[PDF] Proof And Disproof In Formal Logic eBook

Author : Richard Bornat
Publisher : OUP Oxford
Page : 264 pages
File Size : 34,33 MB
Release : 2005-07-21
Category : Mathematics
ISBN : 0191586765

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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.

Author : Richard Bornat
Publisher :
Page : 243 pages
File Size : 28,77 MB
Release : 2005-09-29
Category : Evidence
ISBN : 9786610759002

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"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.

Author : Richard Bornat
Publisher : Oxford University Press on Demand
Page : 243 pages
File Size : 15,19 MB
Release : 2005
Category : Mathematics
ISBN : 0198530277

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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...

Author : Martin Aigner
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 18,82 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 3662223430

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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.

Author : Michael Detlefsen
Publisher : Routledge
Page : 251 pages
File Size : 44,42 MB
Release : 2005-07-08
Category : Mathematics
ISBN : 1134975287

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

Author : Richard H. Hammack
Publisher :
Page : 314 pages
File Size : 10,51 MB
Release : 2016-01-01
Category : Mathematics
ISBN : 9780989472111

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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.

Author : Peter Smith
Publisher : Cambridge University Press
Page : 370 pages
File Size : 41,2 MB
Release : 2003-11-06
Category : Mathematics
ISBN : 9780521008044

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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.

Author : Daniel W. Cunningham
Publisher : Springer Science & Business Media
Page : 365 pages
File Size : 48,21 MB
Release : 2012-09-19
Category : Mathematics
ISBN : 1461436311

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The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.

Author : Paolo Mancosu
Publisher : Oxford University Press
Page : 336 pages
File Size : 18,57 MB
Release : 2021-08-12
Category : Philosophy
ISBN : 0192649299

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An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.