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  1. M. E. Adams & R. Cignoli (1990). A Note on the Axiomatization of Equational Classes of $N$-Valued Ł Ukasiewicz Algebras. Notre Dame Journal of Formal Logic 31 (2):304-307.
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  2. Stefano Aguzzoli, Matteo Bianchi & Vincenzo Marra (2009). A Temporal Semantics for Basic Logic. Studia Logica 92 (2):147 - 162.
    In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL formulas (...)
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  3. Stefano Aguzzoli & Agata Ciabattoni (2000). Finiteness in Infinite-Valued Łukasiewicz Logic. Journal of Logic, Language and Information 9 (1):5-29.
    In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued ukasiewicz logic to a suitable m-valued ukasiewicz logic m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in if and only if it is also valid in m. We also reduce the notion of logical consequence in to the same (...)
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  4. Stefano Aguzzoli & Brunella Gerla (2002). Finite-Valued Reductions of Infinite-Valued Logics. Archive for Mathematical Logic 41 (4):361-399.
    In this paper we present a method to reduce the decision problem of several infinite-valued propositional logics to their finite-valued counterparts. We apply our method to Łukasiewicz, Gödel and Product logics and to some of their combinations. As a byproduct we define sequent calculi for all these infinite-valued logics and we give an alternative proof that their tautology problems are in co-NP.
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  5. Hacı Aktaş & Naim Çağman (2007). A Type of Fuzzy Ring. Archive for Mathematical Logic 46 (3-4):165-177.
    In this study, by the use of Yuan and Lee’s definition of the fuzzy group based on fuzzy binary operation we give a new kind of fuzzy ring. The concept of fuzzy subring, fuzzy ideal and fuzzy ring homomorphism are introduced, and we make a theoretical study their basic properties analogous to those of ordinary rings.
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  6. Sam Alxatib, Peter Pagin & Uli Sauerland (2013). Acceptable Contradictions: Pragmatics or Semantics? A Reply to Cobreros Et Al. [REVIEW] 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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  7. K. T. Atanassov & A. G. Shannon (1998). A Note on Intuitionistic Fuzzy Logics. Acta Philosophica 7:121-125.
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  8. Radim B.& X. B.. Lohl& X. 000 E. 1 vek (2002). Fuzzy Equational Logic. Archive for Mathematical Logic 41 (1):83-90.
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  9. R. B.? Lohl├ Ívek & V. M. Vychodil (2006). Fuzzy Horn Logic II. Archive for Mathematical Logic 45 (2):149.
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  10. Franz Baader, Stefan Borgwardt & Rafael Peñaloza (2015). On the Decidability Status of Fuzzy A ℒ C with General Concept Inclusions. 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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  11. Matthias Baaz, Petr Hájek, Franco Montagna & Helmut Veith (2001). Complexity of T-Tautologies. Annals of Pure and Applied Logic 113 (1-3):3-11.
    A t-tautology is a propositional formula which is a tautology in all fuzzy logics defined by continuous triangular norms. In this paper we show that the problem of recognizing t-tautologies is coNP complete, and thus decidable.
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  12. Matthias Baaz & Helmut Veith (1999). Interpolation in Fuzzy Logic. Archive for Mathematical Logic 38 (7):461-489.
    We investigate interpolation properties of many-valued propositional logics related to continuous t-norms. In case of failure of interpolation, we characterize the minimal interpolating extensions of the languages. For finite-valued logics, we count the number of interpolating extensions by Fibonacci sequences.
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  13. Andrew Bacon (2013). Curry's Paradox and Omega Inconsistency. 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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  14. J. F. Baldwin (1996). Fuzzy Logic.
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  15. J. F. Baldwin & N. C. F. Guild (1980). The Resolution of Two Paradoxes by Approximate Reasoning Using a Fuzzy Logic. Synthese 44 (3):397 - 420.
    The method of approximate reasoning using a fuzzy logic introduced by Baldwin (1978 a,b,c), is used to model human reasoning in the resolution of two well known paradoxes. It is shown how classical propositional logic fails to resolve the paradoxes, how multiple valued logic partially succeeds and that a satisfactory resolution is obtained with fuzzy logic. The problem of precise representation of vague concepts is considered in the light of the results obtained.
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  16. Hans Bandemer & Siegfried Gottwald (1995). Fuzzy Sets, Fuzzy Logic, Fuzzy Methods with Applications.
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  17. Senén Barro, Alberto Bugarín & Alejandro Sobrino E. Senén Barro (eds.) (1998). Advances in Fuzzy Logic: Selected Papers (with Comments) of Some Spanish Authors. Universidade De Santiago De Compostela.
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  18. Gordon Beavers (1993). Automated Theorem Proving for Łukasiewicz Logics. Studia Logica 52 (2):183 - 195.
    This paper is concerned with decision proceedures for the 0-valued ukasiewicz logics,. It is shown how linear algebra can be used to construct an automated theorem checker. Two decision proceedures are described which depend on a linear programming package. An algorithm is given for the verification of consequence relations in, and a connection is made between theorem checking in two-valued logic and theorem checking in which implies that determing of a -free formula whether it takes the value one is NP-complete (...)
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  19. Libor Běhounek (2011). Comments on 'Fuzzy Logic and Higher-Order Vagueness' by Nicholas J.J. Smith. In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications 21-8.
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  20. Libor Behounek (2004). Fuzzification of Groenendijk-Stokhof Propositional Erotetic Logic. Logique Et Analyse 47.
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  21. John L. Bell, David DeVidi & Graham Solomon (2001). Logical Options: An Introduction to Classical and Alternative Logics. Broadview Press.
    Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some (...)
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  22. Radim Bělohlávek (2003). Birkhoff Variety Theorem and Fuzzy Logic. Archive for Mathematical Logic 42 (8):781-790.
    An algebra with fuzzy equality is a set with operations on it that is equipped with similarity ≈, i.e. a fuzzy equivalence relation, such that each operation f is compatible with ≈. Described verbally, compatibility says that each f yields similar results if applied to pairwise similar arguments. On the one hand, algebras with fuzzy equalities are structures for the equational fragment of fuzzy logic. On the other hand, they are the formal counterpart to the intuitive idea of having functions (...)
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  23. Radim Bělohlávek (2002). Fuzzy Equational Logic. Archive for Mathematical Logic 41 (1):83-90.
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  24. Radim Belohlavek & George J. Klir (eds.) (2011). Concepts and Fuzzy Logic. The MIT Press.
    In this work - both psychologists working on concepts and mathematicians working on fuzzy logic - reassess the usefulness of fuzzy logic for the psychology of concepts.
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  25. Radim Bělohlávek & Vilém Vychodil (2006). Fuzzy Horn Logic I. Archive for Mathematical Logic 45 (1):3-51.
    The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style completeness theorem (degree of provability equals degree (...)
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  26. Radim Bělohlávek & Vilém Vychodil (2006). Fuzzy Horn Logic II. Archive for Mathematical Logic 45 (2):149-177.
    The paper studies closure properties of classes of fuzzy structures defined by fuzzy implicational theories, i.e. theories whose formulas are implications between fuzzy identities. We present generalizations of results from the bivalent case. Namely, we characterize model classes of general implicational theories, finitary implicational theories, and Horn theories by means of closedness under suitable algebraic constructions.
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  27. Pietro Benvenuti, Doretta Vivona & Maria Divari (1991). A General Information for Fuzzy Sets. In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer 307--316.
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  28. Merrie Bergmann (2008). An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems. Cambridge University Press.
    This volume is an accessible introduction to the subject of many-valued and fuzzy logic suitable for use in relevant advanced undergraduate and graduate courses. The text opens with a discussion of the philosophical issues that give rise to fuzzy logic – problems arising from vague language – and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic.
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  29. Loredana Biacino & Giangiacomo Gerla (2002). Fuzzy Logic, Continuity and Effectiveness. 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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  30. Matteo Bianchi (2013). First-Order Nilpotent Minimum Logics: First Steps. 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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  31. Matteo Bianchi & Franco Montagna (2011). N-Contractive BL-Logics. Archive for Mathematical Logic 50 (3-4):257-285.
    In the field of many-valued logics, Hájek’s Basic Logic BL was introduced in Hájek (Metamathematics of fuzzy logic, trends in logic. Kluwer Academic Publishers, Berlin, 1998). In this paper we will study four families of n-contractive (i.e. that satisfy the axiom ${\phi^n\rightarrow\phi^{n+1}}$ , for some ${n\in\mathbb{N}^+}$ ) axiomatic extensions of BL and their corresponding varieties: BL n , SBL n , BL n and SBL n . Concerning BL n we have that every BL n -chain is isomorphic to an (...)
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  32. D. Boixader & L. Godo (1998). Fuzzy Inference. In Enrique H. Ruspini, Piero Patrone Bonissone & Witold Pedrycz (eds.), Handbook of Fuzzy Computation. Institute of Physics Pub.
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  33. Andrea Bonarini (ed.) (1996). New Trends in Fuzzy Logic: Proceedings of the Wilf '95, Italian Workshop on Fuzzy Logic, Naples, Italy, 21-22 September 1995. [REVIEW] World Scientific.
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  34. Richard Booth & Eva Richter (2005). On Revising Fuzzy Belief Bases. Studia Logica 80 (1):29 - 61.
    We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revision-input formulas can come attached with varying degrees. Working within a very general framework for fuzzy logic which is able to capture certain types of uncertainty calculi as well as truth-functional fuzzy logics, we show how the idea of rational change from “crisp” base revision, as embodied by the idea of partial meet (base) revision, can be (...)
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  35. Michal Botur & Radomír Halaš (2009). Commutative Basic Algebras and Non-Associative Fuzzy Logics. Archive for Mathematical Logic 48 (3-4):243-255.
    Several investigations in probability theory and the theory of expert systems show that it is important to search for some reasonable generalizations of fuzzy logics (e.g. Łukasiewicz, Gödel or product logic) having a non-associative conjunction. In the present paper, we offer a non-associative fuzzy logic L CBA having as an equivalent algebraic semantics lattices with section antitone involutions satisfying the contraposition law, so-called commutative basic algebras. The class (variety) CBA of commutative basic algebras was intensively studied in several recent papers (...)
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  36. Claudi Alsina Català (1996). What Are the Fuzzy Conjuctions and Disjunctions? Agora 15 (2):63-70.
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  37. Ferdinando Cavaliere (2012). Fuzzy Syllogisms, Numerical Square, Triangle of Contraries, Inter-Bivalence. In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser 241--260.
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  38. Marco Cerami & Francesc Esteva (2011). Strict Core Fuzzy Logics and Quasi-Witnessed Models. Archive for Mathematical Logic 50 (5-6):625-641.
    In this paper we prove strong completeness of axiomatic extensions of first-order strict core fuzzy logics with the so-called quasi-witnessed axioms with respect to quasi-witnessed models. As a consequence we obtain strong completeness of Product Predicate Logic with respect to quasi-witnessed models, already proven by M.C. Laskowski and S. Malekpour in [19]. Finally we study similar problems for expansions with Δ, define Δ-quasi-witnessed axioms and prove that any axiomatic extension of a first-order strict core fuzzy logic, expanded with Δ, and (...)
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  39. Timothy Childers & Ondrej Majer (2014). Introduction to the Special Issue Epistemic Aspects of Many-Valued Logics. 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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  40. Roberto Cignoli (1999). Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publishers.
    This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as (...)
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  41. Roberto Cignoli & Antoni Torrens (2003). Hájek Basic Fuzzy Logic and Łukasiewicz Infinite-Valued Logic. Archive for Mathematical Logic 42 (4):361-370.
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  42. Petr Cintula (2006). Weakly Implicative (Fuzzy) Logics I: Basic Properties. [REVIEW] Archive for Mathematical Logic 45 (6):673-704.
    This paper presents two classes of propositional logics (understood as a consequence relation). First we generalize the well-known class of implicative logics of Rasiowa and introduce the class of weakly implicative logics. This class is broad enough to contain many “usual” logics, yet easily manageable with nice logical properties. Then we introduce its subclass–the class of weakly implicative fuzzy logics. It contains the majority of logics studied in the literature under the name fuzzy logic. We present many general theorems for (...)
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  43. Petr Cintula (2003). Advances in the ŁΠ and Logics. Archive for Mathematical Logic 42 (5):449-468.
    The ŁΠ and logics were introduced by Godo, Esteva and Montagna. These logics extend many other known propositional and predicate logics, including the three mainly investigated ones (Gödel, product and Łukasiewicz logic). The aim of this paper is to show some advances in this field. We will see further reduction of the axiomatic systems for both logics. Then we will see many other logics contained in the ŁΠ family of logics (namely logics induced by the continuous finitely constructed t-norms and (...)
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  44. Petr Cintula, Francesc Esteva, Joan Gispert, Lluís Godo, Franco Montagna & Carles Noguera (2009). Distinguished Algebraic Semantics for T-Norm Based Fuzzy Logics: Methods and Algebraic Equivalencies. Annals of Pure and Applied Logic 160 (1):53-81.
    This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics–namely the class of algebras defined over the real unit (...)
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  45. Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.) (2011). Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications.
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  46. Petr Cintula, Christian Fermüller & Carles Noguera (eds.) (2015). Handbook of Mathematical Fuzzy Logic - Volume 3. College Publications.
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  47. Petr Cintula, Petr Hájek & Rostislav Horčík (2007). Formal Systems of Fuzzy Logic and Their Fragments. Annals of Pure and Applied Logic 150 (1):40-65.
    Formal systems of fuzzy logic are well-established logical systems and respected members of the broad family of the so-called substructural logics closely related to the famous logic BCK. The study of fragments of logical systems is an important issue of research in any class of non-classical logics. Here we study the fragments of nine prominent fuzzy logics to all sublanguages containing implication. However, the results achieved in the paper for those nine logics are usually corollaries of theorems with much wider (...)
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  48. Petr Cintula, Erich Peter Klement, Radko Mesiar & Mirko Navara (2006). Residuated Logics Based on Strict Triangular Norms with an Involutive Negation. Mathematical Logic Quarterly 52 (3):269-282.
    In general, there is only one fuzzy logic in which the standard interpretation of the strong conjunction is a strict triangular norm, namely, the product logic. We study several equations which are satisfied by some strict t-norms and their dual t-conorms. Adding an involutive negation, these equations allow us to generate countably many logics based on strict t-norms which are different from the product logic.
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  49. Petr Cintula & Ondrej Majer (2009). Towards Evaluation Games for Fuzzy Logics. In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Springer Verlag 117--138.
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  50. Petr Cintula & George Metcalfe (2009). Structural Completeness in Fuzzy Logics. Notre Dame Journal of Formal Logic 50 (2):153-182.
    Structural completeness properties are investigated for a range of popular t-norm based fuzzy logics—including Łukasiewicz Logic, Gödel Logic, Product Logic, and Hájek's Basic Logic—and their fragments. General methods are defined and used to establish these properties or exhibit their failure, solving a number of open problems.
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