Mathematical Logic and the Foundations of Mathematics

Mathematical Logic and the Foundations of Mathematics

Author: G. T. Kneebone

Publisher: Dover Publications

Published: 2001

Total Pages: 0

ISBN-13: 9780486417127

DOWNLOAD EBOOK

Ideal for students intending to specialize in the topic. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics. Part III focuses on the philosophy of mathematics.


Mathematical Logic and Formalized Theories

Mathematical Logic and Formalized Theories

Author: Robert L. Rogers

Publisher: Elsevier

Published: 2014-05-12

Total Pages: 248

ISBN-13: 1483257975

DOWNLOAD EBOOK

Mathematical Logic and Formalized Theories: A Survey of Basic Concepts and Results focuses on basic concepts and results of mathematical logic and the study of formalized theories. The manuscript first elaborates on sentential logic and first-order predicate logic. Discussions focus on first-order predicate logic with identity and operation symbols, first-order predicate logic with identity, completeness theorems, elementary theories, deduction theorem, interpretations, truth, and validity, sentential connectives, and tautologies. The text then tackles second-order predicate logic, as well as second-order theories, theory of definition, and second-order predicate logic F2. The publication takes a look at natural and real numbers, incompleteness, and the axiomatic set theory. Topics include paradoxes, recursive functions and relations, Gödel's first incompleteness theorem, axiom of choice, metamathematics of R and elementary algebra, and metamathematics of N. The book is a valuable reference for mathematicians and researchers interested in mathematical logic and formalized theories.


Epistemic Logic

Epistemic Logic

Author: Nicholas Rescher

Publisher: University of Pittsburgh Pre

Published: 2005-02-27

Total Pages: 153

ISBN-13: 0822970929

DOWNLOAD EBOOK

Epistemic logic is the branch of philosophical thought that seeks to formalize the discourse about knowledge. Its object is to articulate and clarify the general principles of reasoning about claims to and attributions of knowledge. This comprehensive survey of the topic offers the first systematic account of the subject as it has developed in the journal literature over recent decades. Rescher gives an overview of the discipline by setting out the general principles for reasoning about such matters as propositional knowledge and interrogative knowledge. Aimed at graduate students and specialists, Epistemic Logic elucidates both Rescher's pragmatic view of knowledge and the field in general.


Introducing Symbolic Logic

Introducing Symbolic Logic

Author: Robert M. Martin

Publisher: Broadview Press

Published: 2004-05-14

Total Pages: 274

ISBN-13: 1460401158

DOWNLOAD EBOOK

This accessible, SHORT introduction to symbolic logic includes coverage of sentential and predicate logic, translations, truth tables, and derivations. The author's engaging style makes this the most informal of introductions to formal logic. Topics are explained in a conversational, easy-to-understand way for readers not familiar with mathematics or formal systems, and the author provides patient, reader-friendly explanations—even with the occasional bit of humour. The first half of the book deals with all the basic elements of Sentential Logic: the five truth-functional connectives, formation rules and translation into this language, truth-tables for validity, logical truth/falsity, equivalency, consistency and derivations. The second half deals with Quantifier Logic: the two quantifiers, formation rules and translation, demonstrating certain logical characteristics by “Finding an Interpretation” and derivations. There are plenty of exercises scattered throughout, more than in many texts, arranged in order of increasing difficulty and including separate answer keys.


Introduction to Symbolic Logic and Its Applications

Introduction to Symbolic Logic and Its Applications

Author: Rudolf Carnap

Publisher: Courier Corporation

Published: 2012-07-12

Total Pages: 280

ISBN-13: 048614349X

DOWNLOAD EBOOK

Clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. Hundreds of problems, examples, and exercises. 1958 edition.


Modern Logic — A Survey

Modern Logic — A Survey

Author: E. Agazzi

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 470

ISBN-13: 9400990561

DOWNLOAD EBOOK

Logic has attained in our century a development incomparably greater than in any past age of its long history, and this has led to such an enrichment and proliferation of its aspects, that the problem of some kind of unified recom prehension of this discipline seems nowadays unavoidable. This splitting into several subdomains is the natural consequence of the fact that Logic has intended to adopt in our century the status of a science. This always implies that the general optics, under which a certain set of problems used to be con sidered, breaks into a lot of specialized sectors of inquiry, each of them being characterized by the introduction of specific viewpoints and of technical tools of its own. The first impression, that often accompanies the creation of one of such specialized branches in a diSCipline, is that one has succeeded in isolating the 'scientific core' of it, by restricting the somehow vague and redundant generality of its original 'philosophical' configuration. But, after a while, it appears that some of the discarded aspects are indeed important and a new specialized domain of investigation is created to explore them. By follOwing this procedure, one finally finds himself confronted with such a variety of independent fields of research, that one wonders whether the fact of labelling them under a common denomination be nothing but the contingent effect of a pure historical tradition.


An Introduction to Symbolic Logic

An Introduction to Symbolic Logic

Author: Langer

Publisher: Courier Corporation

Published: 1967-01-01

Total Pages: 388

ISBN-13: 9780486601649

DOWNLOAD EBOOK

Famous classic has introduced countless readers to symbolic logic with its thorough and precise exposition. Starts with simple symbols and conventions and concludes with the Boole-Schroeder and Russell-Whitehead systems. No special knowledge of mathematics necessary. "One of the clearest and simplest introductions to a subject which is very much alive." — Mathematics Gazette.


Symbolic Logic and Mechanical Theorem Proving

Symbolic Logic and Mechanical Theorem Proving

Author: Chin-Liang Chang

Publisher: Academic Press

Published: 2014-06-28

Total Pages: 349

ISBN-13: 0080917283

DOWNLOAD EBOOK

This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.