Alan Turing's Systems of Logic

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Publisher : Princeton University Press
ISBN 13 : 0691164738
Total Pages : 160 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Alan Turing's Systems of Logic by : Andrew W. Appel

Download or read book Alan Turing's Systems of Logic written by Andrew W. Appel and published by Princeton University Press. This book was released on 2014-11-16 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: A facsimile edition of Alan Turing's influential Princeton thesis Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal—a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.

Leśniewski's Systems of Logic and Foundations of Mathematics

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Publisher : Springer Science & Business Media
ISBN 13 : 3319004824
Total Pages : 240 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Leśniewski's Systems of Logic and Foundations of Mathematics by : Rafal Urbaniak

Download or read book Leśniewski's Systems of Logic and Foundations of Mathematics written by Rafal Urbaniak and published by Springer Science & Business Media. This book was released on 2013-09-24 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw Leśniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsaw school. The author’s nuanced survey eschews secondary commentary, analyzing Leśniewski's core philosophical views and evaluating the formulations that were to have such a profound influence on the evolution of mathematical logic. One of the undisputed leaders of the cohort of brilliant logicians that congregated in Poland in the early twentieth century, Leśniewski was a guide and mentor to a generation of celebrated analytical philosophers (Alfred Tarski was his PhD student). His primary achievement was a system of foundational mathematical logic intended as an alternative to the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. Its three strands—‘protothetic’, ‘ontology’, and ‘mereology’, are detailed in discrete sections of this volume, alongside a wealth other chapters grouped to provide the fullest possible coverage of Leśniewski’s academic output. With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great pioneers.​

Systems of Formal Logic

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Publisher : Springer Science & Business Media
ISBN 13 : 9401035474
Total Pages : 367 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Systems of Formal Logic by : L.H. Hackstaff

Download or read book Systems of Formal Logic written by L.H. Hackstaff and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present work constitutes an effort to approach the subject of symbol ic logic at the elementary to intermediate level in a novel way. The book is a study of a number of systems, their methods, their rela tions, their differences. In pursuit of this goal, a chapter explaining basic concepts of modern logic together with the truth-table techniques of definition and proof is first set out. In Chapter 2 a kind of ur-Iogic is built up and deductions are made on the basis of its axioms and rules. This axiom system, resembling a propositional system of Hilbert and Ber nays, is called P +, since it is a positive logic, i. e. , a logic devoid of nega tion. This system serves as a basis upon which a variety of further sys tems are constructed, including, among others, a full classical proposi tional calculus, an intuitionistic system, a minimum propositional calcu lus, a system equivalent to that of F. B. Fitch (Chapters 3 and 6). These are developed as axiomatic systems. By means of adding independent axioms to the basic system P +, the notions of independence both for primitive functors and for axiom sets are discussed, the axiom sets for a number of such systems, e. g. , Frege's propositional calculus, being shown to be non-independent. Equivalence and non-equivalence of systems are discussed in the same context. The deduction theorem is proved in Chapter 3 for all the axiomatic propositional calculi in the book.

What is a Logical System?

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Publisher : Studies in Logic and Computati
ISBN 13 :
Total Pages : 472 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis What is a Logical System? by : Dov M. Gabbay

Download or read book What is a Logical System? written by Dov M. Gabbay and published by Studies in Logic and Computati. This book was released on 1994 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This extraordinary collection of papers addresses a fundamental question of logic and computation. "What is a logical system?". With contributions from many world famous researchers, it presents a wide spectrum of views on the problem, reflecting mainstream current approaches to logic andhow it is applied.

Temporal Logic and State Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 3540674012
Total Pages : 440 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Temporal Logic and State Systems by : Fred Kröger

Download or read book Temporal Logic and State Systems written by Fred Kröger and published by Springer Science & Business Media. This book was released on 2008-03-27 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Temporal logic has developed over the last 30 years into a powerful formal setting for the specification and verification of state-based systems. Based on university lectures given by the authors, this book is a comprehensive, concise, uniform, up-to-date presentation of the theory and applications of linear and branching time temporal logic; TLA (Temporal Logic of Actions); automata theoretical connections; model checking; and related theories. All theoretical details and numerous application examples are elaborated carefully and with full formal rigor, and the book will serve as a basic source and reference for lecturers, graduate students and researchers.

Logic in Computer Science

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Publisher :
ISBN 13 : 9780521543101
Total Pages : 427 pages
Book Rating : 4.5/5 (431 download)

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Book Synopsis Logic in Computer Science by : Michael Huth

Download or read book Logic in Computer Science written by Michael Huth and published by . This book was released on 2004-08-26 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a sound basis in logic, and introduces logical frameworks used in modelling, specifying and verifying computer systems.

Symbolic Logic

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Publisher :
ISBN 13 :
Total Pages : 342 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Symbolic Logic by : Harry J. Gensler

Download or read book Symbolic Logic written by Harry J. Gensler and published by . This book was released on 1990 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Logic for Philosophy

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Publisher : Oxford University Press
ISBN 13 : 0192658816
Total Pages : 305 pages
Book Rating : 4.1/5 (926 download)

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Book Synopsis Logic for Philosophy by : Theodore Sider

Download or read book Logic for Philosophy written by Theodore Sider and published by Oxford University Press. This book was released on 2010-01-07 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.

The Structure of Aristotelian Logic

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Publisher : Routledge
ISBN 13 : 1317375424
Total Pages : 97 pages
Book Rating : 4.3/5 (173 download)

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Book Synopsis The Structure of Aristotelian Logic by : James Wilkinson Miller

Download or read book The Structure of Aristotelian Logic written by James Wilkinson Miller and published by Routledge. This book was released on 2015-08-14 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1938. This compact treatise is a complete treatment of Aristotle’s logic as containing negative terms. It begins with defining Aristotelian logic as a subject-predicate logic confining itself to the four forms of categorical proposition known as the A, E, I and O forms. It assigns conventional meanings to these categorical forms such that subalternation holds. It continues to discuss the development of the logic since the time of its founder and address traditional logic as it existed in the twentieth century. The primary consideration of the book is the inclusion of negative terms - obversion, contraposition etc. – within traditional logic by addressing three questions, of systematization, the rules, and the interpretation.

Design of Logic Systems

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Publisher : Springer
ISBN 13 : 1489968563
Total Pages : 713 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Design of Logic Systems by : DAVID PROTHEROE DOUGLAS LEWIN

Download or read book Design of Logic Systems written by DAVID PROTHEROE DOUGLAS LEWIN and published by Springer. This book was released on 2013-11-21 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Temporal Logic of Reactive and Concurrent Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 1461209315
Total Pages : 432 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Temporal Logic of Reactive and Concurrent Systems by : Zohar Manna

Download or read book The Temporal Logic of Reactive and Concurrent Systems written by Zohar Manna and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reactive systems are computing systems which are interactive, such as real-time systems, operating systems, concurrent systems, control systems, etc. They are among the most difficult computing systems to program. Temporal logic is a formal tool/language which yields excellent results in specifying reactive systems. This volume, the first of two, subtitled Specification, has a self-contained introduction to temporal logic and, more important, an introduction to the computational model for reactive programs, developed by Zohar Manna and Amir Pnueli of Stanford University and the Weizmann Institute of Science, Israel, respectively.

Arithmetic and Logic in Computer Systems

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Publisher : John Wiley & Sons
ISBN 13 : 0471726214
Total Pages : 270 pages
Book Rating : 4.4/5 (717 download)

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Book Synopsis Arithmetic and Logic in Computer Systems by : Mi Lu

Download or read book Arithmetic and Logic in Computer Systems written by Mi Lu and published by John Wiley & Sons. This book was released on 2005-03-04 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct applications. Alternative methods are examined, and explanations are supplied of the fundamental materials and reasoning behind theories and examples. No other current books deal with this subject, and the author is a leading authority in the field of computer arithmetic. The text introduces the Conventional Radix Number System and the Signed-Digit Number System, as well as Residue Number System and Logarithmic Number System. This book serves as an essential, up-to-date guide for students of electrical engineering and computer and mathematical sciences, as well as practicing engineers and computer scientists involved in the design, application, and development of computer arithmetic units.

Philosophy of Logic

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Publisher : Elsevier
ISBN 13 : 008046663X
Total Pages : 1219 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Philosophy of Logic by :

Download or read book Philosophy of Logic written by and published by Elsevier. This book was released on 2006-11-29 with total page 1219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter

Hybrid Logic and its Proof-Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 9400700024
Total Pages : 240 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Hybrid Logic and its Proof-Theory by : Torben Braüner

Download or read book Hybrid Logic and its Proof-Theory written by Torben Braüner and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).

Logic in Games

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Publisher : MIT Press
ISBN 13 : 0262019906
Total Pages : 567 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Logic in Games by : Johan Van Benthem

Download or read book Logic in Games written by Johan Van Benthem and published by MIT Press. This book was released on 2014-01-24 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive examination of the interfaces of logic, computer science, and game theory, drawing on twenty years of research on logic and games. This book draws on ideas from philosophical logic, computational logic, multi-agent systems, and game theory to offer a comprehensive account of logic and games viewed in two complementary ways. It examines the logic of games: the development of sophisticated modern dynamic logics that model information flow, communication, and interactive structures in games. It also examines logic as games: the idea that logical activities of reasoning and many related tasks can be viewed in the form of games. In doing so, the book takes up the “intelligent interaction” of agents engaging in competitive or cooperative activities and examines the patterns of strategic behavior that arise. It develops modern logical systems that can analyze information-driven changes in players' knowledge and beliefs, and introduces the “Theory of Play” that emerges from the combination of logic and game theory. This results in a new view of logic itself as an interactive rational activity based on reasoning, perception, and communication that has particular relevance for games. Logic in Games, based on a course taught by the author at Stanford University, the University of Amsterdam, and elsewhere, can be used in advanced seminars and as a resource for researchers.

Logic Works

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Publisher : Routledge
ISBN 13 : 1000451275
Total Pages : 666 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Logic Works by : Lorne Falkenstein

Download or read book Logic Works written by Lorne Falkenstein and published by Routledge. This book was released on 2021-11-30 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic Works is a critical and extensive introduction to logic. It asks questions about why systems of logic are as they are, how they relate to ordinary language and ordinary reasoning, and what alternatives there might be to classical logical doctrines. The book covers classical first-order logic and alternatives, including intuitionistic, free, and many-valued logic. It also considers how logical analysis can be applied to carefully represent the reasoning employed in academic and scientific work, better understand that reasoning, and identify its hidden premises. Aiming to be as much a reference work and handbook for further, independent study as a course text, it covers more material than is typically covered in an introductory course. It also covers this material at greater length and in more depth with the purpose of making it accessible to those with no prior training in logic or formal systems. Online support material includes a detailed student solutions manual with a running commentary on all starred exercises, and a set of editable slide presentations for course lectures. Key Features Introduces an unusually broad range of topics, allowing instructors to craft courses to meet a range of various objectives Adopts a critical attitude to certain classical doctrines, exposing students to alternative ways to answer philosophical questions about logic Carefully considers the ways natural language both resists and lends itself to formalization Makes objectual semantics for quantified logic easy, with an incremental, rule-governed approach assisted by numerous simple exercises Makes important metatheoretical results accessible to introductory students through a discursive presentation of those results and by using simple case studies

Logic and Structure

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Publisher : Springer Science & Business Media
ISBN 13 : 3662023822
Total Pages : 218 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Logic and Structure by : Dirk van Dalen

Download or read book Logic and Structure written by Dirk van Dalen and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: New corrected printing of a well-established text on logic at the introductory level.