-06-13
Genre: Computers
ISBN: 0195355865

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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

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

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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

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

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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.


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

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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


Logical Reasoning

Logical Reasoning
Author: Bradley Harris Dowden
Publisher: Bradley Dowden
Total Pages: 516
Release: 1993
Genre: Critical thinking
ISBN: 9780534176884

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This book is designed to engage students' interest and promote their writing abilities while teaching them to think critically and creatively. Dowden takes an activist stance on critical thinking, asking students to create and revise arguments rather than simply recognizing and criticizing them. His book emphasizes inductive reasoning and the analysis of individual claims in the beginning, leaving deductive arguments for consideration later in the course.


Figuring It Out

Figuring It Out
Author: George Englebretsen
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 240
Release: 2019-11-18
Genre: Philosophy
ISBN: 3110621843

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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.


Logic Machines and Diagrams

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

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


Mathematical Reasoning with Diagrams

Mathematical Reasoning with Diagrams
Author: Mateja Jamnik
Publisher: Stanford Univ Center for the Study
Total Pages: 204
Release: 2001-01
Genre: Mathematics
ISBN: 9781575863245

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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.


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

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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.


Elements of Logical Reasoning

Elements of Logical Reasoning
Author: Jan von Plato
Publisher: Cambridge University Press
Total Pages: 275
Release: 2014-01-23
Genre: Mathematics
ISBN: 1139867768

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Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premises have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind it remain intuitive. Jan von Plato provides an accessible but rigorous introduction to an important aspect of contemporary logic: its deductive machinery. He shows that when the forms of logical reasoning are analysed, it turns out that a limited set of first principles can represent any logical argument. His book will be valuable for students of logic, mathematics and computer science.