Systems Of Logic
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Alan Turing S Systems Of Logic
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Author : Andrew W. Appel
language : en
Publisher: Princeton University Press
Release Date : 2014-11-16
Alan Turing S Systems Of Logic written by Andrew W. Appel and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-16 with Computers categories.
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.
Systems Of Formal Logic
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Author : L.H. Hackstaff
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Systems Of Formal Logic written by L.H. Hackstaff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Philosophy categories.
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.
Design Of Logic Systems
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Author : DAVID PROTHEROE DOUGLAS LEWIN
language : en
Publisher: Springer
Release Date : 2013-11-21
Design Of Logic Systems written by DAVID PROTHEROE DOUGLAS LEWIN and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Computers categories.
Systems Of Formal Logic
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Author : L.H. Hackstaff
language : en
Publisher: Springer Science & Business Media
Release Date : 1966-07-31
Systems Of Formal Logic written by L.H. Hackstaff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966-07-31 with Philosophy categories.
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.
Systems Of Logic
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Author : Norman M. Martin
language : en
Publisher: Cambridge University Press
Release Date : 1989-07-28
Systems Of Logic written by Norman M. Martin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-07-28 with Philosophy categories.
This advanced study of systems of propositional logic offers a comprehensive account of a wide variety of logical systems and encourages students to take a critical stance toward the subject. A great variety of systems and subsystems are defined and compared as regards their deductive power and relation to their model theory. Special attention is given to the weakenings of classical logic and a more refined treatment of modal logic is presented.
Le Niewski S Systems Of Logic And Foundations Of Mathematics
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Author : Rafal Urbaniak
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-24
Le Niewski S Systems Of Logic And Foundations Of Mathematics written by Rafal Urbaniak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-24 with Science categories.
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.
Temporal Logic And State Systems
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Author : Fred Kröger
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-27
Temporal Logic And State Systems written by Fred Kröger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-27 with Computers categories.
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.
Design Of Logic Based Intelligent Systems
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Author : Klaus Truemper
language : en
Publisher: John Wiley & Sons
Release Date : 2004-05-20
Design Of Logic Based Intelligent Systems written by Klaus Truemper and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-20 with Technology & Engineering categories.
Principles for constructing intelligent systems Design of Logic-based Intelligent Systems develops principles and methods for constructing intelligent systems for complex tasks that are readily done by humans but are difficult for machines. Current Artificial Intelligence (AI) approaches rely on various constructs and methods (production rules, neural nets, support vector machines, fuzzy logic, Bayesian networks, etc.). In contrast, this book uses an extension of propositional logic that treats all aspects of intelligent systems in a unified and mathematically compatible manner. Topics include: * Levels of thinking and logic * Special cases: expert systems and intelligent agents * Formulating and solving logic systems * Reasoning under uncertainty * Learning logic formulas from data * Nonmonotonic and incomplete reasoning * Question-and-answer processes * Intelligent systems that construct intelligent systems Design of Logic-based Intelligent Systems is both a handbook for the AI practitioner and a textbook for advanced undergraduate and graduate courses on intelligent systems. Included are more than forty algorithms, and numerous examples and exercises. The purchaser of the book may obtain an accompanying software package (Leibniz System) free of charge via the internet at leibnizsystem.com.
The Temporal Logic Of Reactive And Concurrent Systems
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Author : Zohar Manna
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Temporal Logic Of Reactive And Concurrent Systems written by Zohar Manna and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
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.
Mill S A System Of Logic
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Author : Antis Loizides
language : en
Publisher: Routledge
Release Date : 2014-05-23
Mill S A System Of Logic written by Antis Loizides and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-23 with Philosophy categories.
John Stuart Mill considered his A System of Logic, first published in 1843, the methodological foundation and intellectual groundwork of his later works in ethical, social, and political theory. Yet no book has attempted in the past to engage with the most important aspects of Mill's Logic. This volume brings together leading scholars to elucidate the key themes of this influential work, looking at such topics as his philosophy of language and mathematics, his view on logic, induction and deduction, free will, argumentation, ethology and psychology, as well as his account of normativity, kinds of pleasure, philosophical and political method and the "Art of Life."