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A Simple Logic for Comparisons and Vagueness
THEODORE J. EVERETT A SIMPLE LOGIC FOR COMPARISONS AND VAGUENESS ABSTRACT. I provide an intuitive, semantic account of a new logic for comparisons (CL), in which atomic statements are assigned both a classical truth-value and a “how much” value or extension in the range [0, 1]. The truth-value of each comparison is determined by the extensions of its component sentences; the truth-value of each atomic depends on whether its extension matches a separate standard for its predicate; everything else is computed classically. CL is less radical than Casari’s comparative logics, in that it does not allow for the formation of comparative statements out of truth-functional molecules. I argue that CL provides a better analysis of comparisons and predicate vagueness than classical logic, fuzzy logic or supervaluation theory. CL provides a model for descriptions of the world in terms of comparisons only. The sorites paradox can be solved by the elimination of atomic sentences. In his recent book on vagueness, Timothy Williamson (1994) attacks accounts of vagueness arising from either fuzzy logic or supervaluation theory, both of which have well-known problems, stemming in part from their denial of classical bivalence. He then gives his own, epistemic ac- count of vagueness, according to which the vagueness of a predicate is fundamentally a matter of our not knowing whether or not it applies in every case. My main purpose in this paper is not to criticize William- son’s positive view, but to provide an alternative, non-epistemic account of predicate vagueness, based on a very simple logic for comparisons (CL), which preserves bivalence. -
Does Informal Logic Have Anything to Learn from Fuzzy Logic?
University of Windsor Scholarship at UWindsor OSSA Conference Archive OSSA 3 May 15th, 9:00 AM - May 17th, 5:00 PM Does informal logic have anything to learn from fuzzy logic? John Woods University of British Columbia Follow this and additional works at: https://scholar.uwindsor.ca/ossaarchive Part of the Philosophy Commons Woods, John, "Does informal logic have anything to learn from fuzzy logic?" (1999). OSSA Conference Archive. 62. https://scholar.uwindsor.ca/ossaarchive/OSSA3/papersandcommentaries/62 This Paper is brought to you for free and open access by the Conferences and Conference Proceedings at Scholarship at UWindsor. It has been accepted for inclusion in OSSA Conference Archive by an authorized conference organizer of Scholarship at UWindsor. For more information, please contact [email protected]. Title: Does informal logic have anything to learn from fuzzy logic? Author: John Woods Response to this paper by: Rolf George (c)2000 John Woods 1. Motivation Since antiquity, philosophers have been challenged by the apparent vagueness of everyday thought and experience. How, these philosophers have wanted to know, are the things we say and think compatible with logical laws such as Excluded Middle?1 A kindred attraction has been the question of how truth presents itself — relatively and in degrees? in approximations? in resemblances, or in bits and pieces? F.H. Bradley is a celebrated (or as the case may be, excoriated) champion of the degrees view of truth. There are, one may say, two main views of error, the absolute and relative. According to the former view there are perfect truths, and on the other side there are sheer errors.. -
Intransitivity and Vagueness
Intransitivity and Vagueness Joseph Y. Halpern∗ Cornell University Computer Science Department Ithaca, NY 14853 [email protected] http://www.cs.cornell.edu/home/halpern Abstract preferences. Moreover, it is this intuition that forms the ba- sis of the partitional model for knowledge used in game the- There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the in- ory (see, e.g., [Aumann 1976]) and in the distributed sys- distinguishability relation is typically taken to be an equiv- tems community [Fagin, Halpern, Moses, and Vardi 1995]. alence relation (and thus transitive). It is shown that if the On the other hand, besides the obvious experimental obser- uncertainty perception and the question of when an agent vations, there have been arguments going back to at least reports that two things are indistinguishable are both care- Poincare´ [1902] that the physical world is not transitive in fully modeled, the problems disappear, and indistinguishabil- this sense. In this paper, I try to reconcile our intuitions ity can indeed be taken to be an equivalence relation. More- about indistinguishability with the experimental observa- over, this model also suggests a logic of vagueness that seems tions, in a way that seems (at least to me) both intuitively to solve many of the problems related to vagueness discussed appealing and psychologically plausible. I then go on to ap- in the philosophical literature. In particular, it is shown here ply the ideas developed to the problem of vagueness. how the logic can handle the Sorites Paradox. To understand the vagueness problem, consider the well- n+1 1 Introduction known Sorites Paradox: If grains of sand make a heap, then so do n. -
On the Relationship Between Fuzzy Autoepistemic Logic and Fuzzy Modal Logics of Belief
JID:FSS AID:6759 /FLA [m3SC+; v1.204; Prn:31/03/2015; 9:42] P.1(1-26) Available online at www.sciencedirect.com ScienceDirect Fuzzy Sets and Systems ••• (••••) •••–••• www.elsevier.com/locate/fss On the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief ∗ Marjon Blondeel d, ,1, Tommaso Flaminio a,2, Steven Schockaert b, Lluís Godo c,3, Martine De Cock d,e a Università dell’Insubria, Department of Theorical and Applied Science, Via Mazzini 5, 21100 Varese, Italy b Cardiff University, School of Computer Science and Informatics, 5The Parade, Cardiff, CF24 3AA, UK c Artficial Intelligence Research Institute (IIIA) – CSIC, Campus UAB, 08193 Bellaterra, Spain d Ghent University, Department of Applied Mathematics, Computer Science and Statistics, Krijgslaan 281 (S9), 9000 Gent, Belgium e University of Washington Tacoma – Center for Web and Data Science, 1900 Commerce Street, Tacoma, WA 98402-3100, USA Received 12 February 2014; received in revised form 30 September 2014; accepted 26 February 2015 Abstract Autoepistemic logic is an important formalism for nonmonotonic reasoning originally intended to model an ideal rational agent reflecting upon his own beliefs. Fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent’s rational beliefs on gradable propositions. It has recently been shown that, in the same way as autoepistemic logic generalizes answer set programming, fuzzy autoepistemic logic generalizes fuzzy answer set programming as well. Besides being related to answer set programming, autoepistemic logic is also closely related to several modal logics. To investigate whether a similar relationship holds in a fuzzy logical setting, we firstly generalize the main modal logics for belief to the setting of finitely-valued c Łukasiewicz logic with truth constants Łk, and secondly we relate them with fuzzy autoepistemic logics. -
Consequence and Degrees of Truth in Many-Valued Logic
Consequence and degrees of truth in many-valued logic Josep Maria Font Published as Chapter 6 (pp. 117–142) of: Peter Hájek on Mathematical Fuzzy Logic (F. Montagna, ed.) vol. 6 of Outstanding Contributions to Logic, Springer-Verlag, 2015 Abstract I argue that the definition of a logic by preservation of all degrees of truth is a better rendering of Bolzano’s idea of consequence as truth- preserving when “truth comes in degrees”, as is often said in many-valued contexts, than the usual scheme that preserves only one truth value. I review some results recently obtained in the investigation of this proposal by applying techniques of abstract algebraic logic in the framework of Łukasiewicz logics and in the broader framework of substructural logics, that is, logics defined by varieties of (commutative and integral) residuated lattices. I also review some scattered, early results, which have appeared since the 1970’s, and make some proposals for further research. Keywords: many-valued logic, mathematical fuzzy logic, truth val- ues, truth degrees, logics preserving degrees of truth, residuated lattices, substructural logics, abstract algebraic logic, Leibniz hierarchy, Frege hierarchy. Contents 6.1 Introduction .............................2 6.2 Some motivation and some history ...............3 6.3 The Łukasiewicz case ........................8 6.4 Widening the scope: fuzzy and substructural logics ....9 6.5 Abstract algebraic logic classification ............. 12 6.6 The Deduction Theorem ..................... 16 6.7 Axiomatizations ........................... 18 6.7.1 In the Gentzen style . 18 6.7.2 In the Hilbert style . 19 6.8 Conclusions .............................. 21 References .................................. 23 1 6.1 Introduction Let me begin by calling your attention to one of the main points made by Petr Hájek in the introductory, vindicating section of his influential book [34] (the italics are his): «Logic studies the notion(s) of consequence. -
A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics
FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS (fourth edition) NL(A1 A2) = ( T1 ({1}T2) T2 ({1}T1) T1T2 ({1}T1) ({1}T2), I1 ({1}I2) I2 ({1}I1) I1 I2 ({1}I1) ({1} I2), F1 ({1}F2) F2 ({1} F1) F1 F2 ({1}F1) ({1}F2) ). NL(A1 A2) = ( {1}T1T1T2, {1}I1I1I2, {1}F1F1F2 ). NL(A1 A2) = ( ({1}T1T1T2) ({1}T2T1T2), ({1} I1 I1 I2) ({1}I2 I1 I2), ({1}F1F1 F2) ({1}F2F1 F2) ). ISBN 978-1-59973-080-6 American Research Press Rehoboth 1998, 2000, 2003, 2005 FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS (fourth edition) NL(A1 A2) = ( T1 ({1}T2) T2 ({1}T1) T1T2 ({1}T1) ({1}T2), I1 ({1}I2) I2 ({1}I1) I1 I2 ({1}I1) ({1} I2), F1 ({1}F2) F2 ({1} F1) F1 F2 ({1}F1) ({1}F2) ). NL(A1 A2) = ( {1}T1T1T2, {1}I1I1I2, {1}F1F1F2 ). NL(A1 A2) = ( ({1}T1T1T2) ({1}T2T1T2), ({1} I1 I1 I2) ({1}I2 I1 I2), ({1}F1F1 F2) ({1}F2F1 F2) ). ISBN 978-1-59973-080-6 American Research Press Rehoboth 1998, 2000, 2003, 2005 1 Contents: Preface by C. Le: 3 0. Introduction: 9 1. Neutrosophy - a new branch of philosophy: 15 2. Neutrosophic Logic - a unifying field in logics: 90 3. Neutrosophic Set - a unifying field in sets: 125 4. Neutrosophic Probability - a generalization of classical and imprecise probabilities - and Neutrosophic Statistics: 129 5. Addenda: Definitions derived from Neutrosophics: 133 2 Preface to Neutrosophy and Neutrosophic Logic by C. -
Modality and Factivity: One Perspective on the Meaning of the English Modal Auxiliaries
MODALITY AND FACTIVITY: ONE PERSPECTIVE ON THE MEANING OF THE ENGLISH MODAL AUXILIARIES by NICOLA M,BREWER Submitted in accordance with the requirements for the degree of PhD The University of Leeds Department of Linguistics and Phonetics December 1987 ii ABSTRACT This study concentrates on modality as expressed by the set of modal auxiliaries and seeks to establish that these verbs share semantic as well as syntactic properties by identifying a single core meaning which they share. The relationship between modality and factivity is examined with the aim of gaining an insight into the former, more complex concept. When viewed from this perspective, the defining characteristic of all the modal auxiliary verbs in almost all of their uses is found to be nonfactivity. The meanings expressed by this set of verbs are classified according to a framework derived from modal logic consisting of three basic types of modality each of which relates to a different set of laws or principles; the relative factivity associated with the modal auxiliaries is seen to vary with the nature of modality as defined and classified by this framework. Within each of the three types of modality, a semantic scale is identified and modality is described as a gradable concept for which scalar analysis is appropriate, both within and beyond these three scales. Relative factivity is also shown to vary according to the degree of modality expressed by each of the modal verbs. The nature and degree of modality expressed interact with features of the linguistic (and pragmatic) context to determine the particular factive or a contrafactive interpretation conveyed by a given modal auxiliary token. -
Irrationality and Human Reasoning Michael Aristidou Louisiana State University and Agricultural and Mechanical College
Louisiana State University LSU Digital Commons LSU Master's Theses Graduate School 2004 Irrationality and human reasoning Michael Aristidou Louisiana State University and Agricultural and Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_theses Part of the Arts and Humanities Commons Recommended Citation Aristidou, Michael, "Irrationality and human reasoning" (2004). LSU Master's Theses. 2918. https://digitalcommons.lsu.edu/gradschool_theses/2918 This Thesis is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Master's Theses by an authorized graduate school editor of LSU Digital Commons. For more information, please contact [email protected]. IRRATIONALITY AND HUMAN REASONING A Thesis Submitted to the Graduate Faculty of the Louisiana State University in partial fulfillment of the requirements of the degree of Master of Arts in The Department of Philosophy by Michael Aristidou BSc, Aristotle University of Thessaloniki, 1999 MSc, Louisiana State University, 2001 May, 2004 To my parents Theodotos and Kristia, to my sister Eliza, and to my brother Konstantinos for all their love and support through all these years. ii ACKNOWLEDGMENTS I would like to thank my advisor Dr. Jon Cogburn for his great patience and valuable instruction on my thesis. I would also like to thank, Dr. Mary Sirridge for her advising and help through my graduate years in Philosophy, the members of my thesis committee Dr. Husain Sarkar and Dr. Ian Crystal for their cooperation, and Taneka Welch for her constant willingness to discuss issues related to my thesis, and her technical support. -
Arxiv:1009.3391V3 [Cs.LO] 4 Nov 2010
Fuzzy Ontology Representation using OWL 2 I Fernando Bobilloa, Umberto Stracciab aDepartment of Computer Science and Systems Engineering, University of Zaragoza, Spain bIstituto di Scienza e Tecnologie dell'Informazione (ISTI - CNR), Pisa, Italy Abstract The need to deal with vague information in Semantic Web languages is rising in importance and, thus, calls for a standard way to represent such information. We may address this issue by either extending current Semantic Web languages to cope with vagueness, or by providing a procedure to represent such informa- tion within current standard languages and tools. In this work, we follow the latter approach, by identifying the syntactic differences that a fuzzy ontology language has to cope with, and by proposing a concrete methodology to rep- resent fuzzy ontologies using OWL 2 annotation properties. We also report on the prototypical implementations. Key words: Fuzzy OWL 2, Fuzzy Ontologies, Fuzzy Languages for the Semantic Web, Fuzzy Description Logics 1. Introduction Today, there is a growing interest in the development of knowledge representa- tion formalisms able to deal with uncertainty, which is a very common require- ment in real world applications. Despite the undisputed success of ontologies, classical ontology languages are not appropriate to deal with vagueness or impre- cision in the knowledge, which is inherent to most of the real world application domains [29]. Since fuzzy set theory and fuzzy logic [30] are suitable formalisms to handle these types of knowledge, fuzzy ontologies emerge as useful in several applica- arXiv:1009.3391v3 [cs.LO] 4 Nov 2010 tions, ranging from (multimedia) information retrieval to image interpretation, ontology mapping, matchmaking, decision making, or the Semantic Web [19]. -
Twentieth-Century French Philosophy Twentieth-Century French Philosophy
Twentieth-Century French Philosophy Twentieth-Century French Philosophy Key Themes and Thinkers Alan D. Schrift ß 2006 by Alan D. Schrift blackwell publishing 350 Main Street, Malden, MA 02148-5020, USA 9600 Garsington Road, Oxford OX4 2DQ, UK 550 Swanston Street, Carlton, Victoria 3053, Australia The right of Alan D. Schrift to be identified as the Author of this Work has been asserted in accordance with the UK Copyright, Designs, and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs, and Patents Act 1988, without the prior permission of the publisher. First published 2006 by Blackwell Publishing Ltd 1 2006 Library of Congress Cataloging-in-Publication Data Schrift, Alan D., 1955– Twentieth-Century French philosophy: key themes and thinkers / Alan D. Schrift. p. cm. Includes bibliographical references and index. ISBN-13: 978-1-4051-3217-6 (hardcover: alk. paper) ISBN-10: 1-4051-3217-5 (hardcover: alk. paper) ISBN-13: 978-1-4051-3218-3 (pbk.: alk. paper) ISBN-10: 1-4051-3218-3 (pbk.: alk. paper) 1. Philosophy, French–20th century. I. Title. B2421.S365 2005 194–dc22 2005004141 A catalogue record for this title is available from the British Library. Set in 11/13pt Ehrhardt by SPI Publisher Services, Pondicherry, India Printed and bound in India by Gopsons Papers Ltd The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp processed using acid-free and elementary chlorine-free practices. -
The Politics O F Aesthetics Also Available from Continuum
The Politics o f Aesthetics Also available from Continuum: Infinite Thought, Alain Badiou (trans. by Oliver Feltham and Justin Clemens) Francis Bacon: The Logic o f Sensation, Gilles Deleuze (trans. by David W. Smith) The Way o f Love, Luce Irigaray (trans. by Heidi Bostic and Stephen Pluhacek) Time for Revolution, Antonio Negri (trans. by Matteo Mandarini) Art and Fear, Paul Virilio (trans. by Julie Rose) Interrogating the Real, Slavoj Zizek (trans. by Rex Butler and Scott T. Stephens) The Universal Exception, Slavoj Zizek (trans. by Rex Butler and Scott T. Stephens) Life After Theory, edited by Michael Payne and John Schad The Politics o f Aesthetics The Distribution o f the Sensible JACQUES RANCIÈRE Translated with an Introduction by Gabriel Rockhill continuumA The Tower Building, 11 York Road, London SEI 7NX, 80 Maiden Lane, Suite 704, New York NY 10038 First published in France under the title Le Partage du sensible: Esthétique et politique © La Fabrique-Éditions, 2000 © Gabriel Rockhill, 2004 All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage or retrieval system, without prior permission in writing from the publishers. First published 2004 Reprinted 2005 Paperback edition first published 2006 Reprinted 2006, 2007 (twice), 2008, 2011 (twice) British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN 10: HB: 0-8264-7067-X -
Warren Montag
Warren Montag _________________________________________________________________ CURRICULUM VITAE Positions Held: Occidental College, 2000- (Professor) 1994-2000 (Associate Professor) 1991-1994 (Assistant Professor) 1987-1991 (Adjunct Assistant Professor) 1982-1987 (part-time) Otis Art Institute 1984-1987 (Instructor) Pitzer College 1982-1984 (Instructor) Visiting Professorships: Graduate Seminar, Department of Comparative Literature, UCLA Spring 2006 Doctoral Seminar, Universidad de Buenos Aires, Sciencias Sociales, November 2013 Editor of Décalages: a Journal of Althusser Studies Areas of Specialization: Restoration and Eighteenth-Century Literature, the Enlightenment, Literature and Philosophy 1600-1800, Hobbes, Spinoza, Locke, Twentieth-Century French Philosophy. Publications: Books: Selected Essays (provisional title) (Leiden, E.J. Brill, forthcoming). (with Mike Hill) The Other Adam Smith (Stanford: Stanford University Press, 2014) (Chinese translation 2018) Althusser and his Contemporaries; Philosophy’s Perpetual War. (Durham: Duke University Press, 2013) (Persian and Korean translations, 2019, Spanish forthcoming). Louis Althusser (London: Palgrave, 2003) (partial Spanish Translation, 2011) Bodies, Masses, Power: Spinoza and his Contemporaries, (London: Verso, 1999). (Persian translation 2019, Korean translation 2019, Spanish translation 2005) The Unthinkable Swift: The Spontaneous Philosophy of a Church of England Man, (London: Verso, 1994). Edited Collections (Co-editor) Systems of Life: Biopolitics, Economics, and Literature, 1750-1859 (New York: Fordham UP, 2018). (Co-Editor) Balibar and the Citizen Subject (Edinburgh, Edinburgh UP, 2017). (Co-Editor) Masses, Classes and the Public Sphere (London: Verso, 2001). (Editor) In a Materialist Way: Selected Essays by Pierre Macherey (London: Verso, 1998). (Co-Editor) The New Spinoza (Minneapolis: University of Minnesota Press, 1997). Publications: Journal Special Issues (Co-editor with Nancy Armstrong) Differences: A Journal of Feminist Cultural Studies, Vol 20, n.