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  1. 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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  2. 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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  3. On the Expressive Power of Łukasiewicz Square Operator.Marcelo E. Coniglio, Francesc Esteva, Tommaso Flaminio & Lluis Godo - forthcoming - Journal of Logic and Computation.
    The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...)
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  4. G'3 as the Logic of Modal 3-Valued Heyting Algebras.Marcelo E. Coniglio, Aldo Figallo-Orellano, Alejandro Hernández-Tello & Miguel Perez-Gaspar - 2022 - IfCoLog Journal of Logics and Their Applications 9 (1):175-197.
    In 2001, W. Carnielli and Marcos considered a 3-valued logic in order to prove that the schema ϕ ∨ (ϕ → ψ) is not a theorem of da Costa’s logic Cω. In 2006, this logic was studied (and baptized) as G'3 by Osorio et al. as a tool to define semantics of logic programming. It is known that the truth-tables of G'3 have the same expressive power than the one of Łukasiewicz 3-valued logic as well as the one of Gödel (...)
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  5. Performance Investigation of AC Servomotor Position Control Using Fuzzy Logic and Observer Based Controllers.Mustefa Jibril, Mesay Tadesse & Elias Alemayehu - 2021 - Report and Opinion Journal 13 (1):1-5.
    An AC servomotor which is mostly a two-phase induction motor with two stator field coils placed 90 electrical degrees apart used for controlling position, speed and acceleration in manufacturing industries. In this paper, a two-phase induction motor has been designed with a fuzzy logic and observer based controllers to improve the performance of the system. Comparison of the AC servomotor with the proposed controllers for tracking a step and a square desired position signal input has been done using Matlab/Simulink toolbox (...)
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  6. 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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  7. Logics Based on Linear Orders of Contaminating Values.Roberto Ciuni, Thomas Macaulay Ferguson & Damian Szmuc - 2019 - Journal of Logic and Computation 29 (5):631–663.
    A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula φ⁠, any complex formula in which φ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple contaminating (...)
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  8. 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.
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  9. 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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  10. 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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  11. 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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  12. 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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  13. 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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  14. Concepts and Fuzzy Logic. (Review Article). [REVIEW]Mihai Nadin - 2012 - International Journal of General Systems 41 (8):860-867.
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  15. Being Metaphysically Unsettled: Barnes and Williams on Metaphysical Indeterminacy and Vagueness.Matti Eklund - 2011 - Oxford Studies in Metaphysics 6:6.
    This chapter discusses the defence of metaphysical indeterminacy by Elizabeth Barnes and Robert Williams and discusses a classical and bivalent theory of such indeterminacy. Even if metaphysical indeterminacy arguably is intelligible, Barnes and Williams argue in favour of it being so and this faces important problems. As for classical logic and bivalence, the chapter problematizes what exactly is at issue in this debate. Can reality not be adequately described using different languages, some classical and some not? Moreover, it is argued (...)
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  16. 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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  17. 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 the (...)
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  18. 4. Contradictorial Gradualism Vs. Discontinuism: Two Views On Fuzziness And The Transition Problem.Marcelo VÁsconez - 2006 - Logique Et Analyse 49 (195).
    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 the (...)
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  19. 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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  20. 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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  21. A Simple Logic for Comparisons and Vagueness.Theodore J. Everett - 2000 - Synthese 123 (2):263-278.
    This article 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 (...)
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  22. 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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  23. 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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  24. Self-Reference and Chaos in Fuzzy Logic.Patrick Grim - 1993 - IEEE Transactions on Fuzzy Systems 1:237-253.
    The purpose of this paper is to open for investigation a range of phenomena familiar from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the [0, 1] interval. Strange attractors and fractals appear in two dimensions in the graphing of pairs of mutually referential sentences and appear in three dimensions in the graphing of (...)
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  25. Hedges: A Study in Meaning Criteria and the Logic of Fuzzy Concepts. [REVIEW]George Lakoff - 1973 - Journal of Philosophical Logic 2 (4):458 - 508.
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  26. The Metaphysics of Trust.Rowland Stout -
    I argue against the claim that the fundamental form of trust is a 2-place relation of A trusting B and in favour of the fundamental form being a 4-place relation of A, by ψ-ing, trusting B to φ. I characterize trusting behaviour as behaviour that knowingly makes one reliant on someone doing what they are supposed to do in the collaborative enterprise that the trusting behaviour belongs to. I explain how trust is involved in the following collaborative enterprises: knowledge transfer (...)
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