Lectures on Linear Logic

Author: Anne Sjerp Troelstra

Publisher: Center for the Study of Language and Information Publications

ISBN: 9780937073773

Category: Mathematics

Page: 215

View: 6821

The initial sections of this text deal with syntactical matters such as logical formalism, cut-elimination, and the embedding of intuitionistic logic in classical linear logic. Concluding chapters focus on proofnets for the multiplicative fragment and the algorithmic interpretation of cut-elimination in proofnets.

Logic and Scientific Methods

Volume One of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995

Author: Maria Luisa Dalla Chiara,Kees Doets,Daniele Mundici,Johan van Benthem

Publisher: Springer Science & Business Media

ISBN: 9780792343837

Category: Science

Page: 534

View: 4225

This is the first of two volumes comprising the papers submitted for publication by the invited participants to the Tenth International Congress of Logic, Methodology and Philosophy of Science, held in Florence, August 1995. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science. The invited lectures published in the two volumes demonstrate much of what goes on in the fields of the Congress and give the state of the art of current research. The two volumes cover the traditional subdisciplines of mathematical logic and philosophical logic, as well as their interfaces with computer science, linguistics and philosophy. Philosophy of science is broadly represented, too, including general issues of natural sciences, social sciences and humanities. The papers in Volume One are concerned with logic, mathematical logic, the philosophy of logic and mathematics, and computer science.

Lectures on the Curry-Howard Isomorphism

Author: Morten Heine Sørensen,Pawel Urzyczyn

Publisher: Elsevier

ISBN: 9780080478920

Category: Mathematics

Page: 456

View: 1212

The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transforms proofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq). This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features - The Curry-Howard Isomorphism treated as common theme - Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics - Thorough study of the connection between calculi and logics - Elaborate study of classical logics and control operators - Account of dialogue games for classical and intuitionistic logic - Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme. · Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics. · Elaborate study of classical logics and control operators. · Account of dialogue games for classical and intuitionistic logic. · Theoretical foundations of computer-assisted reasoning

Logic Colloquium '88

Author: R. Ferro,C. Bonotto,S. Valentini,A. Zanardo

Publisher: Elsevier

ISBN: 9780080887678

Category: Mathematics

Page: 402

View: 560

The result of the European Summer Meeting of the Association for Symbolic Logic, this volume gives an overview of the latest developments in most of the major fields of logic being actively pursued today. As well as selected papers, the two panel discussions are also included, on ``Trends in Logic'' and ``The Teaching of Logic''.

Advances in Linear Logic

Author: Jean-Yves Girard,Yves Lafont,Laurent Regnier

Publisher: Cambridge University Press

ISBN: 9780521559614

Category: Mathematics

Page: 389

View: 7764

Linear logic, introduced in 1986 by J.-Y. Girard, is based upon a fine grain analysis of the main proof-theoretical notions of logic. The subject develops along the lines of denotational semantics, proof nets and the geometry of interaction. Its basic dynamical nature has attracted computer scientists, and various promising connections have been made in the areas of optimal program execution, interaction nets and knowledge representation. This book is the refereed proceedings of the first international meeting on linear logic held at Cornell University, in June 1993. Survey papers devoted to specific areas of linear logic, as well as an extensive general introduction to the subject by J.-Y. Girard, have been added, so as to make this book a valuable tool both for the beginner and for the advanced researcher.

Lectures on Soft Computing and Fuzzy Logic

Author: Antonio Di Nola,Giangiacomo Gerla

Publisher: Springer Science & Business Media

ISBN: 9783790813968

Category: Computers

Page: 337

View: 6389

The present volume collects selected papers arising from lectures delivered by the authors at the School on Fuzzy Logic and Soft Computing held during the years 1996/97/98/99 and sponsored by the Salerno University. The authors contributing to this volume agreed with editors to write down, to enlarge and, in many cases, to rethink their original lectures, in order to offer to readership, a more compact presentation of the proposed topics. The aim of the volume is to offer a picture, as a job in progress, of the effort that is coming in founding and developing soft computing's techniques. The volume contains papers aimed to report on recent results containing genuinely logical aspects of fuzzy logic. The topics treated in this area cover algebraic aspects of Lukasiewicz Logic, Fuzzy Logic as the logic of continuous t-norms, Intuitionistic Fuzzy Logic. Aspects of fuzzy logic based on similar ity relation are presented in connection with the problem of flexible querying in deductive database. Departing from fuzzy logic, some papers present re sults in Probability Logic treating computational aspects, results based on indishernability relation and a non commutative version of generalized effect algebras. Several strict applications of soft computing are presented in the book. Indeed we find applications ranging among pattern recognition, image and signal processing, evolutionary agents, fuzzy cellular networks, classi fication in fuzzy environments. The volume is then intended to serve as a reference work for foundational logico-algebraic aspect of Soft Computing and for concrete applications of soft computing technologies.

The Syntax of Anaphoric Binding

Author: Mary Dalrymple

Publisher: Center for the Study of Language (CSLI)

ISBN: 9781881526063

Category: Language Arts & Disciplines

Page: 188

View: 6912

Mary Dalrymple provides a theory of the syntax of anaphoric binding, couched in the framework of Lexical-Functional Grammar. Cross-linguistically, anaphoric elements vary a great deal. One finds long- and short-distance reflexives, sometimes within the same language; pronominals may require local noncoreference or coreference only with nonsubjects. Analyses of the syntax of anaphoric binding which have attempted to fit all languages into the mold of English are inadequate to account for the rich range of syntactic constraints that are attested. How, then, can the cross-linguistic regularities exhibited by anaphoric elements be captured, while at the same time accounting for the diversity that is found? Dalrymple shows that syntactic constraints on anaphoric binding can be expressed in terms of just three grammatical concepts: subject, predicate, and tense. These concepts define a set of complex constraints, combinations of which interact to predict the wide range of universally available syntactic conditions that anaphoric elements obey. Mary Dalrymple is a member of the research staff of the Natural Language Theory and Technology group at the Xerox Palo Alto Research Center.

The Blind Spot

Lectures on Logic

Author: Jean-Yves Girard

Publisher: European Mathematical Society

ISBN: 9783037190883

Category: Mathematics

Page: 537

View: 3823

Popular Lectures on Mathematical Logic

Author: Hao Wang

Publisher: Courier Corporation

ISBN: 0486171043

Category: Mathematics

Page: 292

View: 4292

Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.

Typed Lambda Calculi and Applications

International Conference on Typed Lambda Calculi and Applications, TLCA : Proceedings

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Lambda calculus

Page: N.A

View: 8447

Logical Foundations of Computer Science

4th International Symposium, LFCS'97, Yaroslavl, Russia, July, 6 - 12, 1997, Proceedings

Author: Sergei Adian,Anil Nerode

Publisher: Springer

ISBN: N.A

Category: Computers

Page: 431

View: 5388

This book constitutes the refereed proceedings of the 4th International Symposium on Logical Foundations of Computer Science, LFCS'97, held in Yaroslavl, Russia, in July 1997. The volume presents 42 revised refereed papers carefully selected by the program committee. All current issues of computer science logic are addressed. There is a certain emphasis on reporting the progress achieved by scientists from various parts of the former Soviet Union; but there are also many other strong papers from the international research community.

Lectures on Petri Nets I: Basic Models

Advances in Petri Nets

Author: Wolfgang Reisig,Grzegorz Rozenberg

Publisher: Springer Science & Business Media

ISBN: 9783540653066

Category: Computers

Page: 691

View: 8002

The two-volume set originates from the Advanced Course on Petri Nets held in Dagstuhl, Germany in September 1996; beyond the lectures given there, additional chapters have been commissioned to give a well-balanced presentation of the state of the art in the area. Together with its companion volume "Lectures on Petri Nets II: Applications" this book is the actual reference for the area and addresses professionals, students, lecturers, and researchers who are - interested in systems design and would like to learn to use Petri nets familiar with subareas of the theory or its applications and wish to view the whole area - interested in learning about recent results presented within a unified framework - planning to apply Petri nets in practical situations - interested in the relationship of Petri nets to other models of concurrent systems.

Towards new logic and semantics

Franco-Japanese collaborative lectures on philosophy of logic

Author: Jocelyn Benoist,Jean-Yves Girard,Yoshinori Ogawa

Publisher: N.A

ISBN: N.A

Category:

Page: 263

View: 1337

David Hilbert’s Lectures on the Foundations of Geometry 1891–1902

Author: Michael Hallett,Ulrich Majer

Publisher: Springer Science & Business Media

ISBN: 9783540643739

Category: Mathematics

Page: 661

View: 7316

This volume contains six sets of notes for lectures on the foundations of geometry held by Hilbert in the period 1891-1902. It also reprints the first edition of Hilbert’s celebrated Grundlagen der Geometrie of 1899, together with the important additions which appeared first in the French translation of 1900. The lectures document the emergence of a new approach to foundational study and contain many reflections and investigations which never found their way into print.

Linear Logic in Computer Science

Author: Thomas Ehrhard

Publisher: Cambridge University Press

ISBN: 9780521608572

Category: Computers

Page: 381

View: 9475

This book illustrates linear logic in the application of proof theory to computer science.

Lectures on the Ricci Flow

Author: Peter Topping

Publisher: Cambridge University Press

ISBN: 0521689473

Category: Mathematics

Page: 113

View: 3844

An introduction to Ricci flow suitable for graduate students and research mathematicians.

Lectures on Profinite Topics in Group Theory

Author: Benjamin Klopsch,Nikolay Nikolov,Christopher Voll

Publisher: Cambridge University Press

ISBN: 1139495658

Category: Mathematics

Page: N.A

View: 3273

In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. The final chapter provides an overview of zeta functions associated to groups and rings. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.

Lectures on Functional Analysis and Applications

Author: Vladimir Semenovich Pugachev,Igor? Nikolaevich Sinit?s?yn

Publisher: World Scientific

ISBN: 9789810237233

Category: Mathematics

Page: 730

View: 8808

This book is intended for those having only a moderate background in mathematics, who need to increase their mathematical knowledge for development in their areas of work and to read the related mathematical literature. The material covered, which includes practically all the information on functional analysis that may be necessary for those working in various areas of applications of mathematics, as well as the simplicity of presentation, differentiates this book from others. About 300 examples and more than 500 problems are provided to help readers understand and master the theories presented. The list of references enables readers to explore those topics in which they are interested, and gather further information about applications used as examples in the book.Applications: Probability Theory and Statistics, Signal and Image Processing, Systems Analysis and Design.