Results for 'fuzzy truth function'

973 found
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  1. Undead argument: the truth-functionality objection to fuzzy theories of vagueness.Nicholas J. J. Smith - 2017 - Synthese 194 (10):3761–3787.
    From Fine and Kamp in the 70’s—through Osherson and Smith in the 80’s, Williamson, Kamp and Partee in the 90’s and Keefe in the 00’s—up to Sauerland in the present decade, the objection continues to be run that fuzzy logic based theories of vagueness are incompatible with ordinary usage of compound propositions in the presence of borderline cases. These arguments against fuzzy theories have been rebutted several times but evidently not put to rest. I attempt to do so (...)
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  2.  54
    Residuated fuzzy logics with an involutive negation.Francesc Esteva, Lluís Godo, Petr Hájek & Mirko Navara - 2000 - Archive for Mathematical Logic 39 (2):103-124.
    Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant $\overline{0}$ , namely $\neg \varphi$ is $\varphi \to \overline{0}$. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which is isomorphic to Łukasiewicz t-norm), it turns out that $\neg$ is (...)
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  3.  75
    Fuzzy logic and arithmetical hierarchy III.Petr Hájek - 2001 - Studia Logica 68 (1):129-142.
    Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies and satisfiable sentences as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated.
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  4.  46
    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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  5.  82
    A new criterion for comparing fuzzy logics for uncertain reasoning.A. D. C. Bennett, J. B. Paris & A. Vencovská - 2000 - Journal of Logic, Language and Information 9 (1):31-63.
    A new criterion is introduced for judging the suitability of various fuzzy logics for practical uncertain reasoning in a probabilistic world and the relationship of this criterion to several established criteria, and its consequences for truth functional belief, are investigated.
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  6. 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 (...)
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  7.  28
    AN ALGEBRAIC PROOF OF COMPLETENESS FOR MONADIC FUZZY PREDICATE LOGIC $\mathbf {MMTL}\boldsymbol {\forall }$.Juntao Wang, W. U. Hongwei, H. E. Pengfei & S. H. E. Yanhong - 2025 - Review of Symbolic Logic 18 (1):213-239.
    Monoidal t-norm based logic $\mathbf {MTL}$ is the weakest t-norm based residuated fuzzy logic, which is a $[0,1]$ -valued propositional logical system having a t-norm and its residuum as truth function for conjunction and implication. Monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ that consists of the formulas with unary predicates and just one object variable, is the monadic fragment of fuzzy predicate logic $\mathbf {MTL\forall }$, which is indeed the predicate version of monoidal t-norm based (...)
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  8.  58
    Fuzzy logics – quantitatively.Zofia Kostrzycka & Marek Zaionc - 2023 - Journal of Applied Non-Classical Logics 34 (1):97-132.
    The Gödel–Dummett logic and Łukasiewicz one are two main many-valued logics used by the fuzzy logic community. Our goal is a quantitative comparison of these two. In this paper, we will mostly consider the 3-valued Gödel–Dummett logic as well as the 3-valued Łukasiewicz one. We shall concentrate on their implicational-negation fragments which are limited to formulas formed with a fixed finite number of variables. First, we investigate the proportion of the number of true formulas of a certain length n (...)
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  9. Vagueness in Language: The Case Against Fuzzy Logic Revisited.Uli Sauerland - manuscript
    Kamp and Fine presented an influential argument against the use of fuzzy logic for linguistic semantics in 1975. However, the argument assumes that contradictions of the form "A and not A" have semantic value zero. The argument has been recently criticized because sentences of this form are actually not perceived as contradictory by naive speakers. I present new experimental evidence arguing that fuzzy logic still isn't useful for linguistic semantics even if we take such naive speaker judgements at (...)
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  10. Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Fourth volume: HyperUncertain Set (Collected Papers).Fujita Takaaki & Florentin Smarandache - 2025 - Gallup, NM, USA: NSIA Publishing House.
    This book represents the fourth volume in the series Collected Papers on Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. This volume specifically delves into the concept of the HyperUncertain Set, building on the foundational advancements introduced in previous volumes. The series aims to explore the ongoing evolution of uncertain combinatorics through innovative methodologies such as graphization, hyperization, and uncertainization. These approaches integrate and extend core concepts from fuzzy, neutrosophic, soft, and rough (...)
     
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  11. New Trends and Open Problems in Fuzzy Logic and Approximate Reasoning.Didier Dubois & Henri Prade - 1996 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 11 (3):109-121.
    This short paper about fuzzy set-based approximate reasoning first emphasizes the three main semantics for fuzzy sets: similarity, preference and uncertainty. The difference between truth-functional many-valued logics of vague or gradual propositions and non fully compositional calculi such as possibilistic logic or similarity logics is stressed. Then, potentials of fuzzy set-based reasoning methods are briefly outlined for various kinds of approximate reasoning: deductive reasoning about flexible constraints, reasoning under uncertainty and inconsistency, hypothetical reasoning, exception-tolerant plausible reasoning (...)
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  12. Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Second volume.Takaaki Fujita & Florentin Smarandache - 2024
    The second volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” presents a deep exploration of the progress in uncertain combinatorics through innovative methodologies like graphization, hyperization, and uncertainization. This volume integrates foundational concepts from fuzzy, neutrosophic, soft, and rough set theory, among others, to further advance the field. Combinatorics and set theory, two central pillars of mathematics, focus on counting, arrangement, and the study of collections under defined rules. Combinatorics excels (...)
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  13. Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Third volume.Florentin Smarandache - 2024
    The third volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” presents an in-depth exploration of the cutting-edge developments in uncertain combinatorics and set theory. This comprehensive collection highlights innovative methodologies such as graphization, hyperization, and uncertainization, which enhance combinatorics by incorporating foundational concepts from fuzzy, neutrosophic, soft, and rough set theories. These advancements open new mathematical horizons, offering novel approaches to managing uncertainty within complex systems. Combinatorics, a discipline focused on (...)
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  14.  39
    T-norms and ϕ-operators as truth functions of many valued connectives.Siegfried Gottwald - 1984 - Bulletin of the Section of Logic 13 (2):55-58.
    The choice of connectives for many valued propositional logics suitable for theoretical and applicational interests in most cases is an open problem up to now. We will not offer a general solution here, but support the point of view of some recent developments in fuzzy set theory that the triangular norms – t-norms for short – of Schweizer/Sklar [3] and the ϕ-operators of Pedrycz [2] represent quite general classes of connectives at least for many valued logics with truth (...)
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  15.  81
    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 (...)
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  16. A simple logic for comparisons and vagueness.Theodore J. Everett - 2000 - Synthese 123 (2):263-278.
    This article provides 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 (...)
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  17. Philosophy of Logics.Susan Haack - 1978 - London and New York: Cambridge University Press.
    The first systematic exposition of all the central topics in the philosophy of logic, Susan Haack's book has established an international reputation for its accessibility, clarity, conciseness, orderliness, and range as well as for its thorough scholarship and careful analyses. Haack discusses the scope and purpose of logic, validity, truth-functions, quantification and ontology, names, descriptions, truth, truth-bearers, the set-theoretical and semantic paradoxes, and modality. She also explores the motivations for a whole range of non-classical systems of logic, (...)
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  18. Recent Work on Vagueness.M. Eklund - 2011 - Analysis 71 (2):352-363.
    Vagueness, as discussed in the philosophical literature, is the phenomenon that paradigmatically rears its head in the sorites paradox, one prominent version of which is: One grain of sand does not make a heap. For any n, if n grains of sand do not make a heap, then n + 1 grains of sand do not make a heap. So, ten billion grains of sand do not make a heap. It is common ground that the different versions of the sorites (...)
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  19.  52
    An Application of Peircean Triadic Logic: Modelling Vagueness.Asim Raza, Asim D. Bakhshi & Basit Koshul - 2019 - Journal of Logic, Language and Information 28 (3):389-426.
    Development of decision-support and intelligent agent systems necessitates mathematical descriptions of uncertainty and fuzziness in order to model vagueness. This paper seeks to present an outline of Peirce’s triadic logic as a practical new way to model vagueness in the context of artificial intelligence. Charles Sanders Peirce was an American scientist–philosopher and a great logician whose triadic logic is a culmination of the study of semiotics and the mathematical study of anti-Cantorean model of continuity and infinitesimals. After presenting Peircean semiotics (...)
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  20.  26
    Sample logic.Matthias Gerner - 2022 - Logic Journal of the IGPL 30 (5):728-776.
    The need for a ‘many-valued logic’ in linguistics has been evident since the 1970s, but there was lack of clarity as to whether it should come from the family of fuzzy logics or from the family of probabilistic logics. In this regard, Fine [14] and Kamp [26] pointed out undesirable effects of fuzzy logic (the failure of idempotency and coherence) which kept two generations of linguists and philosophers at arm’s length. (Another unwanted feature of fuzzy logic is (...)
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  21. Computing Fuzzy Time Function.Farzad Didehvar - manuscript
    We consider time as a fuzzy concept. Based on this, the Fuzzy Time-Particle interpretation Of Quantum Mechanics is introduced as an interpretation of Quantum Mechanics [4],[5],[6]. Here, we show how to compute the function associated to Fuzzy time.
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  22. Pragmatism, skepticism, and over-compatibilism: on Michael Hannon’s What’s the Point of Knowledge?Georgi Gardiner - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    Function-first approaches illuminate phenomena by investigating their functional roles. I first describe virtues of this approach. By foregrounding normal instances of knowledge, for example, function-first theorising offers a much-needed corrective to epistemology's counterexample-driven momentum towards increasingly byzantine, marginal cases. And epistemic practices are shaped by human limitations, needs, vices, and power relations. These non-ideal, naturalistic forces of embodied sociality form the roots of function-first theorising, which creates a fecund foundation for social epistemology. Secondly, I consider an objection (...)
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  23. Fuzzy logic and approximate reasoning.L. A. Zadeh - 1975 - Synthese 30 (3-4):407-428.
    The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very false, etc. The truth-value set, , of FL is assumed to be generated by a context-free grammar, with a semantic rule providing a means of computing the meaning of each linguistic (...)
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  24. Truth transformation fuzzy logic controllers: Outlines of the design of a new generation of fuzzy controllers.L. H. Sultan & T. H. Janabi - 1991 - Ai 1991 Frontiers in Innovative Computing for the Nuclear Industry Topical Meeting, Jackson Lake, Wy, Sept. 15-18, 1991 1.
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  25. On d-Fuzzy Functions in d-Algebras.J. Neggers, A. Dvurečenskij & Hee Sik Kim - 2000 - Foundations of Physics 30 (10):1807-1816.
    In this paper we introduce the concept of d-fuzzy function which generalizes the concept of fuzzy subalgebra to a much larger class of functions in a natural way. In addition we discuss a method of fuzzification of a wide class of algebraic systems onto [0, 1] along with some consequences.
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  26.  46
    Lógica fuzzy, verdad y cognición.Alejandro Ramírez - 2014 - Revista de filosofía (Chile) 70:133-147.
    S.Haack has defended the idea that in fuzzy logic it cannot be affirmed that the true values of a statement are themselves blurry. This article analyzes Haack position in the light of some current approaches of classic philosophy of logic, and from the cognitive point of view of philosophy of logic, especially from the theory of concepts. Under the said approaches, the thesis on non-gradation of truth appears significantly weakened.
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  27.  98
    Fuzzy Galois Connections.Radim Bêlohlávek - 1999 - Mathematical Logic Quarterly 45 (4):497-504.
    The concept of Galois connection between power sets is generalized from the point of view of fuzzy logic. Studied is the case where the structure of truth values forms a complete residuated lattice. It is proved that fuzzy Galois connections are in one-to-one correspondence with binary fuzzy relations. A representation of fuzzy Galois connections by Galois connections is provided.
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  28.  25
    On witnessed models in fuzzy logic.Petr Hájek - 2007 - Mathematical Logic Quarterly 53 (1):66-77.
    Witnessed models of fuzzy predicate logic are models in which each quantified formula is witnessed, i.e. the truth value of a universally quantified formula is the minimum of the values of its instances and similarly for existential quantification. Systematic theory of known fuzzy logics endowed with this semantics is developed with special attention paid to problems of arithmetical complexity of sets of tautologies and of satisfiable formulas.
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  29.  18
    Modal, Fuzzy, ..., Vanilla Fixpoint Theories of Truth: A Uniform Approach.Melvin Fitting - 2024 - In Yale Weiss & Romina Birman, Saul Kripke on Modal Logic. Cham: Springer. pp. 151-192.
    Kripke’s work on modal logic has been immensely influential. It hardly needs remarking that this is not his only work. Here we address his pioneering applications of fixpoint constructions to the theory of truth, and related work by others. In his fundamental paper on this he explicitly described a modal version, applying a fixpoint construction world by world within a modal frame. This can certainly be carried out, and doubtless has been somewhere. Others have suggested a variety of other (...)
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  30. Grounding and truth-functions.Fabrice Correia - 2010 - Logique Et Analyse 53 (211):251-279.
    How does metaphysical grounding interact with the truth-functions? I argue that the answer varies according to whether one has a worldly conception or a conceptual conception of grounding. I then put forward a logic of worldly grounding and give it an adequate semantic characterisation.
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  31.  27
    Mathematics Behind Fuzzy Logic.Esko Turunen - 1999 - Physica-Verlag Heidelberg.
    Many results in fuzzy logic depend on the mathematical structure the truth value set obeys. In this textbook the algebraic foundations of many-valued and fuzzy reasoning are introduced. The book is self-contained, thus no previous knowledge in algebra or in logic is required. It contains 134 exercises with complete answers, and can therefore be used as teaching material at universities for both undergraduated and post-graduated courses. Chapter 1 starts from such basic concepts as order, lattice, equivalence and (...)
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  32.  22
    Fuzzy Logic and Mathematics: A Historical Perspective.Radim Bělohlávek, Joseph W. Dauben & George J. Klir - 2017 - Oxford, England and New York, NY, USA: Oxford University Press. Edited by Joseph Warren Dauben & George J. Klir.
    The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of (...)
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  33.  79
    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 (...)
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  34. On Truth-Functionality.Daniel J. Hill & Stephen K. Mcleod - 2010 - Review of Symbolic Logic 3 (4):628-632.
    Benjamin Schnieder has argued that several traditional definitions of truth-functionality fail to capture a central intuition informal characterizations of the notion often capture. The intuition is that the truth-value of a sentence that employs a truth-functional operator depends upon the truth-values of the sentences upon which the operator operates. Schnieder proposes an alternative definition of truth-functionality that is designed to accommodate this intuition. We argue that one traditional definition of ‘truth-functionality’ is immune from the (...)
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  35.  49
    Function vector synchronization based on fuzzy control for uncertain chaotic systems with dead-zone nonlinearities.Sarah Hamel, Abdesselem Boulkroune & Amel Bouzeriba - 2016 - Complexity 21 (S1):234-249.
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  36. A fuzzy measure for explanatory coherence.Daniel Schoch - 2000 - Synthese 122 (3):291-311.
    In a series of articles, Paul Thagard has developed a connectionist''s modelfor the evaluation of explanatory coherence for competing systems ofhypotheses. He has successfully applied it to various examples from thehistory of science and common language reasoning. However, I will argue thathis formalism does not adequately represent explanatory relations betweenmore than two propositions.In this paper, I develop a generalization of Thagard''s approach. It is notsubject to the connectionist paradigm of neural nets, but is based on fuzzylogic: Explanatory coherence increases with (...)
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  37. Fuzzy Logic and Higher-Order Vagueness.Nicholas J. J. Smith - 2011 - In Petr Cintula, Chris Fermüller, Lluis Godo & Petr Hájek, Logical Models of Reasoning with Vague Information. pp. 1--19.
    The major reason given in the philosophical literature for dissatisfaction with theories of vagueness based on fuzzy logic is that such theories give rise to a problem of higherorder vagueness or artificial precision. In this paper I first outline the problem and survey suggested solutions: fuzzy epistemicism; measuring truth on an ordinal scale; logic as modelling; fuzzy metalanguages; blurry sets; and fuzzy plurivaluationism. I then argue that in order to decide upon a solution, we need (...)
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  38. Kuznetsov V. From studying theoretical physics to philosophical modeling scientific theories: Under influence of Pavel Kopnin and his school.Volodymyr Kuznetsov - 2017 - ФІЛОСОФСЬКІ ДІАЛОГИ’2016 ІСТОРІЯ ТА СУЧАСНІСТЬ У НАУКОВИХ РОЗМИСЛАХ ІНСТИТУТУ ФІЛОСОФІЇ 11:62-92.
    The paper explicates the stages of the author’s philosophical evolution in the light of Kopnin’s ideas and heritage. Starting from Kopnin’s understanding of dialectical materialism, the author has stated that category transformations of physics has opened from conceptualization of immutability to mutability and then to interaction, evolvement and emergence. He has connected the problem of physical cognition universals with an elaboration of the specific system of tools and methods of identifying, individuating and distinguishing objects from a scientific theory domain. The (...)
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  39. Fuzziness and the sorites paradox.Marcelo Vasconez - 2006 - Dissertation, Catholic University of Louvain
    The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to (...)
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  40. On Vagueness, Truth Values and Fuzzy Logics.Petr Hájek - 2009 - Studia Logica 91 (3):367-382.
    Some aspects of vagueness as presented in Shapiro’s book Vagueness in Context [23] are analyzed from the point of fuzzy logic. Presented are some generalizations of Shapiro’s formal apparatus.
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  41.  6
    Literary Criticism: Reflections from a Damaged Field.William M. Chace - 2024 - Common Knowledge 30 (2):204-207.
    From mid-2020 until early 2023, the Chronicle of Higher Education published a series of essays that, when summed up, represents a valediction for English and American literary studies as practiced during the last half century. Some of the Chronicle authors, enjoying the privilege of tenure, speak for the profession as it was in healthier times. Others, representing a younger generation of scholars, hold on to unstable teaching positions. All are disconsolate.The essays, collected on the Chronicle website, look back to those (...)
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  42.  97
    On Retaining Classical Truths and Classical Deducibility in Many-Valued and Fuzzy Logics.Richard DeWitt - 2005 - Journal of Philosophical Logic 34 (5-6):545-560.
    In this paper, I identify the source of the differences between classical logic and many-valued logics (including fuzzy logics) with respect to the set of valid formulas and the set of inferences sanctioned. In the course of doing so, we find the conditions that are individually necessary and jointly sufficient for any many-valued semantics (again including fuzzy logics) to validate exactly the classically valid formulas, while sanctioning exactly the same set of inferences as classical logic. This in turn (...)
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  43. Many-Valued Logics.Nicholas J. J. Smith - 2011 - In Gillian Russell & Delia Graff Fara, Routledge Companion to Philosophy of Language. New York, USA: Routledge. pp. 636--51.
    A many-valued (aka multiple- or multi-valued) semantics, in the strict sense, is one which employs more than two truth values; in the loose sense it is one which countenances more than two truth statuses. So if, for example, we say that there are only two truth values—True and False—but allow that as well as possessing the value True and possessing the value False, propositions may also have a third truth status—possessing neither truth value—then we have (...)
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  44.  76
    Against the Spirit of Foundations: Postmodernism and David Hume.Zuzana Parusnikova - 1993 - Hume Studies 19 (1):1-17.
    In lieu of an abstract, here is a brief excerpt of the content:Against the Spirit of Foundations: Postmodernism and David Hume1 Zuzana Parusnikova Introduction David Hume lived at the very dawn ofthe modern age and belonged to the Scottish Enlightenment. The Enlightenment is often conceived of as the essence of modernity, thus standing in firm opposition to postmodernism. According to postmodernists, the Enlightenmentideal of a universal liberating rationality and the principle of universally shared norms ofhumanism have not only lost their (...)
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  45.  51
    Fuzzy equational logic.Radim Bělohlávek - 2002 - Archive for Mathematical Logic 41 (1):83-90.
    Presented is a completeness theorem for fuzzy equational logic with truth values in a complete residuated lattice: Given a fuzzy set Σ of identities and an identity p≈q, the degree to which p≈q syntactically follows (is provable) from Σ equals the degree to which p≈q semantically follows from Σ. Pavelka style generalization of well-known Birkhoff's theorem is therefore established.
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  46.  65
    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 (...)
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  47. Non-Axiomatic Reasoning System: Exploring the Essence of Intelligence.Pei Wang - 1995 - Dissertation, Indiana University
    Every artificial-intelligence research project needs a working definition of "intelligence", on which the deepest goals and assumptions of the research are based. In the project described in the following chapters, "intelligence" is defined as the capacity to adapt under insufficient knowledge and resources. Concretely, an intelligent system should be finite and open, and should work in real time. ;If these criteria are used in the design of a reasoning system, the result is NARS, a non-axiomatic reasoning system. ;NARS uses a (...)
     
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  48. Fuzzy Topology and Łukasiewicz Logics from the Viewpoint of Duality Theory.Yoshihiro Maruyama - 2010 - Studia Logica 94 (2):245-269.
    This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Łukasiewicz n -valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n -valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the algebras of modal Łukasiewicz n -valued logic with truth constants, which generalizes Jónsson-Tarski (...)
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  49. The Fuzzy Brain. Vagueness and Mapping Connectivity in the Human Cerebral Cortex.Philipp Haueis - 2012 - Frontiers in Neuroanatomy 37 (6).
    While the past century of neuroscientific research has brought considerable progress in defining the boundaries of the human cerebral cortex, there are cases in which the demarcation of one area from another remains fuzzy. Despite the existence of clearly demarcated areas, examples of gradual transitions between areas are known since early cytoarchitectonic studies. Since multi-modal anatomical approaches and functional connectivity studies brought renewed attention to the topic, a better understanding of the theoretical and methodological implications of fuzzy boundaries (...)
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  50. Fuzzy Epistemicism.John MacFarlane - 2010 - In Richard Dietz & Sebastiano Moruzzi, Cuts and clouds: vagueness, its nature, and its logic. New York: Oxford University Press.
    It is taken for granted in much of the literature on vagueness that semantic and epistemic approaches to vagueness are fundamentally at odds. If we can analyze borderline cases and the sorites paradox in terms of degrees of truth, then we don’t need an epistemic explanation. Conversely, if an epistemic explanation suffices, then there is no reason to depart from the familiar simplicity of classical bivalent semantics. I question this assumption, showing that there is an intelligible motivation for adopting (...)
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