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  1. 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 face value. (...)
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  2. Some Strong Conditionals for Sentential Logics.Jason Zarri - manuscript
    In this article I define a strong conditional for classical sentential logic, and then extend it to three non-classical sentential logics. It is stronger than the material conditional and is not subject to the standard paradoxes of material implication, nor is it subject to some of the standard paradoxes of C. I. Lewis’s strict implication. My conditional has some counterintuitive consequences of its own, but I think its pros outweigh its cons. In any case, one can always augment one’s language (...)
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  3. The Principle of the Impossibility of Contradiction: The Transcendent Philosophy and Fuzzy Logic.Mahdi Yazdi - unknown - Kheradnameh Sadra Quarterly 50.
    In today's academic circles, many are of the opinion that fuzzy logic has brought the age-old principle of contradiction to an end. In this light, objective reality can no longer be reduced to A and non-A, or to zero and one. But is this presumption correct? Does fuzzy logic really violate the principle of contradiction? Is it true that fuzzy logic - in contrast to the Transcendent Philosophy - is based on the assumption that two contradictories can be true and (...)
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  4. How Much Propositional Logic Suffices for Rosser’s Essential Undecidability Theorem?Guillermo Badia, Petr Cintula, Petr Hajek & Andrew Tedder - forthcoming - Review of Symbolic Logic:1-18.
    In this paper we explore the following question: how weak can a logic be for Rosser's essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson's Q is essentially undecidable in intuitionistic logic, and P. Hajek proved it in the fuzzy logic BL for Grzegorczyk's variant of Q which interprets the arithmetic operations as non-total non-functional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much (...)
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  5. Syntactic Characterizations of First-Order Structures in Mathematical Fuzzy Logic.Guillermo Badia, Pilar Dellunde, Vicent Costa & Carles Noguera - forthcoming - Soft Computing.
    This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.
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  6. A Lindström Theorem in Many-Valued Modal Logic Over a Finite MTL-Chain.Guillermo Badia & Grigory Olkhovikov - forthcoming - Fuzzy Sets and Systems.
    We consider a modal language over crisp frames and formulas evaluated on a finite MTL-chain (a linearly ordered commutative integral residuated lattice). We first show that the basic modal abstract logic with constants for the values of the MTL-chain is the maximal abstract logic satisfying Compactness, the Tarski Union Property and strong invariance for bisimulations. Finally, we improve this result by replacing the Tarski Union Property by a relativization property.
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  7. Many-Valued Logic and Sequence Arguments in Value Theory.Simon Knutsson - forthcoming - Synthese.
    Some find it plausible that a sufficiently long duration of torture is worse than any duration of mild headaches. Similarly, it has been claimed that a million humans living great lives is better than any number of worm-like creatures feeling a few seconds of pleasure each. Some have related bad things to good things along the same lines. For example, one may hold that a future in which a sufficient number of beings experience a lifetime of torture is bad, regardless (...)
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  8. On Monotonic Fuzzy Conditionals, Enviado 2I.E. Trillas & S. Cubillo - forthcoming - Journal of Applied Non-Classical Logics.
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  9. Fuzzy Logic.Kazem Sadegh-Zadeh - 2nd ed. 2015 - In Handbook of Analytic Philosophy of Medicine. Springer Verlag.
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  10. Many-Valued Logics. A Mathematical and Computational Introduction.Luis M. Augusto - 2020 - London: College Publications.
    2nd edition. 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 (...)
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  11. Maximality in Finite-Valued Lukasiewicz Logics Defined by Order Filters.Marcelo E. Coniglio, Francesc Esteva, Joan Gispert & Lluis Godo - 2019 - Journal of Logic and Computation 29 (1):125-156.
  12. Problems of Precision in Fuzzy Theories of Vagueness and Bayesian Epistemology.Nicholas J. J. Smith - 2019 - In Richard Dietz (ed.), Vagueness and Rationality in Language Use and Cognition. Springer Verlag. pp. 31-48.
    A common objection to theories of vagueness based on fuzzy logics centres on the idea that assigning a single numerical degree of truth -- a real number between 0 and 1 -- to each vague statement is excessively precise. A common objection to Bayesian epistemology centres on the idea that assigning a single numerical degree of belief -- a real number between 0 and 1 -- to each proposition is excessively precise. In this paper I explore possible parallels between these (...)
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  13. On the Borders of Vagueness and the Vagueness of Borders.Rory Collins - 2018 - Vassar College Journal of Philosophy 5:30-44.
    This article argues that resolutions to the sorites paradox offered by epistemic and supervaluation theories fail to adequately account for vagueness. After explaining the paradox, I examine the epistemic theory defended by Timothy Williamson and discuss objections to his semantic argument for vague terms having precise boundaries. I then consider Rosanna Keefe's supervaluationist approach and explain why it fails to accommodate the problem of higher-order vagueness. I conclude by discussing how fuzzy logic may hold the key to resolving the sorites (...)
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  14. “Do the Gods Play Dice?”. Sensible Sequentialism and Fuzzy Logic in Plato’s Timaeus.Francesco Fronterotta - 2018 - Discipline Filosofiche 28 (1):13-32.
    In this paper I propose a reconstruction of the onto-cosmological perspective of Plato’s Timaeus and suggest an interpretation of it in the light of some contemporary approaches to ontology and logic, i.e. “ontological sequentialism” and “fuzzy logic”, attempting to use the categories and language of present-day ontology and logic to examine from a different point of view some aspects of the Timaeus onto-cosmology and of its logical scaffolding.
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  15. Many-Valued And Fuzzy Logic Systems From The Viewpoint Of Classical Logic.Ekrem Sefa Gül - 2018 - Tasavvur - Tekirdag Theology Journal 4 (2):624 - 657.
    The thesis that the two-valued system of classical logic is insufficient to explanation the various intermediate situations in the entity, has led to the development of many-valued and fuzzy logic systems. These systems suggest that this limitation is incorrect. They oppose the law of excluded middle (tertium non datur) which is one of the basic principles of classical logic, and even principle of non-contradiction and argue that is not an obstacle for things both to exist and to not exist at (...)
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  16. 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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  17. A Logical Framework for Graded Predicates.Petr Cintula, Carles Noguera & Nicholas J. J. Smith - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction: LORI 2017. Berlin: Springer. pp. 3-16.
    In this position paper we present a logical framework for modelling reasoning with graded predicates. We distinguish several types of graded predicates and discuss their ubiquity in rational interaction and the logical challenges they pose. We present mathematical fuzzy logic as a set of logical tools that can be used to model reasoning with graded predicates, and discuss a philosophical account of vagueness that makes use of these tools. This approach is then generalized to other kinds of graded predicates. Finally, (...)
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  18. Vagueness and Formal Fuzzy Logic: Some Criticisms.Giangiacomo Gerla - 2017 - Logic and Logical Philosophy 26 (4).
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  19. Fuzzy Sets and Fuzzy Logic in Austria.Erich Peter Klement - 2017 - Archives for the Philosophy and History of Soft Computing 2017 (1).
    We sketch the development of fuzzy sets and fuzzy logic in Austria during the last 50 years which started, after some early traces, in 1976 in Linz with my own work and in Vienna with Klaus-Peter Adlassnig’s work. Therefore we first discuss the history of our research group at the Johannes Kepler University Linz and at the JKU-Softwarepark Hagenberg. Next we have a closer look at the developments at the Vienna University Medical School, at the logic group at the Vienna (...)
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  20. A Brief History of Fuzzy Logic in the Czech Republic and Significance of P. Hájek for Its Development.Vilém Novák - 2017 - Archives for the Philosophy and History of Soft Computing 2017 (1).
    In this paper, we will briefly look at the history of mathematical fuzzy logic in Czechoslovakia starting from the 1970s and extending until 2009. The role of P. Ha ́jek in the development of fuzzy logic is especially emphasized.
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  21. Undead Argument: The Truth-Functionality Objection to Fuzzy Theories of Vagueness.Nicholas Smith - 2017 - Synthese 194 (10):1-27.
    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 in this (...)
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  22. On How Fuzzy Logic Began in Spain.Enric Trillas - 2017 - Archives for the Philosophy and History of Soft Computing 2017 (1).
    Historically, there have been some problems that initially were philosophically posed, either in mystical or in metaphysical terms but that, latter on and step-by-step, were translated into scientific terms and through a process of successive clarifications allowing to arrive, finally, at a scientific theory in which its more essential treats are clearly defined and facilitates its measuring.
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  23. Pavelka-Style Fuzzy Justification Logics.Meghdad Ghari - 2016 - Logic Journal of the IGPL 24 (5):743-773.
    Justification logics provide a framework for reasoning about justifications and evidence. In this article, we study a fuzzy variant of justification logics in which an agent’s justification for a belief has certainty degree between 0 and 1. We replace the classical base of justification logics with Hájek’s rational Pavelka logic. We introduce fuzzy possible world semantics with crisp accessibility relation and also single world models for our logics. We establish soundness and graded-style completeness for both kinds of semantics. We also (...)
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  24. Multiple Criteria Decision Making Method Based on Normal Interval-Valued Intuitionistic Fuzzy Generalized Aggregation Operator.Peide Liu & Fei Teng - 2016 - Complexity 21 (5):277-290.
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  25. 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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  26. Handbook of Mathematical Fuzzy Logic - Volume 3.Petr Cintula, Christian Fermüller & Carles Noguera (eds.) - 2015 - College Publications.
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  27. Pragmatic Interpretations of Vague Expressions: Strongest Meaning and Nonmonotonic Consequence.Pablo Cobreros, Paul Egré, Dave Ripley & Robert van Rooij - 2015 - Journal of Philosophical Logic 44 (4):375-393.
    Recent experiments have shown that naive speakers find borderline contradictions involving vague predicates acceptable. In Cobreros et al. we proposed a pragmatic explanation of the acceptability of borderline contradictions, building on a three-valued semantics. In a reply, Alxatib et al. show, however, that the pragmatic account predicts the wrong interpretations for some examples involving disjunction, and propose as a remedy a semantic analysis instead, based on fuzzy logic. In this paper we provide an explicit global pragmatic interpretation rule, based on (...)
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  28. Fuzzy Ethics.Michael James Heron & Pauline Belford - 2015 - Acm Sigcas Computers and Society 45 (4):4-6.
    The recent death of a Volkswagen worker at the hand of a factory robot has resulted in a number of editorials and opinion pieces discussing moral responsibility and robots. In this short response piece we outline some of the wider context of this discussion, with reference to the classic ethical study the Case of the Killer Robot. We argue that there is a growing need for the field of computer ethics to consider with some urgency what it means to be (...)
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  29. Vague Heuristics.María G. Navarro - 2015 - In Rudolf Seising and Luis Argüelles (ed.), Conjectures, Hypotheses, and Fuzzy Logic. Springer. pp. 281-294.
    Even when they are defined with precision, one can often read and hear judgments about the vagueness of heuristics in debates about heuristic reasoning. This opinion is not just frequent but also quite reasonable. In fact, during the 1990s, there was a certain controversy concerning this topic that confronted two of the leading groups in the field of heuristic reasoning research, each of whom held very different perspectives. In the present text, we will focus on two of the papers published (...)
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  30. Fuzzy Logics in Theories of Vagueness.Nicholas J. J. Smith - 2015 - In Petr Cintula, Christian Fermüller & Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic - Volume 3. College Publications.
  31. Substructural Fuzzy-Relevance Logic.Eunsuk Yang - 2015 - Notre Dame Journal of Formal Logic 56 (3):471-491.
    This paper proposes a new topic in substructural logic for use in research joining the fields of relevance and fuzzy logics. For this, we consider old and new relevance principles. We first introduce fuzzy systems satisfying an old relevance principle, that is, Dunn’s weak relevance principle. We present ways to obtain relevant companions of the weakening-free uninorm systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication and its neighbors. The algebraic structures corresponding to (...)
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  32. Algebraic Geometry for Mv-Algebras.Lawrence P. Belluce, Antonio di Nola & Giacomo Lenzi - 2014 - Journal of Symbolic Logic 79 (4):1061-1091.
  33. Introduction to the Special Issue Epistemic Aspects of Many-Valued Logics.Timothy Childers & Ondrej Majer - 2014 - Erkenntnis 79 (5):969-970.
    The papers in this special issue are based on presentations delivered at the conference Epistemic Aspects of Many-valued Logics, held at the Institute of Philosophy of the Academy of Sciences of the Czech Republic, in Prague, 2010. All papers consequently revolve around the application of non-classical logical tools—mathematical fuzzy logic and/or probability theory—to epistemological issues.Timothy Williamson employs a modal epistemic logic enriched with probabilities to generalize an argument against the KK-principle. He argues that we can know a proposition even if (...)
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  34. Logics of Formal Inconsistency Arising From Systems of Fuzzy Logic.Marcelo E. Coniglio, Francesc Esteva & Lluís Godo - 2014 - Logic Journal of the IGPL 22 (6):880-904.
    This article proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this article we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and inconsistency in the style of the so-called Logics of Formal Inconsistency (LFIs). The main novelty of the present approach is the definition of postulates for this type of operators over MTL-algebras, leading to the definition and axiomatization of a family of logics, expansions of (...)
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  35. Radim Belohlavek and George J. Klir , Concepts and Fuzzy Logic.Igor Douven - 2014 - Studia Logica 102 (5):1075-1077.
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  36. Reasoning About Opinion Dynamics in Social Networks.Jens Ulrik Hansen - 2014 - In Thomas Ågotnes, Giacomo Bonanno & Wiebe Van Der Hoek (eds.), Proceedings of the eleventh conference on logic and the foundations of game and decision theory (LOFT 11). pp. 1121-1137.
    This paper introduces a logic to reason about a well-known model of opinion dynamics in socialnetworks initially developed by Morris DeGroot as well as Keith Lehrer and Carl Wagner. The proposed logic is an extension of Lukasiewicz' famous fuzzy logic with additional equational expressivity, modal operators, machinery from hybrid logic, and dynamic modalities. The model of opinion dynamics in social networks is simple enough to be easily grasped, but still complex enough to have interesting mathematical properties and applications. Thus, developing (...)
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  37. 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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  38. 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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  39. Curry’s Paradox and Ω -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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  40. 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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  41. Generalized Bosbach States: Part I. [REVIEW]Lavinia Corina Ciungu, George Georgescu & Claudia Mureşan - 2013 - Archive for Mathematical Logic 52 (3-4):335-376.
    States have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in [0,1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0,1], in this paper we introduce Bosbach states defined on residuated lattices with values in residuated lattices. We are led to two types of generalized Bosbach states, with distinct behaviours. Properties of generalized states are useful for the development of an (...)
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  42. How Far Can We Go with Fuzzy Logic? Perspectives on Model-Based Reasoning and Stochastic Resonance in Scientific Models.S. De Bianchi & S. Gaudenzi - 2013 - Logic Journal of the IGPL 21 (6):1044-1056.
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  43. On Elementary Equivalence in Fuzzy Predicate Logics.Pilar Dellunde & Francesc Esteva - 2013 - Archive for Mathematical Logic 52 (1-2):1-17.
    Our work is a contribution to the model theory of fuzzy predicate logics. In this paper we characterize elementary equivalence between models of fuzzy predicate logic using elementary mappings. Refining the method of diagrams we give a solution to an open problem of Hájek and Cintula (J Symb Log 71(3):863–880, 2006, Conjectures 1 and 2). We investigate also the properties of elementary extensions in witnessed and quasi-witnessed theories, generalizing some results of Section 7 of Hájek and Cintula (J Symb Log (...)
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  44. Richard Dietz and Sebastiano Moruzzi (Eds.): Cuts and Clouds. Vagueness, its Nature, and its Logic. [REVIEW]Tania Eden - 2013 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 44 (1):247-251.
  45. Arguments Whose Strength Depends on Continuous Variation.James Franklin - 2013 - Informal Logic 33 (1):33-56.
    Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so (...)
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  46. Some Remarks on Cantor-Lukasiewicz Fuzzy Set Theory.P. Hajek - 2013 - Logic Journal of the IGPL 21 (2):183-186.
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  47. Interpreting Lattice-Valued Set Theory in Fuzzy Set Theory.P. Hajek & Z. Hanikova - 2013 - Logic Journal of the IGPL 21 (1):77-90.
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  48. How to Explain 2% Barrier in Teaching Computer Science: Towards New Applications of Fuzzy Ideas.Olga Kosheleva & Vladik Kreinovich - 2013 - Archives for the Philosophy and History of Soft Computing 2013 (1).
    Computer science educators observed that in the present way of teaching computing, only 2% of students can easily handle computational concepts -- and, as a result, only 2% of the students specialize in computer science. With the increasing role of computers in the modern world, and the increasing need for computer-related jobs, this 2% barrier creates a shortage of computer scientists. We notice that the current way of teaching computer science is based on easiness of using two-valued logic, on easiness (...)
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  49. Logic, Metalogic and Neutrality.Timothy Williamson - 2013 - Erkenntnis 79 (Suppl 2):211-231.
    The paper is a critique of the widespread conception of logic as a neutral arbiter between metaphysical theories, one that makes no `substantive’ claims of its own. A familiar observation is that virtually every putatively fundamental principle of logic has been challenged over the last century on broadly metaphysical grounds, with a consequent proliferation of alternative logics. However, this apparent contentiousness of logic is often treated as though it were neutralized by the possibility of studying all these alternative logics within (...)
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  50. 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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