logical reasoning with diagrams studies in logic and computation

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Logical Reasoning With Diagrams

Author : Gerard Allwein
ISBN : 0195355865
Genre : Computers
File Size : 32. 47 MB
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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

Author : Amirouche Moktefi
ISBN : 9783034806008
Genre : Mathematics
File Size : 73. 94 MB
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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.

Computational Logic

Author : Dov M. Gabbay
ISBN : 9780080930671
Genre : Mathematics
File Size : 28. 59 MB
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Handbook of the History of Logic brings to the development of logic the best in modern techniques of historical and interpretative scholarship. Computational logic was born in the twentieth century and evolved in close symbiosis with the advent of the first electronic computers and the growing importance of computer science, informatics and artificial intelligence. With more than ten thousand people working in research and development of logic and logic-related methods, with several dozen international conferences and several times as many workshops addressing the growing richness and diversity of the field, and with the foundational role and importance these methods now assume in mathematics, computer science, artificial intelligence, cognitive science, linguistics, law and many engineering fields where logic-related techniques are used inter alia to state and settle correctness issues, the field has diversified in ways that even the pure logicians working in the early decades of the twentieth century could have hardly anticipated. Logical calculi, which capture an important aspect of human thought, are now amenable to investigation with mathematical rigour and computational support and fertilized the early dreams of mechanised reasoning: “Calculemus . The Dartmouth Conference in 1956 – generally considered as the birthplace of artificial intelligence – raised explicitly the hopes for the new possibilities that the advent of electronic computing machinery offered: logical statements could now be executed on a machine with all the far-reaching consequences that ultimately led to logic programming, deduction systems for mathematics and engineering, logical design and verification of computer software and hardware, deductive databases and software synthesis as well as logical techniques for analysis in the field of mechanical engineering. This volume covers some of the main subareas of computational logic and its applications. Chapters by leading authorities in the field Provides a forum where philosophers and scientists interact Comprehensive reference source on the history of logic

Logical Reasoning With Diagrams And Sentences

Author : David Barker-Plummer
ISBN : 1575869519
Genre : Language Arts & Disciplines
File Size : 90. 60 MB
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The Hyperproof courseware package teaches the principles of analytical reasoning and proof construction using a carefully crafted combination of a textbook, desktop applications and online materials. Unlike traditional formal treatments of reasoning, the Hyperproof approach uses both graphical and sentential representations of information. This reflects common situations in everyday reasoning which involve information expressed in many forms, such as finding your way to a location using a map and an address, or interpreting a newspaper story involving both text and a graphic. Using Hyperproof the student learns to construct proofs of both consequence and non-consequence using an intuitive proof system which extends standard treatments of proof with sentential, graphical and heterogeneous inference rules. The approach allows students to focus on the content of proofs, rather than on the syntactic structure of formal sentences. Proofs of consistency and inconsistency as well as independence proofs may also be constructed in the system. The desktop application can be used to check the logical validity of all of the different types of proof. The Hyperproof courseware package contains more than 300 exercises, of which more than 250 can assessed by the Grade Grinder online assessment service. The courseware is supported by an extensive web site through which students and instructors can access online video lectures by the authors. Instructors also have the ability to create their own exercises for assessment and access to assessments of the work submitted by their students. Hyperproof builds on the Tarski s World and Language, Proof and Logic courseware packages from the same authors. The material in these packages can be combined to create a variety of different courses, or incorporate as engaging components of courses that teach logical reasoning, including formal linguistics, philosophy, mathematics, and computer science. "

Mathematical Logic For Computer Science

Author : Mordechai Ben-Ari
ISBN : 9781447141297
Genre : Mathematics
File Size : 46. 8 MB
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Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and easy to understand. The uniform use of tableaux-based techniques facilitates learning advanced logical systems based on what the student has learned from elementary systems. The logical systems presented are: propositional logic, first-order logic, resolution and its application to logic programming, Hoare logic for the verification of sequential programs, and linear temporal logic for the verification of concurrent programs. The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking.

Boolean Reasoning

Author : Frank Markham Brown
ISBN : 0486427854
Genre : Mathematics
File Size : 51. 39 MB
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A systematic treatment of Boolean reasoning, this concise, newly revised edition combines the works of early logicians with recent investigations, including previously unpublished research results. Brown begins with an overview of elementary mathematical concepts and outlines the theory of Boolean algebras. Two concluding chapters deal with applications. 1990 edition.

Logic In Computer Science

Author : Michael Huth
ISBN : 9781139453059
Genre : Computers
File Size : 66. 66 MB
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Recent years have seen the development of powerful tools for verifying hardware and software systems, as companies worldwide realise the need for improved means of validating their products. There is increasing demand for training in basic methods in formal reasoning so that students can gain proficiency in logic-based verification methods. The second edition of this successful textbook addresses both those requirements, by continuing to provide a clear introduction to formal reasoning which is both relevant to the needs of modern computer science and rigorous enough for practical application. Improvements to the first edition have been made throughout, with extra and expanded sections on SAT solvers, existential/universal second-order logic, micro-models, programming by contract and total correctness. The coverage of model-checking has been substantially updated. Further exercises have been added. Internet support for the book includes worked solutions for all exercises for teachers, and model solutions to some exercises for students.

Hyperproof

Author : Jon Barwise
ISBN : 1881526119
Genre : Mathematics
File Size : 30. 18 MB
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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.

Computational Logic And Human Thinking

Author : Robert Kowalski
ISBN : 9781139498159
Genre : Computers
File Size : 84. 26 MB
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The practical benefits of computational logic need not be limited to mathematics and computing. As this book shows, ordinary people in their everyday lives can profit from the recent advances that have been developed for artificial intelligence. The book draws upon related developments in various fields from philosophy to psychology and law. It pays special attention to the integration of logic with decision theory, and the use of logic to improve the clarity and coherence of communication in natural languages such as English. This book is essential reading for teachers and researchers who may be out of touch with the latest developments in computational logic. It will also be useful in any undergraduate course that teaches practical thinking, problem solving or communication skills. Its informal presentation makes the book accessible to readers from any background, but optional, more formal, chapters are also included for those who are more technically oriented.

The Iconic Logic Of Peirce S Graphs

Author : Sun-Joo Shin
ISBN : 0262194708
Genre : Mathematics
File Size : 56. 34 MB
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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.

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