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  1. Fuzzy Grammar: A Reader.Bas Aarts, David Denison, Evelien Keizer & Gergana Popova (eds.) - 2004 - Oxford University Press UK.
    This book brings together classic and recent papers in the philosophical and linguistic analysis of fuzzy grammar, gradience in meaning, word classes, and syntax. Issues such as how many grains make a heap, when a puddle becomes a pond, and so forth, have occupied thinkers since Aristotle and over the last two decades been the subject of increasing interest among linguists as well as in fields such as artificial intelligence and computational linguistics. The work is designed to be of use (...)
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  2. A Note on the Axiomatization of Equational Classes of $N$-Valued Ł Ukasiewicz Algebras.M. E. Adams & R. Cignoli - 1990 - Notre Dame Journal of Formal Logic 31 (2):304-307.
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  3. Basic Hoops: An Algebraic Study of Continuous T -Norms.P. Aglianò, I. M. A. Ferreirim & F. Montagna - 2007 - Studia Logica 87 (1):73 - 98.
    A continuoxis t- norm is a continuous map * from [0, 1]² into [0,1] such that ([ 0,1], *, 1) is a commutative totally ordered monoid. Since the natural ordering on [0,1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and ([ 0,1], *, →, 1) becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras ([ 0,1], *, →, 1), where (...)
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  4. A Temporal Semantics for Basic Logic.Stefano Aguzzoli, Matteo Bianchi & Vincenzo Marra - 2009 - Studia Logica 92 (2):147-162.
    In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL formulas (...)
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  5. Finiteness in Infinite-Valued Łukasiewicz Logic.Stefano Aguzzoli & Agata Ciabattoni - 2000 - Journal of Logic, Language and Information 9 (1):5-29.
    In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued ukasiewicz logic to a suitable m-valued ukasiewicz logic m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in if and only if it is also valid in m. We also reduce the notion of logical consequence in to the same (...)
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  6. A Unification of Two Approaches to Vagueness: The Boolean Many-Valued Approach and the Modal-Precisificational Approach.Ken Akiba - 2017 - Journal of Philosophical Logic 46 (4):419-441.
    The Boolean many-valued approach to vagueness is similar to the infinite-valued approach embraced by fuzzy logic in the respect in which both approaches seek to solve the problems of vagueness by assigning to the relevant sentences many values between falsity and truth, but while the fuzzy-logic approach postulates linearly-ordered values between 0 and 1, the Boolean approach assigns to sentences values in a many-element complete Boolean algebra. On the modal-precisificational approach represented by Kit Fine, if a sentence is indeterminate in (...)
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  7. A Type of Fuzzy Ring.Hacı Aktaş & Naim Çağman - 2007 - Archive for Mathematical Logic 46 (3-4):165-177.
    In this study, by the use of Yuan and Lee’s definition of the fuzzy group based on fuzzy binary operation we give a new kind of fuzzy ring. The concept of fuzzy subring, fuzzy ideal and fuzzy ring homomorphism are introduced, and we make a theoretical study their basic properties analogous to those of ordinary rings.
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  8. Acceptable Contradictions: Pragmatics or Semantics? A Reply to Cobreros Et Al. [REVIEW]Sam Alxatib, Peter Pagin & Uli Sauerland - 2013 - Journal of Philosophical Logic 42 (4):619-634.
    Naive speakers find some logical contradictions acceptable, specifically borderline contradictions involving vague predicates such as Joe is and isn’t tall. In a recent paper, Cobreros et al. (J Philos Logic, 2012) suggest a pragmatic account of the acceptability of borderline contradictions. We show, however, that the pragmatic account predicts the wrong truth conditions for some examples with disjunction. As a remedy, we propose a semantic analysis instead. The analysis is close to a variant of fuzzy logic, but conjunction and disjunction (...)
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  9. Book Reviews: Richard Dietz and Sebastiano Moruzzi (Eds.), Cuts and Clouds: Vagueness, its Nature, and its Logic.Doroteya Angelova - 2012 - Logic and Logical Philosophy 21 (1):97-104.
    Richard Dietz and Sebastiano Moruzzi (eds.), Cuts and Clouds: Vagueness, its Nature, and its Logic, Oxford University Press, 2010, 586 pp., ISBN 9780199570386.
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  10. A Category-Theoretic Approach to Systems in a Fuzzy World.Michael A. Arbib & Ernest G. Manes - 1975 - Synthese 30 (3-4):381 - 406.
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  11. A Note on Intuitionistic Fuzzy Logics.K. T. Atanassov & A. G. Shannon - 1998 - Acta Philosophica 7 (1):121-125.
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  12. Many-Valued Logics. A Mathematical and Computational Introduction.Luis M. Augusto - 2017 - London: College Publications.
    Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and they are (...)
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  13. Fuzzy Equational Logic.Radim B.& X. B.. Lohl& X. 000 E. 1 vek - 2002 - Archive for Mathematical Logic 41 (1):83-90.
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  14. Fuzzy Horn Logic II.R. B.? Lohl├ Ívek & V. M. Vychodil - 2006 - Archive for Mathematical Logic 45 (2):149.
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  15. On the Decidability Status of Fuzzy A ℒ C with General Concept Inclusions.Franz Baader, Stefan Borgwardt & Rafael Peñaloza - 2015 - Journal of Philosophical Logic 44 (2):117-146.
    The combination of Fuzzy Logics and Description Logics has been investigated for at least two decades because such fuzzy DLs can be used to formalize imprecise concepts. In particular, tableau algorithms for crisp Description Logics have been extended to reason also with their fuzzy counterparts. It has turned out, however, that in the presence of general concept inclusion axioms this extension is less straightforward than thought. In fact, a number of tableau algorithms claimed to deal correctly with fuzzy DLs with (...)
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  16. Quantified Propositional Gödel Logics.Matthias Baaz, Agata Ciabattoni & Richard Zach - 2000 - In Andrei Voronkov & Michel Parigot (eds.), Logic for Programming and Automated Reasoning. 7th International Conference, LPAR 2000. Berlin: Springer. pp. 240-256.
    It is shown that Gqp↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp↑ as the intersection of all finite-valued quantified propositional Gödel logics.
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  17. Note on Witnessed Gödel Logics with Delta.Matthias Baaz & Oliver Fasching - 2009 - Annals of Pure and Applied Logic 161 (2):121-127.
    Witnessed Gödel logics are based on the interpretation of () by minimum instead of supremum . Witnessed Gödel logics appear for many practical purposes more suited than usual Gödel logics as the occurrence of proper infima/suprema is practically irrelevant. In this note we characterize witnessed Gödel logics with absoluteness operator w.r.t. witnessed Gödel logics using a uniform translation.
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  18. Complexity of T-Tautologies.Matthias Baaz, Petr Hájek, Franco Montagna & Helmut Veith - 2001 - Annals of Pure and Applied Logic 113 (1-3):3-11.
    A t-tautology is a propositional formula which is a tautology in all fuzzy logics defined by continuous triangular norms. In this paper we show that the problem of recognizing t-tautologies is coNP complete, and thus decidable.
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  19. Incompleteness of a First-Order Gödel Logic and Some Temporal Logics of Programs.Matthias Baaz, Alexander Leitsch & Richard Zach - 1996 - In Hans Kleine Büning (ed.), Computer Science Logic. CSL 1995. Selected Papers. Berlin: Springer. pp. 1--15.
    It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal (...)
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  20. Completeness of a Hypersequent Calculus for Some First-Order Gödel Logics with Delta.Matthias Baaz, Norbert Preining & Richard Zach - 2006 - In 36th International Symposium on Multiple-valued Logic. May 2006, Singapore. Proceedings. Los Alamitos: IEEE Press.
    All first-order Gödel logics G_V with globalization operator based on truth value sets V C [0,1] where 0 and 1 lie in the perfect kernel of V are axiomatized by Ciabattoni’s hypersequent calculus HGIF.
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  21. Interpolation in Fuzzy Logic.Matthias Baaz & Helmut Veith - 1999 - Archive for Mathematical Logic 38 (7):461-489.
    We investigate interpolation properties of many-valued propositional logics related to continuous t-norms. In case of failure of interpolation, we characterize the minimal interpolating extensions of the languages. For finite-valued logics, we count the number of interpolating extensions by Fibonacci sequences.
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  22. Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic.Matthias Baaz & Richard Zach - 2000 - In Peter G. Clote & Helmut Schwichtenberg (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Berlin: Springer. pp. 187– 201.
    Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and complete, and (...)
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  23. Compact Propositional Gödel Logics.Matthias Baaz & Richard Zach - 1998 - In 28th IEEE International Symposium on Multiple-Valued Logic, 1998. Proceedings. Los Alamitos: IEEE Press. pp. 108-113.
    Entailment in propositional Gödel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Gödel logics, only one of which is compact. It is also shown that the compact infinite-valued Gödel logic is the only one which interpolates, and the only one with an r.e. entailment relation.
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  24. Curry's Paradox and Omega Inconsistency.Andrew Bacon - 2013 - Studia Logica 101 (1):1-9.
    In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, but (...)
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  25. Fuzzy Logic.J. F. Baldwin - 1996
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  26. The Resolution of Two Paradoxes by Approximate Reasoning Using a Fuzzy Logic.J. F. Baldwin & N. C. F. Guild - 1980 - Synthese 44 (3):397 - 420.
    The method of approximate reasoning using a fuzzy logic introduced by Baldwin (1978 a,b,c), is used to model human reasoning in the resolution of two well known paradoxes. It is shown how classical propositional logic fails to resolve the paradoxes, how multiple valued logic partially succeeds and that a satisfactory resolution is obtained with fuzzy logic. The problem of precise representation of vague concepts is considered in the light of the results obtained.
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  27. Fuzzy Sets, Fuzzy Logic, Fuzzy Methods with Applications.Hans Bandemer & Siegfried Gottwald - 1995
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  28. Advances in Fuzzy Logic: Selected Papers (with Comments) of Some Spanish Authors.Senén Barro, Alberto Bugarín & Alejandro Sobrino E. Senén Barro (eds.) - 1998 - Universidade De Santiago De Compostela.
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  29. Automated Theorem Proving for Łukasiewicz Logics.Gordon Beavers - 1993 - Studia Logica 52 (2):183 - 195.
    This paper is concerned with decision proceedures for the 0-valued ukasiewicz logics,. It is shown how linear algebra can be used to construct an automated theorem checker. Two decision proceedures are described which depend on a linear programming package. An algorithm is given for the verification of consequence relations in, and a connection is made between theorem checking in two-valued logic and theorem checking in which implies that determing of a -free formula whether it takes the value one is NP-complete (...)
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  30. Comments on 'Fuzzy Logic and Higher-Order Vagueness' by Nicholas J.J. Smith.Libor Běhounek - 2011 - In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications. pp. 21-8.
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  31. Fuzzification of Groenendijk-Stokhof Propositional Erotetic Logic.Libor Behounek - 2004 - Logique Et Analyse 47.
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  32. Logical Options: An Introduction to Classical and Alternative Logics.John L. Bell, David DeVidi & Graham Solomon - 2001 - Broadview Press.
    Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some (...)
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  33. Fuzzy Classifications.Antonio Bellacicco - 1976 - Synthese 33 (1):273 - 281.
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  34. Algebraic Geometry for Mv-Algebras.Lawrence P. Belluce, Antonio di Nola & Giacomo Lenzi - 2014 - Journal of Symbolic Logic 79 (4):1061-1091.
  35. Birkhoff Variety Theorem and Fuzzy Logic.Radim Bělohlávek - 2003 - Archive for Mathematical Logic 42 (8):781-790.
    An algebra with fuzzy equality is a set with operations on it that is equipped with similarity ≈, i.e. a fuzzy equivalence relation, such that each operation f is compatible with ≈. Described verbally, compatibility says that each f yields similar results if applied to pairwise similar arguments. On the one hand, algebras with fuzzy equalities are structures for the equational fragment of fuzzy logic. On the other hand, they are the formal counterpart to the intuitive idea of having functions (...)
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  36. Fuzzy Equational Logic.Radim Bělohlávek - 2002 - Archive for Mathematical Logic 41 (1):83-90.
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  37. Concepts and Fuzzy Logic.Radim Belohlavek & George J. Klir (eds.) - 2011 - MIT Press.
    In this work - both psychologists working on concepts and mathematicians working on fuzzy logic - reassess the usefulness of fuzzy logic for the psychology of concepts.
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  38. Fuzzy Horn Logic I.Radim Bělohlávek & Vilém Vychodil - 2006 - Archive for Mathematical Logic 45 (1):3-51.
    The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style completeness theorem (degree of provability equals degree (...)
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  39. Fuzzy Horn Logic II.Radim Bělohlávek & Vilém Vychodil - 2006 - Archive for Mathematical Logic 45 (2):149-177.
    The paper studies closure properties of classes of fuzzy structures defined by fuzzy implicational theories, i.e. theories whose formulas are implications between fuzzy identities. We present generalizations of results from the bivalent case. Namely, we characterize model classes of general implicational theories, finitary implicational theories, and Horn theories by means of closedness under suitable algebraic constructions.
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  40. A General Information for Fuzzy Sets.Pietro Benvenuti, Doretta Vivona & Maria Divari - 1991 - In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. pp. 307--316.
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  41. An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems.Merrie Bergmann - 2008 - Cambridge University Press.
    Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical (...)
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  42. Fuzzy Clustering.James C. Bezdek - 1998 - In Enrique H. Ruspini, Piero Patrone Bonissone & Witold Pedrycz (eds.), Handbook of Fuzzy Computation. Institute of Physics. pp. 2.
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  43. Fuzzy Logic, Continuity and Effectiveness.Loredana Biacino & Giangiacomo Gerla - 2002 - Archive for Mathematical Logic 41 (7):643-667.
    It is shown the complete equivalence between the theory of continuous (enumeration) fuzzy closure operators and the theory of (effective) fuzzy deduction systems in Hilbert style. Moreover, it is proven that any truth-functional semantics whose connectives are interpreted in [0,1] by continuous functions is axiomatizable by a fuzzy deduction system (but not by an effective fuzzy deduction system, in general).
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  44. First-Order Nilpotent Minimum Logics: First Steps.Matteo Bianchi - 2013 - Archive for Mathematical Logic 52 (3-4):295-316.
    Inspired by the work done by Baaz et al. (Ann Pure Appl Log 147(1–2): 23–47, 2007; Lecture Notes in Computer Science, vol 4790/2007, pp 77–91, 2007) for first-order Gödel logics, we investigate Nilpotent Minimum logic NM. We study decidability and reciprocal inclusion of various sets of first-order tautologies of some subalgebras of the standard Nilpotent Minimum algebra, establishing also a connection between the validity in an NM-chain of certain first-order formulas and its order type. Furthermore, we analyze axiomatizability, undecidability and (...)
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  45. N-Contractive BL-Logics.Matteo Bianchi & Franco Montagna - 2011 - Archive for Mathematical Logic 50 (3-4):257-285.
    In the field of many-valued logics, Hájek’s Basic Logic BL was introduced in Hájek (Metamathematics of fuzzy logic, trends in logic. Kluwer Academic Publishers, Berlin, 1998). In this paper we will study four families of n-contractive (i.e. that satisfy the axiom ${\phi^n\rightarrow\phi^{n+1}}$ , for some ${n\in\mathbb{N}^+}$ ) axiomatic extensions of BL and their corresponding varieties: BL n , SBL n , BL n and SBL n . Concerning BL n we have that every BL n -chain is isomorphic to an (...)
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  46. Aggregation of Preferences: The Fuzzy Case.Antoine Billot - 1991 - Theory and Decision 30 (1):51-93.
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  47. The Role of Vagueness in the Numerical Translation of Verbal Probabilities: A Fuzzy Approach.Franziska Bocklisch, Steffen F. Bocklisch, Martin Rk Baumann, Agnes Scholz & Josef F. Krems - 2010 - In S. Ohlsson & R. Catrambone (eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society. Cognitive Science Society.
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  48. Fuzzy Inference.D. Boixader & L. Godo - 1998 - In Enrique H. Ruspini, Piero Patrone Bonissone & Witold Pedrycz (eds.), Handbook of Fuzzy Computation. Institute of Physics.
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  49. New Trends in Fuzzy Logic: Proceedings of the Wilf '95, Italian Workshop on Fuzzy Logic, Naples, Italy, 21-22 September 1995'. [REVIEW]Andrea Bonarini (ed.) - 1996 - World Scientific.
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  50. On Revising Fuzzy Belief Bases.Richard Booth & Eva Richter - 2005 - Studia Logica 80 (1):29-61.
    We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revision-input formulas can come attached with varying degrees. Working within a very general framework for fuzzy logic which is able to capture certain types of uncertainty calculi as well as truth-functional fuzzy logics, we show how the idea of rational change from “crisp” base revision, as embodied by the idea of partial meet (base) revision, can be (...)
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