Mathematical Principles of Fuzzy Logic
|
|
- Anthony Norris
- 5 years ago
- Views:
Transcription
1 Mathematical Principles of Fuzzy Logic
2 THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE
3 MATHEMATICAL PRINCIPLES OF FUZZY LOGIC VILEM N O V K University of Ostrava Institute for Research and Applications of Fuzzy Modeling Brafova 7, Ostrava 1, Czech Republic IRINA PERFILIEVA Moscow State Academy of Instrument Making Stromynka 20, Moscow, Russia and University of Ostrava Institute for Research and Applications of Fuzzy Modeling Brafova 7, Ostrava 1, Czech Republic JIRI MOCKOR University of Ostrava Institute for Research and Applications of Fuzzy Modeling Brafova 7, Ostrava 1, Czech Republic... " Springer-Science+Business Media, LLC
4 Library of Congress Cataloging-in-Publication Data Novak, Vilem. Mathematical principles of fuzzy logic I Vilem Novak, Irina Perfilieva and Jiri Mockor. p. cm. -- (The Kluwer international series in engineering and computer science ; secs 517) Includes bibliographical references and index. ISBN ISBN (ebook) DOI / Fuzzy logic. 1. Perfilieva, Irina II. Mockof, Jin. III. Title. IV. Series. QA9.64.N dc CIP Copyright 1999 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 1999 Softcover reprint ofthe hardcover Ist edition 1999 AII rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer-8cience+Business Media, LLC. Printed an acid-free paper.
5 To David and Martin, to Vitalij, to Sona, Marek and Katerina, with love
6 Contents Preface xi 1. FUZZY LOGIC: WHAT, WHY, FOR WHICH? Vagueness and Uncertainty Vagueness and Fuzzy Sets What Is Fuzzy Logic Outline of the Agenda of Fuzzy Logic ALGEBRAIC STRUCTURES FOR LOGICAL CALCULI Algebras for Logics Boolean algebras Residuated lattices and MV-algebras Filters and Representation Theorems Elements of the theory of t-norms Introduction to Topos Theory T opos theory Lattice of subobjects in topos LOGICAL CALCULI AND MODEL THEORY Classical Logic Propositional logic Predicate logic Many-sorted predicate logic Classical Model Theory Formal Logical Systems Model Theory in Categories FUZZY LOGIC IN NARROW SENSE Graded Formal Logical Systems Truth Values Intuition on truth values and operations with them Truth values as algebras Why Lukasiewicz algebra Enriching structure of truth values Predicate Fuzzy Logic of First-Order 114
7 Vlll MATHEMATICAL PRINCIPLES OF FUZZY LOGIC Syntax and semantics Basic properties of fuzzy theories Consistency of fuzzy theories Extension of fuzzy theories Henkin fuzzy theories Complete fuzzy theories Lindenbaum algebra of formulas and its properties Completeness theorems Sorites fuzzy theories Partial inconsistency and the consistency threshold Additional connectives Disposing irrational logical constants 4.4 Fuzzy Theories with Equality and Open Fuzzy Theories Fuzzy theories with equality Consistency theorem in fuzzy logic Herbrand theorem in fuzzy logic 4.5 Model Theory in Fuzzy Logic Basic concepts of fuzzy model theory Chains of models Ultraproduct theorem 4.6 Recursive Properties of Fuzzy Theories FUNCTIONAL SYSTEMS IN FUZZY LOGIC THEORIES Fuzzy Logic Functions and Their Representation by Formulas Formulas and their relation to fuzzy logic functions Piecewise linear functions and their representation by formulas Normal Forms for FL-Functions and Formulas of Propositional Fuzzy Logic Normal forms for L-valued FL-functions Normal forms for functions represented by formulas FL-Relations and Their Connection with Formulas of Predicate Fuzzy Logic FL-Relations and Their Representation by Formulas Normal Forms and Approximation Theorems Representation of FL-relations and Consistency of Fuzzy Theories Approximation of Continuous Functions by Fuzzy Logic Normal Forms Approximation of continuous functions through FL- relations Approximation of continuous functions determined by a defuzzification operation Representation of Continuous Functions by the Conjunctive Normal Form FUZZY LOGIC IN BROADER SENSE Partial Formalization of Natural Language Evaluating and simple conditional linguistic syntagms Translation of evaluating syntagms and predications into fuzzy logic The meaning of simple evaluating syntagms Formal Scheme of FLb Special Theories in FLb Independence of formulas Deduction on simple linguistic descriptions Fuzzy approximation based on simple linguistic descriptions 249
8 Contents IX 7. TOPOl AND CATEGORIES OF FUZZY SETS 7.1 Category of O-sets as generalization of fuzzy sets 7.2 Category of O-fuzzy sets O-fuzzy sets over MV-algebras 7.3 Interpretation of formulas in the category CO - Set 8. FEW HISTORICAL AND CONCLUDING REMARKS References Index
9 Preface This book is an attempt to provide a systematic course of the formal theory of fuzzy logic. We made a lot of effort to be precise, but at the same time to explain the motivation and interpretation of all the results and, if possible, to accompany the theory by examples. There are a lot of other books on various aspects of fuzzy logic. Our book is more specific from the point of view of several aspects. First, it is based on logical formalism demonstrating that fuzzy logic is a well developed logical theory. Second, it includes the theory of functional systems in fuzzy logic, which provide explanation of what, and how can be represented by formulas of fuzzy logic calculi. Third, except for the generalization of the classical way of interpretation within the environment of fuzzy sets constructed over classical sets, it also presents much more general interpretation of fuzzy logic within the environment of other proper categories of fuzzy sets stemming either from the topos theory, or even generalizing the latter. Last but not least, the leading philosophical point of view is presentation of fuzzy logic especially as the theory of vagueness as well as the theory of the common-sense human reasoning, which is based on the use of natural language, the distinguished feature of which is vagueness of its semantics. We expect the book to be read by people interested in fuzzy logic and related areas, and also by logicians, mathematicians and computer scientists interested in mathematical aspects of fuzzy logic. It can be used in special courses of fuzzy logic, artificial and computational intelligence, in master and post-gradual university studies, in advanced courses on various applications including fuzzy control, decision-making and others. The book is divided into eight chapters. The first chapter is introductory and it provides motivation for the development of fuzzy logic, describes its structure and outlines its potential for applications. Fuzzy logic is there divided into that in narrow sense (FLn), which is a special many-valued logic aiming at description of the vagueness phenomenon and that in broader sense (FLb), whose aim is to provide a formal theory for modeling of natural human deduction based on the use of natural language. It is argued that characterization of the vagueness phenomenon is fundamental for further development of fuzzy logic as well as its applications.
10 xii MATHEMATICAL PRINCIPLES OF FUZZY LOGIC The second chapter is an overview of the basic algebraic concepts necessary for characterization of the structure of truth values and for understanding to the subsequent chapters. The third chapter briefly reminds basic concepts of classical logic, and also the notation which is employed further. The main chapters of the book are fourth to seventh. The fourth chapter contains explanation of fuzzy logic in narrow sense. We confine ourselves mainly to fuzzy logic based on the Lukasiewicz algebra of the truth values. Many reasons have been given arguing that this requirement is a necessary consequence of the assumptions, which seem to be natural and convincing. Among them, essential are continuity of the connectives (this follows from the conviction that vagueness phenomenon requires continuity) and completeness (balance between syntax and semantics). We prove lemmas and theorems characterizing behaviour of FLn, including deduction, contradiction, and others. The main result is the completeness theorem. Besides this, we also outline fundamentals of the model theory and discuss questions concerning computability. The fifth chapter describes functional systems related to propositional and predicate calculi of fuzzy logic. A notable role here is played by the well known McNaughton theorem. We provide a constructive proof of it and then, deduce a canonical representation of formulas of propositional fuzzy logic as well as some special representation of formulas of predicate fuzzy logic. A special attention has been paid to the generalization of disjunctive and conjunctive normal forms into fuzzy logic. Among the main properties of them, the ability to represent approximately continuous functions including evaluation of the quality of the approximation has been investigated. The sixth chapter extends the previous theory to obtain a theory of parts of natural language to constitute fuzzy logic in broader sense. We present a formalization of the concepts of intension and extension, evaluating linguistic syntagms and linguistic description (a set of IF-THEN rules), and demonstrate some theorems characterizing their behaviour. The seventh chapter is more abstract and deals with fuzzy sets and fuzzy logic within category theory. First, we present properties of three possible categories of fuzzy sets. The subsequent sections provide the reader with a general picture of fuzzy logic interpreted in top os and its place in topos logic. We tried to show two possible approaches. The first one is based on top os theory and Heyting algebra structures defined on the set of subobjects. The second one is based on the MV -algebra structures defined on these sets. In this book, we present some of the results and consequences, which could be useful from the point of view of fuzzy set theory. In particular, we tried to show explicitly similarities between the obtained categories and topoi, and to show how the internal logic in these categories could be directly developed. The book is concluded by a short, eighth chapter giving a brief overview of the history of fuzzy logic and outlining some of its actual problems to be solved in the future. Sections 2.4, 3.4 and Chapter 7 have been written by J. Mockor. Chapter 5 has been written by 1. Perfilieva and Chapters 4 and 6 by V. Novak. The rest has has been written by by the latter two authors together.
11 PREFACE xiii This book has been prepared mostly in the Institute for Research and Applications of Fuzzy Modeling of the University of Ostrava, Czech Republic, which has been established on the basis of the project VS of the Ministry of Education, Youth and Physical Training of the Czech Republic. Some parts have been prepared also in the Moscow State Academy of Instrument-Making and Informatics, Russia, and Institute of the Theory of Information and Automation of the Academy of Sciences of the Czech Republic. We wish to express our thanks to all who helped us in the preparation of this book. On the first place, we thank to people whose work has been for us the main source of knowledge and inspiration, namely P. Hajek from UI AS OR, U. Hahle from the University of Wuppertal, D. Mundici form the University of Milano and A. dinola from the University of Salerno. Further, we thank to the people who have read the manuscript and helped us to improve it on many places, namely to R. Belohlavek and A. Dvorak from IRAFM, University of Ostrava, and to S. Gottwald from the University of Leipzig. We want also to thank to our Chinese friends, M. Ying and G. Chen from Beijing Tschingua University, and G. Wang from ShaanXi Normal University for their hospitality, which helped to write some parts of this book during the stay of the first two authors in China. Last but not least, we want to thank to Prof. T. Kreck, director of the Institut fur Mathematik in Oberwolfach, and also to other workers of it for providing us unexceptionable working conditions in which significant portions of the book have been written. Ostrava, May 1999 Vilem Novak, Irina Perfilieva, Jiif Mockof
METAMATHEMATICS OF FUZZY LOGIC
METAMATHEMATICS OF FUZZY LOGIC TRENDS IN LOGIC Studia Logica Library VOLUME 4 Managing Editor Ryszard Wojcicki, Institute ofphilosophy and Sociology, Polish Academy ofsciences, Warsaw, Poland Editors Petr
More informationLOGIC, LANGUAGE AND REASONING
LOGIC, LANGUAGE AND REASONING TRENDS IN LOGIC Studia Logica Library VOLUME 5 Managing Editor Ryszard W6jcicki, Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland Editors
More informationBirkhäuser Advanced Texts
Birkhäuser Advanced Texts Basler Lehrbücher Edited by Herbert Amann, University of Zürich Steven G. Krantz, Washington University, St. Louis Shrawan Kumar, University of North Carolina at Chapel Hili Steven
More informationLattice-Ordered Groups. An Introduction
Lattice-Ordered Groups An Introduction Reidel Texts in the Mathematical Sciences A Graduate-Level Book Series Lattice-Ordered Groups An Introduction by Marlow Anderson The Colorado College, Colorado Springs,
More informationStudies in Natural Language and Linguistic Theory
THE MANDARIN VP Studies in Natural Language and Linguistic Theory VOLUME 44 Managing Editors Liliane Haegeman, University a/geneva Joan Maling, Brandeis University James McCloskey, University a/california,
More informationFormal Concept Analysis
Formal Concept Analysis Springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo Bernhard Ganter Rudolf Wille Formal Concept Analysis Mathematical Foundations With 105
More informationQuality Assurance in Seafood Processing: A Practical Guide
Quality Assurance in Seafood Processing: A Practical Guide Quality Assurance in Seafood Processing: A Practical Guide A. D. Bonnell SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. 1994 Springer Science+Business
More informationModule 11. Reasoning with uncertainty-fuzzy Reasoning. Version 2 CSE IIT, Kharagpur
Module 11 Reasoning with uncertainty-fuzzy Reasoning 11.1 Instructional Objective The students should understand the use of fuzzy logic as a method of handling uncertainty The student should learn the
More informationIntroduction p. 1 The Elements of an Argument p. 1 Deduction and Induction p. 5 Deductive Argument Forms p. 7 Truth and Validity p. 8 Soundness p.
Preface p. xi Introduction p. 1 The Elements of an Argument p. 1 Deduction and Induction p. 5 Deductive Argument Forms p. 7 Truth and Validity p. 8 Soundness p. 11 Consistency p. 12 Consistency and Validity
More informationNon-Classical Logics. Viorica Sofronie-Stokkermans Winter Semester 2012/2013
Non-Classical Logics Viorica Sofronie-Stokkermans E-mail: sofronie@uni-koblenz.de Winter Semester 2012/2013 1 Non-Classical Logics Alternatives to classical logic Extensions of classical logic 2 Non-Classical
More informationPROBLEMS OF SEMANTICS
PROBLEMS OF SEMANTICS BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE EDITED BY ROBERT S. COHEN AND MARX W. WARTOFSKY VOLUME 66 LADISLA V TONDL PROBLEMS OF SEMANTICS A Contribution to the Analysis of the Language
More information'if it was so, it might be; and if it were so, it would be: but as it isn't, it ain't. That's logic'
Basic Digital Electronics 'Contrariwise,' continued Tweedledee, 'if it was so, it might be; and if it were so, it would be: but as it isn't, it ain't. That's logic' (Carroll: Alice Through the Looking
More informationLOCALITY DOMAINS IN THE SPANISH DETERMINER PHRASE
LOCALITY DOMAINS IN THE SPANISH DETERMINER PHRASE Studies in Natural Language and Linguistic Theory VOLUME 79 Managing Editors Marcel den Dikken, City University of New York Liliane Haegeman, University
More informationTen Essays in the Development of Economic Thought. Ronald L. Meek Tyler Professor of Economics at the University of Leicester
SMITH, MARX, & AFTER SMITH, MARX, & AFTER Ten Essays in the Development of Economic Thought Ronald L. Meek Tyler Professor of Economics at the University of Leicester SPRINGER-SCIENCE+BUSINESS MEDIA. B.V.
More informationA Hybrid Theory of Metaphor
A Hybrid Theory of Metaphor A Hybrid Theory of Metaphor Relevance Theory and Cognitive Linguistics Markus Tendahl University of Dortmund, Germany Markus Tendahl 2009 Softcover reprint of the hardcover
More informationHigh-Frequency Trading and Probability Theory
High-Frequency Trading and Probability Theory East China Normal University Scientific Reports Chief Editor Weian Zheng Changjiang Chair Professor School of Finance and Statistics East China Normal University,
More informationDamage Mechanics with Finite Elements
Damage Mechanics with Finite Elements Springer-Verlag Berlin Heidelberg GmbH P. 1. Kattan. G. Z. Voyiadjis Damage Mechanics with Finite Elements Practical Applications with Computer Tools With 28 Figures
More informationSYNTHESE LIBRARY STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE. JAAKKO HINTIKKA, Boston University
NAMING THE RAINBOW SYNTHESE LIBRARY STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE Managing Editor: JAAKKO HINTIKKA, Boston University Editors: DIRK VAN DALEN, University of Utrecht,
More informationPhilosophy of Development
Philosophy of Development Philosophy and Education VOLUME 8 Series Editors: C. J. B. Macmillan College ofeducation, The Florida State University, Tallahassee D. C. Phillips School ofeducation, Stanford
More informationTHE COUNTER-CREATIONISM HANDBOOK
THE COUNTER-CREATIONISM HANDBOOK This page intentionally left blank THE COUNTER-CREATIONISM HANDBOOK Mark Isaak University of California Press Berkeley Los Angeles London University of California Press,
More informationMULTIMEDIA SIGNALS AND SYSTEMS
MULTIMEDIA SIGNALS AND SYSTEMS THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE MULTIMEDIA SIGNALS ANDSYSTEMS Mrinal Kr. Mandal University of Alberta, Canada SPRINGER SCIENCE+BUSINESS
More informationTHE THEORY OF BEAUTY IN THE CLASSICAL AESTHETICS OF JAPAN
THE THEORY OF BEAUTY IN THE CLASSICAL AESTHETICS OF JAPAN The series "Philosophy and World Community" appears under the auspices of the International Federation of Philosophical Societies and of the Conseil
More informationANNOTATED BIBLIOGRAPHY OF CORPORATE FINANCE
ANNOTATED BIBLIOGRAPHY OF CORPORATE FINANCE ANNOTATED BIBLIOGRAPHY OF CORPORATE FINANCE Compiled by Roger and Eva Lister Roger and Eva Lister 1979 Softcover reprint of the hardcover 15t edition 1979 978-0-333-18399-1
More informationTEXT ENCODING INITIATIVE
TEXT ENCODING INITIATIVE Text Encoding Initiative Background and Context Edited by Nancy Ide Department o/computer Science, Vassar College, Poughkeepsie, NY, USA AND J ean Veronis Laboratoire Parole et
More informationThis page intentionally left blank
Terrorism This page intentionally left blank Terrorism Origins and Evolution James M. Lutz and Brenda J. Lutz TERRORISM James M. Lutz and Brenda J. Lutz, 2005. Softcover reprint of the hardcover 1st edition
More informationPolymer Technology Dictionary
Polymer Technology Dictionary Polymer Technology Dictionary Tony Whelan MSC, Consultant Formerly Director London Polymer Consultants Ltd New Southgate, London, UK SPRINGER-SCIENCE+BUSINESS MEDIA, B.V First
More informationAbbreviations and Acronyms in Medicine and Nursing
Abbreviations and Acronyms in Medicine and Nursing SOLOMON GARB, M.D., F.A.C.P. Scientific Director, Associate Clinica[ Professor of Medicine, University ofcolorado Me.dical College ELEANOR KRAKAUER Medical
More informationProblem Books in Mathematics
Problem Books in Mathematics Series Editor: Peter Winkler Department of Mathematics Dartmouth College Hanover, NH 03755 USA More information about this series at http://www.springer.com/series/714 Hayk
More informationIS SCIENCE PROGRESSIVE?
IS SCIENCE PROGRESSIVE? SYNTHESE LIBRARY STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE Managing Editor: JAAKKO HINTIKKA, Florida State University, Tallahassee Editors: DONALD DAVIDSON,
More informationHANDBOOK OF RECORDING ENGINEERING
HANDBOOK OF RECORDING ENGINEERING HANDBOOK OF RECORDING ENGINEERING John Eargle Inm51 VAN NOSTRAND REINHOLD COMPANY ~ New York ISBN 978-94-010-9368-2 ISBN 978-94-010-9366-8 (ebook) 001 10.1007/978-94-010-9366-8
More informationTHEORY AND APPLICATIONS OF SPECIAL FUNCTIONS. A Volume Dedicated to Mizan Rahman
- - - - -- - THEORY AND APPLICATIONS OF SPECIAL FUNCTIONS A Volume Dedicated to Mizan Rahman Developments in Mathematics VOLUME 13 Series Editor: Krishnaswami Alladi, University of Florida, U.S.A. Aims
More informationCOMPUTER ENGINEERING SERIES
COMPUTER ENGINEERING SERIES Musical Rhetoric Foundations and Annotation Schemes Patrick Saint-Dizier Musical Rhetoric FOCUS SERIES Series Editor Jean-Charles Pomerol Musical Rhetoric Foundations and
More informationHow to Write Technical Reports
How to Write Technical Reports Lutz Hering Heike Hering How to Write Technical Reports Understandable Structure, Good Design, Convincing Presentation 123 Dr. Lutz Hering Am Ricklinger Holze 14 30966 Hemmingen
More informationSeeing Film and Reading Feminist Theology
Seeing Film and Reading Feminist Theology This page intentionally left blank Seeing Film and Reading Feminist Theology A Dialogue Ulrike Vollmer SEEING FILM AND READING FEMINIST THEOLOGY Copyright Ulrike
More informationErgebnisse der Mathematik und ihrer Grenzgebiete
Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge. Band 26 A Series of Modem Surveys in Mathematics Editorial Board E. Bombieri, Princeton S. Feferman, Stanford M. Gromov, Bures-sur-Yvette H.W.
More informationEATCS Monographs on Theoretical Computer Science
EATCS Monographs on Theoretical Computer Science Volume 23 Editors: W. Brauer G. Rozenberg A. Salomaa Advisory Board: G.Ausiello M.Broy S.Even IHartmanis N.Jones T. Leighton M.Nivat C. Papadimitriou D.
More informationFuzzy Logic as a Theory of Vagueness: 15 Conceptual Questions
Fuzzy Logic as a Theory of Vagueness: 15 Conceptual Questions Jeremy Bradley Vienna University of Technology jeremy.bradley@gmx.net Abstract In spite of its successes as a tool in the field of engineering,
More informationHardy and the Erotic
HARDY AND THE EROTIC Hardy and the Erotic T. R. Wright Lecturer in English The University of Newcastle upon Tyne Palgrave Macmillan ISBN 978-1-349-09021-1 ISBN 978-1-349-09019-8 (ebook) DOI 10.1007/978-1-349-09019-8
More informationShakespeare: The Tragedies
Shakespeare: The Tragedies ANALYSING TEXTS General Editor: Nicholas Marsh Chaucer: The Canterhury Tales Gail Ashton Shakespeare: The Tragedies Nicholas Marsh Virginia Woolf: The Novels Nicholas Marsh Jane
More informationASPECTS OF ARISTOTLE'S LOGIC OF MODALITIES
ASPECTS OF ARISTOTLE'S LOGIC OF MODALITIES SYNTHESE HISTORICAL LIBRARY TEXTS AND STUDIES IN THE IllSTORY OF LOGIC AND PIffi.,OSOPHY Editors: N. KRETZMANN, Cornell University G. NUCHELMANS, University of
More informationIMAGE AND TEXT COMPRESSION
IMAGE AND TEXT COMPRESSION THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE COMMUNICATIONS AND INFORMATION TIlEORY Other books in the series: Consulting Editor: Robert Gallager Digital
More informationThe Concept of Nature
The Concept of Nature The Concept of Nature The Tarner Lectures Delivered in Trinity College B alfred north whitehead University Printing House, Cambridge CB2 8BS, United Kingdom Cambridge University
More informationPERFUMES ART, SCIENCE AND TECHNOLOGY
PERFUMES ART, SCIENCE AND TECHNOLOGY PERFUMES ART, SCIENCE AND TECHNOLOGY Edited by P. M. MÜLLER and D. LAMPARSKY Givaudan Research Company Ltd, CH-8600 Dübendorf, Zürich, Switzerland Springer-Science+Business
More informationThe New European Left
The New European Left This page intentionally left blank The New European Left A Socialism for the Twenty-First Century? By Kate Hudson Visiting Research Fellow, Department of Social Sciences, London South
More informationCorpus Approaches to Critical Metaphor Analysis
Corpus Approaches to Critical Metaphor Analysis Corpus Approaches to Critical Metaphor Analysis Jonathan Charteris-Black Jonathan Charteris-Black, 2004 Softcover reprint of the hardcover 1st edition 2004
More informationNarrative Dimensions of Philosophy
Narrative Dimensions of Philosophy This page intentionally left blank Narrative Dimensions of Philosophy A Semiotic Exploration in the Work of Merleau-Ponty, Kierkegaard and Austin Sky Marsen Victoria
More informationOUT OF REACH THE POETRY OF PHILIP LARKIN
OUT OF REACH THE POETRY OF PHILIP LARKIN Also by Andrew Swarbrick THE ART OF OLIVER GOLDSMITH (editor) PHILIP LARKIN: The Whitsun Weddings and The Less Deceived T. S. ELIOT: Selected Poems Out of Reach
More informationPaul M. Gauthier. Lectures on Several Complex
Paul M. Gauthier Lectures on Several Complex Variables Paul M. Gauthier Départment de Mathématiques et de Statistique Université de Montréal Montreal, QC, Canada ISBN 978-3-319-11510-8 ISBN 978-3-319-11511-5
More informationAppraising Research: Evaluation in Academic Writing
Appraising Research: Evaluation in Academic Writing Also by Susan Hood ACADEMIC ENCOUNTERS: LIFE IN SOCIETY (with Kristine Brown) Appraising Research: Evaluation in Academic Writing Susan Hood University
More informationZdravko Cvetkovski. Inequalities. Theorems, Techniques and Selected Problems
Inequalities Zdravko Cvetkovski Inequalities Theorems, Techniques and Selected Problems Dipl. Math. Zdravko Cvetkovski Informatics Department European University-Republic of Macedonia Skopje, Macedonia
More informationScreening Post-1989 China
Screening Post-1989 China This page intentionally left blank Screening Post-1989 China Critical Analysis of Chinese Film and Television Wing Shan Ho screening post-1989 china Copyright Wing Shan Ho, 2015.
More informationComputability and Logic, Fifth Edition
Computability and Logic, Fifth Edition Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple
More informationPublications des Archives Henri-Poincaré Publications of the Henri Poincaré Archives
Publications des Archives Henri-Poincaré Publications of the Henri Poincaré Archives Textes et Travaux, Approches Philosophiques en Logique, Mathématiques et Physique autour de 1900 Texts, Studies and
More information1 Introduction. Radim Belohlavek and George J. Klir
1 Introduction Radim Belohlavek and George J. Klir 1.1 Concepts and Fuzzy Logic 1.2 From Classical Logic to Fuzzy Logic 1.3 Fuzzy Logic in the Psychology of Concepts 1.4 Summary of the Book Note References
More informationIntroduction Section 1: Logic. The basic purpose is to learn some elementary logic.
1 Introduction About this course I hope that this course to be a practical one where you learn to read and write proofs yourselves. I will not present too much technical materials. The lecture pdf will
More informationReadability: Text and Context
Readability: Text and Context Also by Alan Bailin THE CRITICAL ASSESSMENT OF RESEARCH Traditional and New Methods of Evaluation ( co- authored) METAPHOR AND THE LOGIC OF LANGUAGE USE Also by Ann Grafstein
More informationINTUITION IN SCIENCE AND MATHEMATICS
INTUITION IN SCIENCE AND MATHEMATICS MATHEMATICS EDUCATION LIBRARY Managing Editor A. J. Bishop, Cambridge, U.K. Editorial Board H. Bauersfeld, Bielefeld, Germany H. Freudenthal, Utrecht, Holland J. Kilpatnck,
More informationAlso by Brian Rosebury and from the same publisher ART AND DESIRE: A STUDY IN THE AESTHETICS OF FICTION
TOLKIEN Also by Brian Rosebury and from the same publisher ART AND DESIRE: A STUDY IN THE AESTHETICS OF FICTION TOLKIEN A Cultural Phenomenon BRIAN ROSEBURY Principal Lecturer Department of Humanities
More informationHYDRAULIC AND ELECTRIC-HYDRAULIC CONTROL SYSTEMS
HYDRAULIC AND ELECTRIC-HYDRAULIC CONTROL SYSTEMS Hydraulic and Electric-Hydraulic Control Systems Second Enlarged Edition by R.B. WALTERS Engineering Consultant. Wembley, U.K. SPRINGER-SCTENCE+BUSINESS
More informationNumerical Analysis. Ian Jacques and Colin Judd. London New York CHAPMAN AND HALL. Department of Mathematics Coventry Lanchester Polytechnic
Numerical Analysis Numerical Analysis Ian Jacques and Colin Judd Department of Mathematics Coventry Lanchester Polytechnic London New York CHAPMAN AND HALL First published in 1987 by Chapman and Hall Ltd
More informationW riting Performances
Writing Performances Writing Performances: The Stages of Dorothy L. Sayers Crystal Downing WRITING PERFORMANCES Crystal Downing, 2004 Softcover reprint of the hardcover 1st edition 2004 978-1-4039-6452-6
More informationTHE PRIX VOLNEY ESSAY SERIES
THE PRIX VOLNEY ESSAY SERIES PRIX VOLNEY ESSAY SERIES Editor JOAN LEOPOLD Advisory Committee HANS AARSLEFF, Princeton University HERBERT E. BREKLE, Regensburg University YAKOV MALKIEL, (d. 1998), University
More informationEPISTEMOLOGY, METHODOLOGY, AND THE SOCIAL SCIENCES
EPISTEMOLOGY, METHODOLOGY, AND THE SOCIAL SCIENCES BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE EDITED BY ROBERT S. COHEN AND MARX W. WARTOFSKY VOLUME 71 EPISTEMOLOGY, METHODOLOGY, AND THE SOCIAL SCIENCES
More informationTOLKIEN: A CRITICAL ASSESSMENT
TOLKIEN: A CRITICAL ASSESSMENT Also by Brian Rosebury and from the same publishers ART AND DESIRE: A STUDY IN THE AESTHETICS OF FICTION Tolkien A Critical Assessment BRIAN ROSEBURY Principal Lecturer i"
More informationNUTS AND BOLTS FOR THE SOCIAL SCIENCES
NUTS AND BOLTS FOR THE SOCIAL SCIENCES Nuts and Bolts for the Social Sciences JON ELSTER CAMBRIDGE UNIVERSITY PRESS cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore,
More informationMax Weber and Postmodern Theory
Max Weber and Postmodern Theory This page intentionally left blank Max Weber and Postmodern Theory: Rationalization versus Re-enchantment Nicholas Gane Nicholas Gane 2002 Softcover reprint of the hardcover
More informationMichel Foucault: Personal Autonomy and Education
Michel Foucault: Personal Autonomy and Education Philosophy and Education VOLUME 7 Series Editors: C. J. B. Macmillan College of Education. The Florida State University. Tallahassee D. C. Phillips School
More informationAnimal Dispersal. Small mammals as a model. WILLIAM Z. LIDICKER, JR Museum of Vertebrate Zoology, University of California, Berkeley, USA
Animal Dispersal Animal Dispersal Small mammals as a model Edited by NILS CHR. STENSETH Department of Biology, University of Oslo, Norway and WILLIAM Z. LIDICKER, JR Museum of Vertebrate Zoology, University
More informationHANDBOOK OF RECORDING ENGINEERING FOURTH EDITION
HANDBOOK OF RECORDING ENGINEERING FOURTH EDITION HANDBOOK OF RECORDING ENGINEERING FOURTH EDITION by John Eargle JME Consulting Corporation Springe] John Eargle JME Consulting Corporation Los Angeles,
More informationThe. Craft of. Editing
The Craft of Editing Springer Science+ Business Media, LLC The Craft of Editing A Guide for Managers, Scientists, and Engineers Michael Alley. ~. T Springer Michael Alley College of Engineering VIrginia
More informationMedia Literacy and Semiotics
Media Literacy and Semiotics Semiotics and Popular Culture Series Editor: Marcel Danesi Written by leading figures in the interconnected fields of popular culture, media, and semiotic studies, the books
More informationJourney through Mathematics
Journey through Mathematics Enrique A. González-Velasco Journey through Mathematics Creative Episodes in Its History Enrique A. González-Velasco Department of Mathematical Sciences University of Massachusetts
More informationEducational Institutions in Horror Film
Educational Institutions in Horror Film This page intentionally left blank Educational Institutions in Horror Film A History of Mad Professors, Student Bodies, and Final Exams Andrew L. Grunzke EDUCATIONAL
More informationSix Lectures. on Modern Natural Philosophy. c. Truesdell. Springer-Verlag Berlin Heidelberg GmbH 1966
Six Lectures on Modern Natural Philosophy c. Truesdell Springer-Verlag Berlin Heidelberg GmbH 1966 ISBN 978-3-662-28239-7 DOI 10.1007/978-3-662-29756-8 ISBN 978-3-662-29756-8 (ebook) All rights, especially
More informationThe Letter in Flora Tristan s Politics,
The Letter in Flora Tristan s Politics, 1835 1844 This page intentionally left blank The Letter in Flora Tristan s Politics, 1835 1844 Máire Fedelma Cross Máire Fedelma Cross 2004 Softcover reprint of
More informationThe Search for Selfhood in Modern Literature
The Search for Selfhood in Modern Literature Also by Murray Roston PROPHET AND POET: The Bible and the Growth of Romanticism BIBLICAL DRAMA IN ENGLAND: From the Middle Ages to the Present Day THE SOUL
More informationFORMAL GROUPS AND APPLICATIONS MICHIEL HAZEWINKEL AMS CHELSEA PUBLISHING
FORMAL GROUPS AND APPLICATIONS MICHIEL HAZEWINKEL AMS CHELSEA PUBLISHING FORMAL GROUPS AND APPLICATIONS http://dx.doi.org/10.1090/chel/375.h FORMAL GROUPS AND APPLICATIONS MICHIEL HAZEWINKEL AMS CHELSEA
More informationAN INTRODUCTION TO CLASSICAL REAL ANALYSIS KARL R. STROMBERG. AMS CHELSEA PUBLISHING American Mathematical Society Providence, Rhode Island
AN INTRODUCTION TO CLASSICAL REAL ANALYSIS KARL R. STROMBERG AMS CHELSEA PUBLISHING American Mathematical Society Providence, Rhode Island AN INTRODUCTION TO CLASSICAL REAL ANALYSIS AN INTRODUCTION TO
More informationEDITH WHARTON: TRAVELLER IN THE LAND OF LETTERS
EDITH WHARTON: TRAVELLER IN THE LAND OF LETTERS Edith Wharton Traveller in the Land of Letters Janet Beer Goodwyn Palgrave Macmillan ISBN 978-0-333-62327-5 ISBN 978-1-349-24006-7 (ebook) DOI 10.1007/978-1-349-24006-7
More informationHuman Rights Violation in Turkey
Human Rights Violation in Turkey Human Rights Violation in Turkey Rethinking Sociological Perspectives David Straw University of Manchester, UK David Straw 2013 Softcover reprint of the hardcover 1st edition
More informationRamanujan's Notebooks
Ramanujan's Notebooks Part II Springer New York Berlin Heidelberg Barcelona Hong Kong London Milan Paris Singapore Tokyo Bust of Ramanujan by Paul Granlund Bruce C. Berndt Ramanujan's Notebooks Part II
More informationLogical Foundations of Mathematics and Computational Complexity a gentle introduction
Pavel Pudlák Logical Foundations of Mathematics and Computational Complexity a gentle introduction January 18, 2013 Springer i Preface As the title states, this book is about logic, foundations and complexity.
More informationPartial and Paraconsistent Approaches to Future Contingents in Tense Logic
Partial and Paraconsistent Approaches to Future Contingents in Tense Logic Seiki Akama (C-Republic) akama@jcom.home.ne.jp Tetsuya Murai (Hokkaido University) murahiko@main.ist.hokudai.ac.jp Yasuo Kudo
More informationCultural Diplomacy in U.S.-Japanese Relations,
Cultural Diplomacy in U.S.-Japanese Relations, 1919 1941 This page intentionally left blank Cultural Diplomacy in U.S.-Japanese Relations, 1919 1941 JON THARES DAVIDANN CULTURAL DIPLOMACY IN U.S.-JAPANESE
More informationBOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE. VOLUME LlI DIALECTICS OF THE CONCRETE
BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE VOLUME LlI DIALECTICS OF THE CONCRETE SYNTHESE LIBRARY MONOGRAPHS ON EPISTEMOLOGY, LOGIC, M ETHO DO LOG Y, PHI LOSOPH Y OF SCI ENCE, SOC 10 LOG Y 0 F SCI E N
More informationThe Identifying Fictions of Toni Morrison
The Identifying Fictions of Toni Morrison This page intentionally left blank The Identifying Fictions of Toni Morrison Modernist Authenticity and Postmodern Blackness John N. Duvall THE IDENTIFYING FICTIONS
More informationDescartes Philosophical Revolution: A Reassessment
Descartes Philosophical Revolution: A Reassessment This page intentionally left blank Descartes Philosophical Revolution: A Reassessment Hanoch Ben-Yami Central European University, Budapest Hanoch Ben-Yami
More informationEATCS Monographs on Theoretical Computer Science
EATCS Monographs on Theoretical Computer Science Volume 5 Editors: W. Brauer G. Rozenberg A. Salomaa Advisory Board: G. Ausiello S. Even M. Nivat Chr. Papadimitriou A.L. Rosenberg D. Scott EATCS Monographs
More informationALGEBRA OF CONSCIENCE
ALGEBRA OF CONSCIENCE THEORY AND DECISION LIBRARY General Editors: W. Leinfellner (Vienna) and G. Eberlein (Munich) Series A: Philosophy and Methodology of the Social Sciences Series B: Mathematical and
More informationTowards a Post-Modern Understanding of the Political
Towards a Post-Modern Understanding of the Political This page intentionally left blank Towards a Post-Modern Understanding of the Political From Genealogy to Hermeneutics Andrius Bielskis Andrius Bielskis
More informationThe Rhetoric of Religious Cults
The Rhetoric of Religious Cults This page intentionally left blank The Rhetoric of Religious Cults Terms of Use and Abuse Annabelle Mooney Centre for Language and Communication Research Cardiff University,
More informationKees van Deemter: Not Exactly: In Praise of Vagueness
Minds & Machines DOI 10.1007/s11023-011-9251-1 Kees van Deemter: Not Exactly: In Praise of Vagueness Oxford University Press, Oxford, 2010, xvi+341, $29.95, ISBN: 0-199-5459-01 Patrick Allo Ó Springer
More informationTheory of Digital Automata
Theory of Digital Automata International Series on INTELLIGENT SYSTEMS, CONTROL AND AUTOMATION: SCIENCE AND ENGINEERING VOLUME 63 Editor Professor S. G. Tzafestas, National Technical University of Athens,
More informationExistentialism and Romantic Love
Existentialism and Romantic Love This page intentionally left blank Existentialism and Romantic Love Skye Cleary Columbia University, New York, USA Skye Cleary 2015 Softcover reprint of the hardcover 1st
More informationIndustrializing Antebellum America
Industrializing Antebellum America Industrializing Antebellum America The Rise of Manufacturing Entrepreneurs in the Early Republic Barbara M. Tucker Kenneth H. Tucker, Jr. palgrave macmillan INDUSTRIALIZING
More informationCopyright Douglas R. Parker (2016) Copyright 2016 for diagrams and illustrations by Douglas R Parker
Copyright Douglas R. Parker (2016) Copyright 2016 for diagrams and illustrations by Douglas R Parker The right of Douglas R. Parker to be identified as author of this work has been asserted by him in accordance
More informationINTRODUCTION TO AXIOMATIC SET THEORY
INTRODUCTION TO AXIOMATIC SET THEORY SYNTHESE LIBRARY MONOGRAPHS ON EPISTEMOLOGY, LOGIC, METHODOLOGY, PHILOSOPHY OF SCIENCE, SOCIOLOGY OF SCIENCE AND OF KNOWLEDGE, AND ON THE MATHEMATICAL METHODS OF SOCIAL
More informationYorick Wilks. Machine Translation. Its Scope and Limits
Machine Translation Yorick Wilks Machine Translation Its Scope and Limits 123 Yorick Wilks Department of Computer Science The University of Sheffield Regent Court, 211 Portobello Street Sheffield, S1 4DP,
More informationThe Elegies of Ted Hughes
The Elegies of Ted Hughes This page intentionally left blank The Elegies of Ted Hughes Edward Hadley Edward Hadley 2010 Softcover reprint of the hardcover 1st edition 2010 978-0-230-23218-1 All rights
More informationThe Philosophy of Friendship
The Philosophy of Friendship This page intentionally left blank The Philosophy of Friendship Mark Vernon Mark Vernon 2005 Softcover reprint of the hardcover 1st edition 2005 978-1-4039-4874-8 All rights
More information