Self Reference And Modal Logic

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Handbook of Philosophical Logic

Author : Dov M. Gabbay
Publisher : Springer Science & Business Media
ISBN 13 : 940170466X
Total Pages : 348 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Handbook of Philosophical Logic by : Dov M. Gabbay

Download or read book Handbook of Philosophical Logic written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.

Self-Reference and Modal Logic

Author : Craig Smorynski
Publisher :
ISBN 13 : 9781461386025
Total Pages : 352 pages
Book Rating : 4.3/5 (86 download)

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Book Synopsis Self-Reference and Modal Logic by : Craig Smorynski

Download or read book Self-Reference and Modal Logic written by Craig Smorynski and published by . This book was released on 1985-09-23 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Self-reference and Modal Logic

Author : C. Smoryński
Publisher :
ISBN 13 :
Total Pages : 358 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Self-reference and Modal Logic by : C. Smoryński

Download or read book Self-reference and Modal Logic written by C. Smoryński and published by . This book was released on 1985 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is Sunday, the 7th of September 1930. The place is Konigsberg and the occasion is a small conference on the foundations of mathematics. Arend Heyting, the foremost disciple of L. E. J. Brouwer, has spoken on intuitionism; Rudolf Carnap of the Vienna Circle has expounded on logicism; Johann (formerly Janos and in a few years to be Johnny) von Neumann has explained Hilbert's proof theory-- the so-called formalism; and Hans Hahn has just propounded his own empiricist views of mathematics. The floor is open for general discussion, in the midst of which Heyting announces his satisfaction with the meeting. For him, the relationship between formalism and intuitionism has been clarified: There need be no war between the intuitionist and the formalist. Once the formalist has successfully completed Hilbert's programme and shown "finitely" that the "idealised" mathematics objected to by Brouwer proves no new "meaningful" statements, even the intuitionist will fondly embrace the infinite. To this euphoric revelation, a shy young man cautions̃ "According to the formalist conception one adjoins to the meaningful statements of mathematics transfinite (pseudo-')statements which in themselves have no meaning but only serve to make the system a well-rounded one just as in geometry one achieves a well rounded system by the introduction of points at infinity.

Self-Reference and Modal Logic

Author : Craig Smorynski
Publisher : Springer Science & Business Media
ISBN 13 : 1461386012
Total Pages : 346 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Self-Reference and Modal Logic by : Craig Smorynski

Download or read book Self-Reference and Modal Logic written by Craig Smorynski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is Sunday, the 7th of September 1930. The place is Konigsberg and the occasion is a small conference on the foundations of mathematics. Arend Heyting, the foremost disciple of L. E. J. Brouwer, has spoken on intuitionism; Rudolf Carnap of the Vienna Circle has expounded on logicism; Johann (formerly Janos and in a few years to be Johnny) von Neumann has explained Hilbert's proof theory-- the so-called formalism; and Hans Hahn has just propounded his own empiricist views of mathematics. The floor is open for general discussion, in the midst of which Heyting announces his satisfaction with the meeting. For him, the relationship between formalism and intuitionism has been clarified: There need be no war between the intuitionist and the formalist. Once the formalist has successfully completed Hilbert's programme and shown "finitely" that the "idealised" mathematics objected to by Brouwer proves no new "meaningful" statements, even the intuitionist will fondly embrace the infinite. To this euphoric revelation, a shy young man cautions~ "According to the formalist conception one adjoins to the meaningful statements of mathematics transfinite (pseudo-')statements which in themselves have no meaning but only serve to make the system a well-rounded one just as in geometry one achieves a well rounded system by the introduction of points at infinity.

Self-Reference

Author : S.J. Bartlett
Publisher : Springer Science & Business Media
ISBN 13 : 940093551X
Total Pages : 365 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Self-Reference by : S.J. Bartlett

Download or read book Self-Reference written by S.J. Bartlett and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-reference, although a topic studied by some philosophers and known to a number of other disciplines, has received comparatively little explicit attention. For the most part the focus of studies of self-reference has been on its logical and linguistic aspects, with perhaps disproportionate emphasis placed on the reflexive paradoxes. The eight-volume Macmillan Encyclopedia of Philosophy, for example, does not contain a single entry in its index under "self-reference", and in connection with "reflexivity" mentions only "relations", "classes", and "sets". Yet, in this volume, the introductory essay identifies some 75 varieties and occurrences of self-reference in a wide range of disciplines, and the bibliography contains more than 1,200 citations to English language works about reflexivity. The contributed papers investigate a number of forms and applications of self-reference, and examine some of the challenges posed by its difficult temperament. The editors hope that readers of this volume will gain a richer sense of the sti11largely unexplored frontiers of reflexivity, and of the indispensability of reflexive concepts and methods to foundational inquiries in philosophy, logic, language, and into the freedom, personality and intelligence of persons.

Raymond Smullyan on Self Reference

Author : Melvin Fitting
Publisher : Springer
ISBN 13 : 3319687328
Total Pages : 195 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Raymond Smullyan on Self Reference by : Melvin Fitting

Download or read book Raymond Smullyan on Self Reference written by Melvin Fitting and published by Springer. This book was released on 2018-01-11 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects, for the first time in one volume, contributions honoring Professor Raymond Smullyan’s work on self-reference. It serves not only as a tribute to one of the great thinkers in logic, but also as a celebration of self-reference in general, to be enjoyed by all lovers of this field. Raymond Smullyan, mathematician, philosopher, musician and inventor of logic puzzles, made a lasting impact on the study of mathematical logic; accordingly, this book spans the many personalities through which Professor Smullyan operated, offering extensions and re-evaluations of his academic work on self-reference, applying self-referential logic to art and nature, and lastly, offering new puzzles designed to communicate otherwise esoteric concepts in mathematical logic, in the manner for which Professor Smullyan was so well known. This book is suitable for students, scholars and logicians who are interested in learning more about Raymond Smullyan's work and life.

Self-reference and Self-awareness

Author : Andrew Brook
Publisher : John Benjamins Publishing
ISBN 13 : 9789027251503
Total Pages : 292 pages
Book Rating : 4.2/5 (515 download)

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Book Synopsis Self-reference and Self-awareness by : Andrew Brook

Download or read book Self-reference and Self-awareness written by Andrew Brook and published by John Benjamins Publishing. This book was released on 2001 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rich in precursors (Kant and Frege) and stimulated by Castañeda's study in the logic of self-consciousness and Shoemaker's seminal paper 'Self-reference and self-awareness', the work of the past thirty-five years on self-reference and self-awareness has generated a wealth of deep, sophisticated philosophy. This volume explores the historical anticipations in Kant and Frege, brings four classic contributions together in one place, and offers five new studies. (Series A)

Metamathematics of First-Order Arithmetic

Author : Petr Hájek
Publisher : Cambridge University Press
ISBN 13 : 1316739457
Total Pages : 476 pages
Book Rating : 4.3/5 (167 download)

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Book Synopsis Metamathematics of First-Order Arithmetic by : Petr Hájek

Download or read book Metamathematics of First-Order Arithmetic written by Petr Hájek and published by Cambridge University Press. This book was released on 2017-03-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).

The Logic of Provability

Author : George Boolos
Publisher : Cambridge University Press
ISBN 13 : 9780521483254
Total Pages : 318 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis The Logic of Provability by : George Boolos

Download or read book The Logic of Provability written by George Boolos and published by Cambridge University Press. This book was released on 1995-04-28 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boolos, a pre-eminent philosopher of mathematics, investigates the relationship between provability and modal logic.

Perspectives on the History of Mathematical Logic

Author : Thomas Drucker
Publisher : Springer Science & Business Media
ISBN 13 : 0817647694
Total Pages : 218 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Perspectives on the History of Mathematical Logic by : Thomas Drucker

Download or read book Perspectives on the History of Mathematical Logic written by Thomas Drucker and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.

Handbook of Philosophical Logic

Author : D.M. Gabbay
Publisher : Springer Science & Business Media
ISBN 13 : 1402035217
Total Pages : 371 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Philosophical Logic by : D.M. Gabbay

Download or read book Handbook of Philosophical Logic written by D.M. Gabbay and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ninth volume of the Second Edition contains major contributions on Rewriting Logic as a Logical and Semantic Framework, Logical Frameworks, Proof Theory and Meaning, Goal Directed Deductions, Negations, Completeness and Consistency as well as Logic as General Rationality. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

Extensions of Logic Programming

Author : Peter Schroeder-Heister
Publisher : Springer Science & Business Media
ISBN 13 : 9783540535904
Total Pages : 376 pages
Book Rating : 4.5/5 (359 download)

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Book Synopsis Extensions of Logic Programming by : Peter Schroeder-Heister

Download or read book Extensions of Logic Programming written by Peter Schroeder-Heister and published by Springer Science & Business Media. This book was released on 1991-02-12 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains finalized versions of papers presented at an international workshop on extensions of logic programming, held at the Seminar for Natural Language Systems at the University of Tübingen in December 1989. Several recent extensions of definite Horn clause programming, especially those with a proof-theoretic background, have much in common. One common thread is a new emphasis on hypothetical reasoning, which is typically inspired by Gentzen-style sequent or natural deduction systems. This is not only of theoretical significance, but also bears upon computational issues. It was one purpose of the workshop to bring some of these recent developments together. The volume covers topics such as the languages Lambda-Prolog, N-Prolog, and GCLA, the relationship between logic programming and functional programming, and the relationship between extensions of logic programming and automated theorem proving. It contains the results of the first conference concentrating on proof-theoretic approaches to logic programming.

Logic and the Modalities in the Twentieth Century

Author : Dov M. Gabbay
Publisher : Elsevier
ISBN 13 : 9780080463032
Total Pages : 732 pages
Book Rating : 4.4/5 (63 download)

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Book Synopsis Logic and the Modalities in the Twentieth Century by : Dov M. Gabbay

Download or read book Logic and the Modalities in the Twentieth Century written by Dov M. Gabbay and published by Elsevier. This book was released on 2006-05-10 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic and the Modalities in the Twentieth Century is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and artificial intelligence, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas. This volume is number seven in the eleven volume Handbook of the History of Logic. It concentrates on the development of modal logic in the 20th century, one of the most important undertakings in logic’s long history. Written by the leading researchers and scholars in the field, the volume explores the logics of necessity and possibility, knowledge and belief, obligation and permission, time, tense and change, relevance, and more. Both this volume and the Handbook as a whole are definitive reference tools for students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, artificial intelligence, for whom the historical background of his or her work is a salient consideration. · Detailed and comprehensive chapters covering the entire range of modal logic. · Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic.

Modal Logic

Author : Patrick Blackburn
Publisher : Cambridge University Press
ISBN 13 : 1316101959
Total Pages : 574 pages
Book Rating : 4.3/5 (161 download)

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Book Synopsis Modal Logic by : Patrick Blackburn

Download or read book Modal Logic written by Patrick Blackburn and published by Cambridge University Press. This book was released on 2002-08-22 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.

The Life and Work of Leon Henkin

Author : María Manzano
Publisher : Springer
ISBN 13 : 3319097199
Total Pages : 356 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis The Life and Work of Leon Henkin by : María Manzano

Download or read book The Life and Work of Leon Henkin written by María Manzano and published by Springer. This book was released on 2014-10-23 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive book on the life and works of Leon Henkin (1921–2006), an extraordinary scientist and excellent teacher whose writings became influential right from the beginning of his career with his doctoral thesis on “The completeness of formal systems” under the direction of Alonzo Church. Upon the invitation of Alfred Tarski, Henkin joined the Group in Logic and the Methodology of Science in the Department of Mathematics at the University of California Berkeley in 1953. He stayed with the group until his retirement in 1991. This edited volume includes both foundational material and a logic perspective. Algebraic logic, model theory, type theory, completeness theorems, philosophical and foundational studies are among the topics covered, as well as mathematical education. The work discusses Henkin’s intellectual development, his relation to his predecessors and contemporaries and his impact on the recent development of mathematical logic. It offers a valuable reference work for researchers and students in the fields of philosophy, mathematics and computer science.

John Buridan on Self-Reference

Author : Jean Buridan
Publisher : CUP Archive
ISBN 13 : 9780521288644
Total Pages : 188 pages
Book Rating : 4.2/5 (886 download)

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Book Synopsis John Buridan on Self-Reference by : Jean Buridan

Download or read book John Buridan on Self-Reference written by Jean Buridan and published by CUP Archive. This book was released on 1982-09-09 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Buridan is now being 'rediscovered' through his relevance to contemporary work in philosophical logic. The final chapter of Buridan's Sophismata deals with problems about self-reference, and in particular with the semantic paradoxes. He offers his own distinctive solution to the well-known 'Liar Paradox' and introduces a number of other paradoxes that will be unfamiliar to most logicians.

Handbook of Modal Logic

Author : Patrick Blackburn
Publisher : Elsevier
ISBN 13 : 9780080466668
Total Pages : 1260 pages
Book Rating : 4.4/5 (666 download)

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Book Synopsis Handbook of Modal Logic by : Patrick Blackburn

Download or read book Handbook of Modal Logic written by Patrick Blackburn and published by Elsevier. This book was released on 2006-11-03 with total page 1260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners approaching the subject for the first time, and advanced articles, which will help those already familiar with the field to deepen their expertise. Please visit: http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html - Compact modal logic reference - Computational approaches fully discussed - Contemporary applications of modal logic covered in depth