Natural Deduction, Hybrid Systems and Modal Logics
Natural Deduction, Hybrid Systems and Modal Logics

Author: Andrzej Indrzejczak

Publisher: Springer Science & Business Media

Published: 2010-07-03

Total Pages: 515

ISBN-13: 9048187850

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This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.

Natural Deduction
Natural Deduction

Author: Richard T.W. Arthur

Publisher: Broadview Press

Published: 2011-05-25

Total Pages: 451

ISBN-13: 1770481974

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Richard Arthur’s Natural Deduction provides a wide-ranging introduction to logic. In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python.

What Truth is
What Truth is

Author: Mark Jago

Publisher: Oxford University Press

Published: 2018

Total Pages: 369

ISBN-13: 0198823819

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Mark Jago offers a new metaphysical account of truth. He argues that to be true is to be made true by the existence of a suitable worldly entity. Truth arises as a relation between a proposition - the content of our sayings, thoughts, beliefs, and so on - and an entity (or entities) in the world.

Natural Deduction
Natural Deduction

Author: Dag Prawitz

Publisher: Courier Dover Publications

Published: 2006-02-24

Total Pages: 132

ISBN-13: 0486446557

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An innovative approach to the semantics of logic, proof-theoretic semantics seeks the meaning of propositions and logical connectives within a system of inference. Gerhard Gentzen invented proof-theoretic semantics in the early 1930s, and Dag Prawitz, the author of this study, extended its analytic proofs to systems of natural deduction. Prawitz's theories form the basis of intuitionistic type theory, and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics. The concept of natural deduction follows a truly natural progression, establishing the relationship between a noteworthy systematization and the interpretation of logical signs. As this survey explains, the deduction's principles allow it to proceed in a direct fashion — a manner that permits every natural deduction's transformation into the equivalent of normal form theorem. A basic result in proof theory, the normal form theorem was established by Gentzen for the calculi of sequents. The proof of this result for systems of natural deduction is in many ways simpler and more illuminating than alternative methods. This study offers clear illustrations of the proof and numerous examples of its advantages.

An Introduction to Logic - Second Edition
An Introduction to Logic - Second Edition

Author: Richard T.W. Arthur

Publisher: Broadview Press

Published: 2016-11-30

Total Pages: 460

ISBN-13: 1770486488

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In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python. A previous edition of this book appeared under the title Natural Deduction. This new edition adds clarifications of the notions of explanation, validity and formal validity, a more detailed discussion of derivation strategies, and another rule of inference, Reiteration.

Basic Proof Theory
Basic Proof Theory

Author: A. S. Troelstra

Publisher: Cambridge University Press

Published: 2000-07-27

Total Pages: 436

ISBN-13: 9780521779111

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This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.

Logic and Structure
Logic and Structure

Author: Dirk van Dalen

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 218

ISBN-13: 3662023822

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New corrected printing of a well-established text on logic at the introductory level.

Justification Logic
Justification Logic

Author: Sergei Artemov

Publisher: Cambridge University Press

Published: 2019-05-02

Total Pages: 271

ISBN-13: 1108424910

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Develops a new logic paradigm which emphasizes evidence tracking, including theory, connections to other fields, and sample applications.

ELEMENTARY LOGIC REV ED P
ELEMENTARY LOGIC REV ED P

Author: W. V. QUINE

Publisher: Harvard University Press

Published: 2009-06-30

Total Pages: 144

ISBN-13: 0674042492

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Now much revised since its first appearance in 1941, this book, despite its brevity, is notable for its scope and rigor. It provides a single strand of simple techniques for the central business of modern logic. Basic formal concepts are explained, the paraphrasing of words into symbols is treated at some length, and a testing procedure is given for truth-function logic along with a complete proof procedure for the logic of quantifiers. Fully one third of this revised edition is new, and presents a nearly complete turnover in crucial techniques of testing and proving, some change of notation, and some updating of terminology. The study is intended primarily as a convenient encapsulation of minimum essentials, but concludes by giving brief glimpses of further matters.