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  1. added 2020-05-27
    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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  2. added 2020-05-13
    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. added 2020-05-13
    Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic Via Linear Nested Sequents.Tim Lyon - 2020 - In Sergei Artemov & Anil Nerode (eds.), Logical Foundations of Computer Science. Cham: pp. 156-176.
    This paper employs the linear nested sequent framework to design a new cut-free calculus (LNIF) for intuitionistic fuzzy logic---the first-order Goedel logic characterized by linear relational frames with constant domains. Linear nested sequents---which are nested sequents restricted to linear structures---prove to be a well-suited proof-theoretic formalism for intuitionistic fuzzy logic. We show that the calculus LNIF possesses highly desirable proof-theoretic properties such as invertibility of all rules, admissibility of structural rules, and syntactic cut-elimination.
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  4. added 2020-05-13
    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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  5. added 2020-05-13
    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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  6. added 2020-05-13
    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).
    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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  7. added 2020-05-13
    Concepts and Fuzzy Logic. (Review Article). [REVIEW]Mihai Nadin - 2012 - International Journal of General Systems 41 (8):860-867.
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  8. added 2020-05-13
    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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  9. added 2020-05-13
    Searching the Arcane Origins of Fuzzy Logic.Angel Garrido - 2011 - BRAIN. Broad Research in Artificial Intelligence and Neuroscience 2.
    ABSTRACT It is well-known that Artificial Intelligence requires Logic. But its Classical version shows too many insufficiencies. So, it is very necessary to introduce more sophisticated tools, as may be Fuzzy Logic, Modal Logic, Non-Monotonic Logic, and so on. When you are searching the possible precedent of such new ideas, we may found that they are not totally new, because some ancient thinkers have suggested many centuries ago similar concepts, certainly without adequate mathematical formulation, but in the same line: against (...)
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  10. added 2020-05-13
    Haack On Fuzzy Logic.Joseph Grunfeld - 1998 - The Paideia Archive: Twentieth World Congress of Philosophy 8:65-69.
    Much of the progress in modern logic beyond Aristotle is due to the invention of a precise and powerful formalism, and this is why Haack is reluctant to weaken it. What motivates her to regard deviant and fuzzy logic as extensions rather than rivals of classical logic is its demonstrated capacity for refinement and progress. Thus she sharply distinguishes between a logic dealing with fuzzy concepts, and one which is itself fuzzy, i.e., where "true" and "false" cease to be precise (...)
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  11. added 2020-05-13
    Computational Complexity and the Origin of Universals.Leonid I. Perlovsky - 1998 - The Paideia Archive: Twentieth World Congress of Philosophy 35:175-185.
    This paper establishes close relationships between fundamental problems in the philosophical and mathematical theories of mind. It reviews the mathematical concepts of intelligence, including pattern recognition algorithms, neural networks and rule systems. Mathematical difficulties manifest as combinatorial complexity of algorithms are related to the roles of a priori knowledge and adaptive learning, the same issues that have shaped the two-thousand year old debate on the origins of the universal concepts of mind. Combining philosophical and mathematical analyses enables tracing current mathematical (...)
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  12. added 2019-10-09
    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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  13. added 2019-06-06
    Fuzzy Membership Mapped Onto Intervals and Many‐Valued Quantities.I. Grattan-Guinness - 1976 - Mathematical Logic Quarterly 22 (1):149-160.
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  14. added 2019-06-03
    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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  15. added 2019-03-26
    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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  16. added 2018-10-15
    “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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  17. added 2018-10-15
    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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  18. added 2018-10-15
    Vagueness and Formal Fuzzy Logic: Some Criticisms.Giangiacomo Gerla - 2017 - Logic and Logical Philosophy 26 (4).
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  19. added 2018-10-15
    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. added 2018-10-15
    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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  21. added 2018-10-15
    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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  22. added 2018-10-15
    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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  23. added 2018-10-15
    N-Ary Fuzzy Logic and Neutrosophic Logic Operators.Florentin Smarandache & Vic Christianto - 2009 - Studies in Logic, Grammar and Rhetoric 17 (30).
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  24. added 2018-10-15
    Epistemic Fundamentals of Fuzzy Logic: A Critical Study.Mehdi Hoseinzādeh Yazdi - 2008 - Journal of Philosophical Theological Research 9 (36):121-146.
    In a vague way, Fuzzy Logic seeks to draw external realities thoroughly as one might say. Epistemic aspects of such an attitude, which enjoys technical origins, were considered further when surprising successes were accomplished in the field of industrial produces. Almost all theorists of fuzzy logic hold that the epistemic fundamentals of fuzzy logic should be looked for in Greek sophists’ thinking and in fact, fuzzy continues the same process of thinking. They build such a thought on the principles which (...)
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  25. added 2018-10-15
    Vagueness by Numbers? No Worries.Nicholas J. J. Smith - 2003 - Mind 112 (446):283-290.
    Rosanna Keefe (`Vagueness by Numbers' MIND 107 1998 565--79) argues that theories of vagueness based upon fuzzy logic and set theory rest on a confusion: once we have assigned a number to an object to represent (for example) its *height*, there is no distinct purpose left to be served by assigning a number to the object to represent its *degree of tallness*; she claims that ``any numbers assigned in an attempt to capture the vagueness of `tall' do no more than (...)
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  26. added 2018-04-07
    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.
  27. added 2017-11-07
    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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  28. added 2017-10-10
    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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  29. added 2017-08-13
    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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  30. added 2017-08-13
    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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  31. added 2017-08-13
    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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  32. added 2017-05-31
    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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  33. added 2017-03-14
    Metamathematics of Fuzzy Logic.P. Hájek - 2002 - Studia Logica 72 (3):433-437.
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  34. added 2017-03-14
    Mathematics Behind Fuzzy Logic.Esko Turunen - 2002 - Studia Logica 71 (1):139-141.
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  35. added 2017-03-14
    The Liar Paradox and Fuzzy Logic.Petr Hajek, Jeff Paris & John Shepherdson - 2000 - Journal of Symbolic Logic 65 (1):339-346.
    Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr saying "x is true" and satisfying the "dequotation schema" $\varphi \equiv \text{Tr}$ for all sentences $\varphi$? This problem is investigated in the frame of Lukasiewicz infinitely valued logic.
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  36. added 2017-02-16
    Vagueness, Logic and Ontology by Dominic Hyde. [REVIEW]Nicholas J. J. Smith - 2010 - Bulletin of Symbolic Logic 16 (4):531-532.
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  37. added 2017-02-15
    On Monotonic Fuzzy Conditionals, Enviado 2I.E. Trillas & S. Cubillo - forthcoming - Journal of Applied Non-Classical Logics.
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  38. added 2017-02-15
    GIUNTINI, Fuzzy Intuitionistic Quantum Logics,(P. 459 Ss.).G. Cattaneo-Ml Dalla Chiara-R. - 1993 - Studia Logica 52 (3).
  39. added 2017-02-14
    Dominic Hyde, Vagueness, Logic and Ontology. Aldershot: Ashgate, 2008. XII Þ 226 Pp.£ 55. Isbn 978-0-7546-1532-3. [REVIEW]Graham Priest - 2010 - History and Philosophy of Logic 31 (2):184.
  40. added 2017-02-14
    Varieties of BL-Algebras Generated by Continuous T-Norms and Their Residua.F. Esteva, L. Godo & F. Montagna - 2004 - Studia Logica 76 (2):161-200.
    In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and its residuum. Actually, the (...)
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  41. added 2017-02-14
    Product Ukasiewicz Logic.Rostislav Hork & Petr Cintula - 2004 - Archive for Mathematical Logic 4.
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  42. added 2017-02-12
    Representation of MV-Algebras by Regular Ultrapowers of [0, 1].Antonio Di Nola, Giacomo Lenzi & Luca Spada - 2010 - Archive for Mathematical Logic 49 (4):491-500.
    We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in a definable (...)
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  43. added 2017-02-12
    Representation and Extension of States on MV-Algebras.TomአKroupa - 2005 - Archive for Mathematical Logic 45 (4):381-392.
    MV-algebras stand for the many-valued Łukasiewicz logic the same as Boolean algebras for the classical logic. States on MV-algebras were first mentioned [20] in probability theory and later also introduced in effort to capture a notion of `an average truth-value of proposition' [15] in Łukasiewicz many-valued logic. In the presented paper, an integral representation theorem for finitely-additive states on semisimple MV-algebra will be proven. Further, we shall prove extension theorems concerning states defined on sub-MV-algebras and normal partitions of unity generalizing (...)
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  44. added 2017-02-12
    Natural Dualities for Varieties of BL-Algebras.Antonio Di Nola & Philippe Niederkorn - 2005 - Archive for Mathematical Logic 44 (8):995-1007.
    BL-algebras are the Lindenbaum algebras for Hájek's Basic Logic, just as Boolean algebras correspond to the classical propositional calculus. The finite totally ordered BL-algebras are ordinal sums of MV-chains. We develop a natural duality, in the sense of Davey and Werner, for each subvariety generated by a finite BL-chain, and we use it to describe the injective and the weak injective members of these classes.
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  45. added 2017-02-12
    Partial Algebras for Łukasiewicz Logics and its Extensions.Thomas Vetterlein - 2005 - Archive for Mathematical Logic 44 (7):913-933.
    It is a well-known fact that MV-algebras, the algebraic counterpart of Łukasiewicz logic, correspond to a certain type of partial algebras: lattice-ordered effect algebras fulfilling the Riesz decomposition property. The latter are based on a partial, but cancellative addition, and we may construct from them the representing ℓ-groups in a straightforward manner. In this paper, we consider several logics differing from Łukasiewicz logics in that they contain further connectives: the PŁ-, PŁ'-, PŁ'△-, and ŁΠ-logics. For all their algebraic counterparts, we (...)
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  46. added 2017-02-12
    On the Continuity Points of Left-Continuous T-Norms.S. Jenei & F. Montagna - 2003 - Archive for Mathematical Logic 42 (8):797-810.
    Left-continuous t-norms are much more complicated than the continuous ones, and obtaining a complete classification of them seems to be a very hard task. In this paper we investigate some aspects of left-continuous t-norms, with emphasis on their continuity points. In particular, we are interested in left-continuous t-norms which are isomorphic to t-norms which are continuous in the rationals. We characterize such a class, and we prove that it contains the class of all weakly cancellative left-continuous t-norms.
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  47. added 2017-02-11
    Book Review: Stewart Shapiro. Vagueness in Context. [REVIEW]Leon Horsten - 2009 - Notre Dame Journal of Formal Logic 50 (2):221-226.
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  48. added 2017-02-11
    Review: Tadeusz Kubinski, Vague Terms. [REVIEW]Czeslaw Lejewski - 1959 - Journal of Symbolic Logic 24 (3):270-271.
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  49. added 2017-02-11
    Review: Max Black, Vagueness. An Exercise in Logical Analysis. [REVIEW]Ernest Nagel - 1938 - Journal of Symbolic Logic 3 (1):48-49.
  50. added 2017-02-10
    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.
1 — 50 / 366