Natural Deduction

Natural Deduction PDF Author: Richard T.W. Arthur
Publisher: Broadview Press
ISBN: 1460401417
Category : Philosophy
Languages : en
Pages : 427

Get Book Here

Book Description
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.

Natural Deduction, Hybrid Systems and Modal Logics

Natural Deduction, Hybrid Systems and Modal Logics PDF Author: Andrzej Indrzejczak
Publisher: Springer Science & Business Media
ISBN: 9048187850
Category : Philosophy
Languages : en
Pages : 515

Get Book Here

Book Description
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.

What Truth is

What Truth is PDF Author: Mark Jago
Publisher: Oxford University Press
ISBN: 0198823819
Category : Philosophy
Languages : en
Pages : 369

Get Book Here

Book Description
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 PDF Author: Dag Prawitz
Publisher: Courier Dover Publications
ISBN: 0486446557
Category : Mathematics
Languages : en
Pages : 132

Get Book Here

Book Description
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.

Forall X

Forall X PDF Author: P. D. Magnus
Publisher:
ISBN:
Category : Logic
Languages : en
Pages : 0

Get Book Here

Book Description


An Introduction to Logic - Second Edition

An Introduction to Logic - Second Edition PDF Author: Richard T.W. Arthur
Publisher: Broadview Press
ISBN: 1770486488
Category : Philosophy
Languages : en
Pages : 460

Get Book Here

Book Description
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 PDF Author: A. S. Troelstra
Publisher: Cambridge University Press
ISBN: 9780521779111
Category : Computers
Languages : en
Pages : 436

Get Book Here

Book Description
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.

Justification Logic

Justification Logic PDF Author: Sergei Artemov
Publisher: Cambridge University Press
ISBN: 1108424910
Category : Mathematics
Languages : en
Pages : 271

Get Book Here

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

Logic and Structure

Logic and Structure PDF Author: Dirk van Dalen
Publisher: Springer Science & Business Media
ISBN: 3662023822
Category : Mathematics
Languages : en
Pages : 218

Get Book Here

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

The Functional Interpretation of Logical Deduction

The Functional Interpretation of Logical Deduction PDF Author: Ruy J. G. B. de Queiroz
Publisher: World Scientific
ISBN: 9814360953
Category : Computers
Languages : en
Pages : 299

Get Book Here

Book Description
This comprehensive book provides an adequate framework to establish various calculi of logical inference. Being an ?enriched? system of natural deduction, it helps to formulate logical calculi in an operational manner. By uncovering a certain harmony between a functional calculus on the labels and a logical calculus on the formulas, it allows mathematical foundations for systems of logic presentation designed to handle meta-level features at the object-level via a labelling mechanism, such as the D Gabbay's Labelled Deductive Systems. The book truly demonstrates that introducing ?labels? is useful to understand the proof-calculus itself, and also to clarify its connections with model-theoretic interpretations.