Proof And Disproof In Formal Logic

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Proof and Disproof in Formal Logic

Richard Bornat
Proof and Disproof in Formal Logic Book PDF

Author : Richard Bornat
Publisher : OUP Oxford
Page : 264 pages
File Size : 53,8 Mb
Release : 2005-07-21
Category : Mathematics
ISBN : 9780191586767

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Proof and Disproof in Formal Logic by Richard Bornat Pdf

Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system—a collection of rules and axioms which define a universe of logical proofs—is what gives us programming languages and modern-day programming. This book concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses—natural deduction—is very small and very simple; working with it helps you see how large mathematical universes can be built on small foundations. The book is divided into four parts: · Part I "Basics" gives an introduction to formal logic with a short history of logic and explanations of some technical words. · Part II "Formal syntactic proof" show you how to do calculations in a formal system where you are guided by shapes and never need to think about meaning. Your experiments are aided by Jape, which can operate as both inquisitor and oracle. · Part III "Formal semantic disproof" shows you how to construct mathematical counterexamples to show that proof is impossible. Jape can check the counterexamples you build. · Part IV "Program specification and proof" describes how to apply your logical understanding to a real computer science problem, the accurate description and verification of programs. Jape helps, as far as arithmetic allows. Aimed at undergraduates and graduates in computer science, logic, mathematics, and philosophy, the text includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the web.

Proof and Disproof in Formal Logic

Richard Bornat
Proof and Disproof in Formal Logic Book PDF

Author : Richard Bornat
Publisher : Unknown
Page : 243 pages
File Size : 52,7 Mb
Release : 2005-09-29
Category : Evidence
ISBN : 6610759006

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Proof and Disproof in Formal Logic by Richard Bornat Pdf

"Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic that provides an excellent insight into how a simple logic works. The text concentrates on practical skills: making proofs and disproofs of particular logical claims. The logic it employs - Natural Deduction - is very small and very simple and teaches the student how to focus on syntactic reasoning." "Aimed at undergraduates and graduates in computer science, logic, mathematics, and philosophy, the text shows how to make proofs and disproofs in Jape, an interactive easy-to-use logic calculator designed and hosted by the author that is freely available on the web."--Jacket.

Proof and Disproof in Formal Logic

Richard Bornat
Proof and Disproof in Formal Logic Book PDF

Author : Richard Bornat
Publisher : Oxford University Press on Demand
Page : 243 pages
File Size : 46,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9780198530275

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Proof and Disproof in Formal Logic by Richard Bornat Pdf

Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. This book concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses - natural deduction - is very simple and shows how large mathematical universes can be built on small foundations. Aimed at undergraduates and graduates in computerscience, logic, mathematics, and philosophy, the text includes reference to...

Proofs from THE BOOK

Martin Aigner,Günter M. Ziegler
Proofs from THE BOOK Book PDF

Author : Martin Aigner,Günter M. Ziegler
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 50,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662223437

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Proofs from THE BOOK by Martin Aigner,Günter M. Ziegler Pdf

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Book of Proof

Richard H. Hammack
Book of Proof Book PDF

Author : Richard H. Hammack
Publisher : Unknown
Page : 314 pages
File Size : 45,7 Mb
Release : 2016-01-01
Category : Mathematics
ISBN : 0989472116

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Book of Proof by Richard H. Hammack Pdf

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

Proof, Logic and Formalization

Michael Detlefsen
Proof Logic and Formalization Book PDF

Author : Michael Detlefsen
Publisher : Routledge
Page : 251 pages
File Size : 51,5 Mb
Release : 2005-07-08
Category : Mathematics
ISBN : 9781134975280

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Proof, Logic and Formalization by Michael Detlefsen Pdf

A collection of essays from distinguished contributors looking at why it is that mathematical proof is given precedence over other forms of mathematical justification.

Logic: A History of its Central Concepts

Dov M. Gabbay,Francis Jeffry Pelletier,John Woods
Logic A History of its Central Concepts Book PDF

Author : Dov M. Gabbay,Francis Jeffry Pelletier,John Woods
Publisher : Newnes
Page : 708 pages
File Size : 50,8 Mb
Release : 2012-12-31
Category : Mathematics
ISBN : 9780080931708

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Logic: A History of its Central Concepts by Dov M. Gabbay,Francis Jeffry Pelletier,John Woods Pdf

The Handbook of the History of Logic is a multi-volume research instrument that brings to the development of logic the best in modern techniques of historical and interpretative scholarship. It is the first work in English in which the history of logic is presented so extensively. The volumes are numerous and large. Authors have been given considerable latitude to produce chapters of a length, and a level of detail, that would lay fair claim on the ambitions of the project to be a definitive research work. Authors have been carefully selected with this aim in mind. They and the Editors join in the conviction that a knowledge of the history of logic is nothing but beneficial to the subject's present-day research programmes. One of the attractions of the Handbook's several volumes is the emphasis they give to the enduring relevance of developments in logic throughout the ages, including some of the earliest manifestations of the subject. Covers in depth the notion of logical consequence Discusses the central concept in logic of modality Includes the use of diagrams in logical reasoning

Concepts of Proof in Mathematics, Philosophy, and Computer Science

Dieter Probst,Peter Schuster
Concepts of Proof in Mathematics Philosophy and Computer Science Book PDF

Author : Dieter Probst,Peter Schuster
Publisher : Walter de Gruyter GmbH & Co KG
Page : 384 pages
File Size : 40,6 Mb
Release : 2016-07-25
Category : Philosophy
ISBN : 9781501502620

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Concepts of Proof in Mathematics, Philosophy, and Computer Science by Dieter Probst,Peter Schuster Pdf

A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.

Logic as a Tool

Valentin Goranko
Logic as a Tool Book PDF

Author : Valentin Goranko
Publisher : John Wiley & Sons
Page : 386 pages
File Size : 52,5 Mb
Release : 2016-10-17
Category : Mathematics
ISBN : 9781118880005

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Logic as a Tool by Valentin Goranko Pdf

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

An Introduction to Formal Logic

Peter Smith
An Introduction to Formal Logic Book PDF

Author : Peter Smith
Publisher : Cambridge University Press
Page : 370 pages
File Size : 54,8 Mb
Release : 2003-11-06
Category : Mathematics
ISBN : 0521008042

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An Introduction to Formal Logic by Peter Smith Pdf

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.

Elementary Logic

Robert Lover
Elementary Logic Book PDF

Author : Robert Lover
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 49,5 Mb
Release : 2008-10-26
Category : Computers
ISBN : 9781848000827

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Elementary Logic by Robert Lover Pdf

The ability to reason correctly is critical to most aspects of computer science and to software development in particular. This book teaches readers how to better reason about software development, to communicate reasoning, to distinguish between good and bad reasoning, and to read professional literature that presumes knowledge of elementary logic. The reader’s knowledge and understanding can be assessed through numerous examples and exercises. This book provides a reader-friendly foundation to logic and offers valuable insight into the topic, thereby serving as a helpful reference for practitioners, as well as students studying software development.

Formal Methods: State of the Art and New Directions

Paul Boca,Jonathan P. Bowen,Jawed Siddiqi
Formal Methods State of the Art and New Directions Book PDF

Author : Paul Boca,Jonathan P. Bowen,Jawed Siddiqi
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 54,9 Mb
Release : 2009-12-04
Category : Computers
ISBN : 9781848827363

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Formal Methods: State of the Art and New Directions by Paul Boca,Jonathan P. Bowen,Jawed Siddiqi Pdf

Through fundamental contributions from leading researchers, this volume describes the use of formal modeling methods in the areas of requirements, design and validation. The self-contained chapters provide readers with rich background information and a diverse breadth of specialist material.

Mathematical Logic

Ian Chiswell,Wilfrid Hodges
Mathematical Logic Book PDF

Author : Ian Chiswell,Wilfrid Hodges
Publisher : Oxford University Press on Demand
Page : 259 pages
File Size : 48,8 Mb
Release : 2007-05-17
Category : Mathematics
ISBN : 9780198571001

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Mathematical Logic by Ian Chiswell,Wilfrid Hodges Pdf

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't becalculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assumingMatiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics andcomputer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic,Mathematics, Philosophy, and Computer Science.

Discrete Mathematics

Oscar Levin
Discrete Mathematics Book PDF

Author : Oscar Levin
Publisher : Createspace Independent Publishing Platform
Page : 238 pages
File Size : 47,5 Mb
Release : 2018-07-30
Category : Electronic
ISBN : 1724572636

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Discrete Mathematics by Oscar Levin Pdf

Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.

Management: A Focus on Leaders

Annie McKee,Travis Kemp,Gordon Spence
Management A Focus on Leaders Book PDF

Author : Annie McKee,Travis Kemp,Gordon Spence
Publisher : Pearson Higher Education AU
Page : 641 pages
File Size : 42,7 Mb
Release : 2012-11-01
Category : Business & Economics
ISBN : 9781442550469

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Management: A Focus on Leaders by Annie McKee,Travis Kemp,Gordon Spence Pdf

A new view of the four functions of Management: through the lens of leadership The pace and scope of change in the world and organisations during the past 10 years is unprecedented. In this environment, staying ahead of the curve and preparing for success in work, management and leadership is challenging. Amidst the financial crises, catastrophic disasters, and business scandals frequently making headlines, Annie McKee and the Australian authors of this new text Management: a Focus on Leaders, believe there is a unique opportunity to re-focus the way students are prepared for their future in business. Show future managers how to lead in a complex, yet exciting, global environment With an engaging writing style and an outcome-driven approach, Annie McKee and Australian authors Travis Kemp and Gordon Spence directly address the many behavioural, social, cognitive and emotional challenges beyond the four functions of management. Management features exciting Australasian and global case studies and easy, student-friendly teaching tools. Unique Decision Making mini-simulations using adaptive technology allow students to make management decisions and see the impact of their decisions.