Bibliography Sorted by Topic

A. General monographs on fuzzy logics

• Cintula, Petr, Petr Hájek, and Carles Noguera (eds.), 2011a, Handbook of Mathematical Fuzzy Logic, Volume 1, (Mathematical Logic and Foundations, Volume 37), London: College Publications.
• ––– (eds.), 2011b, Handbook of Mathematical Fuzzy Logic, Volume 2, (Mathematical Logic and Foundations, Volume 38), London: College Publications.
• Cintula, Petr, Christian G. Fermüller, and Carles Noguera (eds.), 2015, Handbook of Mathematical Fuzzy Logic, Volume 3, (Mathematical Logic and Foundations, Volume 58), London: College Publications.
• Gottwald, Siegfried, 2001, A Treatise On Many-Valued Logics, (Studies in Logic and Computation, Volume 9), Baldock: Research Studies Press Ltd.
• Hájek, Petr, 1998, Metamathematics of Fuzzy Logic, (Trends in Logic, Volume 4), Dordrecht: Kluwer.

B. Fuzzy logics and fuzzy set theory

• Bělohlávek, Radim, Joseph W. Dauben, and George J. Klir, 2017, Fuzzy Logic and Mathematics: A Historical Perspective, Oxford University Press. doi:10.1093/oso/9780190200015.001.0001
• Goguen, Joseph A., 1969, “The Logic of Inexact Concepts”, Synthese, 19(3–4): 325–373.
• Nguyen, Hung T. and Elbert A. Walker, 2005, A First Course in Fuzzy Logic (third edition), Chapman and Hall/CRC.
• Ross, Timothy J., 2016, Fuzzy Logic with Engineering Applications (fourth edition), Hoboken, NJ: Wiley.
• Zadeh, Lotfi A., 1965, “Fuzzy Sets”, Information and Control, 8(3): 338–353. doi:10.1016/S0019-9958(65)90241-X
• –––, 1975, “Fuzzy logic and approximate reasoning”, Synthese, 30: 407 – 428. doi: 10.1007/BF00485052

C. Algebraic and real-valued semantics for fuzzy logics

• Aguzzoli, Stefano, Simone Bova, and Brunella Gerla, 2011, “Free algebras and functional representation for fuzzy logics”, in Cintula, Petr, Petr Hájek, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 2, (Mathematical Logic and Foundations, Volume 38), London: College Publications, pages 713–791.
• Cintula, Petr, Francesc Esteva, Joan Gispert, Lluís Godo, Franco Montagna, and 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. doi:10.1016/j.apal.2009.01.012
• Gehrke, Mai, Carol L. Walker, and Elbert A. Walker, 1997, “A Mathematical Setting for Fuzzy Logics”, International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems, 5(3): 223–238. doi:10.1142/S021848859700021X
• Horčík, Rostislav, 2011, “Algebraic Semantics: Semilinear FL-Algebras”, in Cintula, Petr, Petr Hájek, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 1, (Mathematical Logic and Foundations, Volume 37), London: College Publications, pages 283–353.
• Jenei, Sándor and Franco Montagna, 2002, “A Proof of Standard Completeness for Esteva and Godo’s Logic MTL”, Studia Logica, 70(2): 183–192. doi:10.1023/A:1015122331293
• –––, 2003, “A Proof of Standard Completeness for Non-Commutative Monoidal T-norm Logic”, Neural Network World, 13(5): 481–489.
• Klement, Erich Peter, Radko Mesiar, and Endre Pap, 2000, Triangular Norms, (Trends in Logic, Volume 8), Dordrecht: Kluwer.
• Ling, Cho-Hsin, 1965, “Representation of Associative Functions”, Publicationes Mathematicae Debrecen, 12: 189–212.
• Mostert, Paul S. and Allen L. Shields, 1957, “On the Structure of Semigroups on a Compact Manifold with Boundary”, The Annals of Mathematics, Second Series, 65(1): 117–143. doi:10.2307/1969668
• Vetterlein, Thomas, 2015, “Algebraic Semantics: The Structure of Residuated Chains”, in Cintula, Petr, Christian G. Fermüller, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 3, (Mathematical Logic and Foundations, Volume 58), London: College Publications, pages 929–967.

D. Game-theoretic semantics for fuzzy logics

• Cicalese, Ferdinando and Franco Montagna, 2015, “Ulam–Rényi Game Based Semantics For Fuzzy Logics”, in Cintula, Petr, Christian G. Fermüller, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 3, (Mathematical Logic and Foundations, Volume 58), London: College Publications, pages 1029–1062.
• Fermüller, Christian G., 2015, “Semantic Games for Fuzzy Logics”, in Cintula, Petr, Christian G. Fermüller, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 3, (Mathematical Logic and Foundations, Volume 58), London: College Publications, pages 969–1028.
• Fermüller, Christian G. and Christoph Roschger, 2014, “Randomized Game Semantics for Semi-Fuzzy Quantifiers”, Logic Journal of the Interest Group of Pure and Applied Logic, 22(3): 413–439. doi:10.1093/jigpal/jzt049
• Giles, Robin, 1974, “A Non-Classical Logic for Physics”, Studia Logica, 33(4): 397–415. doi:10.1007/BF02123379
• Mundici, Daniele, 1992, “The Logic of Ulam’s Game with Lies”, in Bicchieri, Cristina and Maria Luisa Dalla Chiara (eds.), Knowledge, Belief, and Strategic Interaction (Castiglioncello, 1989), Cambridge: Cambridge University Press, 275–284.

E. Other semantics for fuzzy logics

• Běhounek, Libor, 2009, “Fuzzy Logics Interpreted as Logics of Resources”, in Peliš, Michal (ed.), The Logica Yearbook 2008, London: College Publications, pages 9–21.
• Hisdal, Ellen, 1988, “Are Grades of Membership Probabilities?” Fuzzy Sets and Systems, 25(3): 325–348. doi:10.1016/0165-0114(88)90018-8
• Lawry, Jonathan, 1998, “A Voting Mechanism for Fuzzy Logic”, International Journal of Approximate Reasoning, 19(3–4): 315–333. doi:10.1016/S0888-613X(98)10013-0
• Montagna, Franco and Hiroakira Ono, “Kripke Semantics, Undecidability and Standard Completeness for Esteva and Godo’s Logic MTL\(\forall\)”, Studia Logica, 71(2): 227–245.
• Paris, Jeff, 1997, “A Semantics for Fuzzy Logic”, Soft Computing, 1(3): 143–147. doi:10.1007/s005000050015
• –––, 2000, “Semantics for Fuzzy Logic Supporting Truth Functionality”, in Novák, Vilém and Irina Perfilieva (eds.), Discovering the World with Fuzzy Logic, (Studies in Fuzziness and Soft Computing, Volume 57), Heidelberg: Springer, pages 82–104.
• Ruspini, Enrique H., 1991, “On the Semantics of Fuzzy Logic”, International Journal of Approximate Reasoning, 5(1): 45–88. doi:10.1016/0888-613X(91)90006-8

F. Łukasiewicz logic

• Cignoli, Roberto, Itala M. D’Ottaviano, and Daniele Mundici, 1999, Algebraic Foundations of Many-Valued Reasoning, (Trends in Logic, Volume 7), Dordrecht: Kluwer.
• Hay, Louise Schmir, 1963, “Axiomatization of the Infinite-Valued Predicate Calculus”, Journal of Symbolic Logic, 28(1): 77–86. doi:10.2307/2271339
• Leştean, Ioana and Antonio Di Nola, 2011, “Łukasiewicz Logic and MV-Algebras”, in Cintula, Petr, Petr Hájek, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 2, (Mathematical Logic and Foundations, Volume 38), London: College Publications, pages 469–583.
• Łukasiewicz, Jan, 1920, “O Logice Trójwartościowej”, Ruch Filozoficzny, 5: 170–171. English translation, “On Three-Valued Logic”, in McCall, Storrs (ed.), 1967, Polish Logic 1920–1939, Oxford: Clarendon Press, pages 16–18, and in Jan Łukasiewicz, 1970, Selected Works, Ludwik Borkowski (ed.), Amsterdam: North-Holland, pages 87–88.
• Łukasiewicz, Jan and Alfred Tarski, 1930, “Untersuchungen über den Aussagenkalkül”, Comptes Rendus Des Séances de La Société Des Sciences et Des Lettres de Varsovie, Cl. III, 23(iii): 30–50.
• McNaughton, Robert, 1951, “A Theorem About Infinite-Valued Sentential Logic”, Journal of Symbolic Logic, 16(1): 1–13. doi:10.2307/2268660
• Mundici, Daniele, 2011, Advanced Łukasiewicz Calculus and MV-Algebras, (Trends in Logic, Volume 35), New York: Springer.

G. Gödel logics

• Baaz, Matthias, 1996, “Infinite-Valued Gödel Logic with 0–1-Projections and Relativisations”, in Hájek, Petr (ed.), Gödel’96: Logical Foundations of Mathematics, Computer Science, and Physics (Lecture Notes in Logic, Volume 6), Brno: Springer, pages 23–33.
• Baaz, Matthias and Norbert Preining, 2011, “Gödel–Dummett Logics”, in Cintula, Petr, Petr Hájek, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 2, (Mathematical Logic and Foundations, Volume 38), London: College Publications, pages 585–625.
• Dummett, Michael, 1959, “A Propositional Calculus with Denumerable Matrix”, Journal of Symbolic Logic, 24(2): 97–106. doi:10.2307/2964753
• Gödel, Kurt, 1932, “Zum intuitionistischen Aussagenkalkül”, Anzeiger Akademie Der Wissenschaften Wien, 69: 65–66.
• Horn, Alfred, 1969, “Logic with Truth Values in a Linearly Ordered Heyting Algebra”, Journal of Symbolic Logic, 34(3): 395–408.

H. Other fuzzy logics

• Busaniche, Manuela and Franco Montagna, 2011, “Hájek’s Logic BL and BL-Algebras”, in Cintula, Petr, Petr Hájek, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 1, (Mathematical Logic and Foundations, Volume 37), London: College Publications, pages 355–447.
• Esteva, Francesc, Joan Gispert, Lluís Godo, and Carles Noguera, 2007, “Adding Truth-Constants to Logics of Continuous T-norms: Axiomatization and Completeness Results”, Fuzzy Sets and Systems, 158(6): 597–618. doi:10.1016/j.fss.2006.11.010
• Esteva, Francesc and Lluís Godo, 2001, “Monoidal T-norm Based Logic: Towards a Logic for Left-Continuous T-norms”, Fuzzy Sets and Systems, 124(3): 271–288. doi:10.1016/S0165-0114(01)00098-7
• Esteva, Francesc, Lluís Godo, Petr Hájek, and Mirko Navara, 2000, “Residuated Fuzzy Logics with an Involutive Negation”, Archive for Mathematical Logic, 39(2): 103–124. doi:10.1007/s001530050006
• Esteva, Francesc, Lluís Godo, and Enrico Marchioni, 2011, “Fuzzy Logics with Enriched Language”, in Cintula, Petr, Petr Hájek, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 2, (Mathematical Logic and Foundations, Volume 38), London: College Publications, pages 627–711.
• Esteva, Francesc, Lluís Godo, and Franco Montagna, 2001, “The \(L\Pi\) and \(L\Pi\frac12\) Logics: Two Complete Fuzzy Systems Joining Łukasiewicz and Product Logics”, Archive for Mathematical Logic, 40(1): 39–67. doi:10.1007/s001530050173
• –––, 2003, “Axiomatization of Any Residuated Fuzzy Logic Defined by a Continuous T-norm”, in Bilgiç, Taner, Bernard De Baets, and Okyay Kaynak (eds.), Fuzzy Sets and Systems: IFSA 2003,(Lecture Notes in Computer Science, Volume 2715), Berlin/Heidelberg: Springer, pages 172–179. doi:10.1007/3-540-44967-1_20
• Hájek, Petr, 2001, “On Very True”, Fuzzy Sets and Systems, 124(3): 329–333.
• Haniková, Zuzana, 2014, “Varieties Generated by Standard BL-Algebras”, Order, 31(1): 15–33. doi:10.1007/s11083-013-9285-5
• Montagna, Franco, Carles Noguera, and Rostislav Horčík, 2006, “On Weakly Cancellative Fuzzy Logics”, Journal of Logic and Computation, 16(4): 423–450.

I. Fuzzy logics as substructural logics

• Cintula, Petr, Rostislav Horčík, and Carles Noguera, 2013, “Non-Associative Substructural Logics and their Semilinear Extensions: Axiomatization and Completeness Properties”, The Review of Symbolic Logic, 6(3): 394–423. doi:10.1017/S1755020313000099
• –––, 2014, “The Quest for the Basic Fuzzy Logic”, in Franco Montagna (ed.), Petr Hájek on Mathematical Fuzzy Logic,(Outstanding Contributions to Logic, Volume 6), Cham: Springer, pages 245–290. doi:10.1007/978-3-319-06233-4_12
• Esteva, Francesc, Lluís Godo, and Àngel García-Cerdaña, 2003, “On the Hierarchy of T-norm Based Residuated Fuzzy Logics”, in Fitting, Melvin and Ewa Orłowska (eds.), Beyond Two: Theory and Applications of Multiple-Valued Logic, (Studies in Fuzziness and Soft Computing, Volume 114), Heidelberg: Springer, pages 251–272.
• Galatos, Nikolaos, Peter Jipsen, Tomasz Kowalski, and Hirakori Ono (eds.), 2007, Residuated Lattices: An Algebraic Glimpse at Substructural Logics, (Studies in Logic and the Foundations of Mathematics, Volume 151), Amsterdam: Elsevier.
• Metcalfe, George and Franco Montagna, 2007, “Substructural Fuzzy Logics”, Journal of Symbolic Logic, 72(3): 834–864. doi:10.2178/jsl/1191333844

J. Fuzzy logics in abstract algebraic logic

• Běhounek, Libor and Petr Cintula, 2006, “Fuzzy Logics as the Logics of Chains”, Fuzzy Sets and Systems, 157(5): 604–610.
• Cintula, Petr, 2006, “Weakly Implicative (Fuzzy) Logics I: Basic Properties”, Archive for Mathematical Logic, 45(6): 673–704.
• Cintula, Petr and Carles Noguera, 2011, “A General Framework for Mathematical Fuzzy Logic”, in Cintula, Petr, Petr Hájek, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 1, (Mathematical Logic and Foundations, Volume 37), London: College Publications, pages 103–207.
• Font, Josep Maria, 2016, Abstract Algebraic Logic: An Introductory Textbook, (Mathematical Logic and Foundations, Volume 60), London: College Publications.

K. First- and higher-fuzzy logics

• Badia, Guillermo and Carles Noguera, 2021, “Lindström theorems in graded model theory”, Annals of Pure and Applied Logic, 172(3): 102916. doi: 10.1016/j.apal.2020.102916
• –––, 2021, “A General Omitting Types Theorem in Mathematical Fuzzy Logic”, IEEE Transactions on Fuzzy Systems, 29(6): 1386–1394. doi: 10.1109/TFUZZ.2020.2975146
• Běhounek, Libor and Petr Cintula, 2005, “Fuzzy Class Theory”, Fuzzy Sets and Systems, 154(1):34–55.
• Běhounek, Libor and Zuzana Haniková, 2014, “Set Theory and Arithmetic in Fuzzy Logic”, in Montagna, Franco (ed.), Petr Hájek on Mathematical Fuzzy Logic, (Outstanding Contributions to Logic, Volume 6), Cham: Springer, pages 63–89.
• Cintula, Petr, Denisa Diaconescu, and George Metcalfe, 2019, “Skolemization and Herbrand theorems for lattice-valued logics”, Theoretical Computer Science, 768: 54–75. doi: 10.1016/j.tcs.2019.02.007
• Dellunde, Pilar, 2012, “Preserving Mappings in Fuzzy Predicate Logics”, Journal of Logic and Computation, 22(6): 1367–1389.
• Dellunde, Pilar, Àngel García-Cerdaña, and Carles Noguera, 2018, “Back-and-forth systems for fuzzy first-order models”, Fuzzy Sets and Systems, 345: 83–98 (2018)
• Di Nola, Antonio and Giangiacomo Gerla, 1986, “Fuzzy Models of First-Order Languages”, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 32(19–24): 331–340.
• Hájek, Petr and Petr Cintula, 2006, “On Theories and Models in Fuzzy Predicate Logics”, Journal of Symbolic Logic, 71(3): 863–880.
• Hájek, Petr and Zuzana Haniková, 2003, “A Development of Set Theory in Fuzzy Logic”, in Fitting, Melvin and Ewa Orłowska (eds.), Beyond Two: Theory and Applications of Multiple-Valued Logic, (Studies in Fuzziness and Soft Computing, Volume 114), Heidelberg: Springer, pages 273–285.
• Hájek, Petr, Jeff Paris, and John Shepherdson, 2000, “The Liar Paradox and Fuzzy Logic”, Journal of Symbolic Logic, 65(1): 339–346.
• Novák, Vilém, 2004, “On Fuzzy Type Theory”, Fuzzy Sets and Systems, 149(2): 235–273.
• Takeuti, Gaisi and Satoko Titani, 1984, “Intuitionistic Fuzzy Logic and Intuitionistic Fuzzy Set Theory”, Journal of Symbolic Logic, 49(3): 851–866.
• –––, 1992, “Fuzzy Logic and Fuzzy Set Theory”, Archive for Mathematical Logic, 32(1): 1–32.

L. Complexity of fuzzy logics

• Baaz, Matthias, Petr Hájek, Franco Montagna, and Helmut Veith, 2002, “Complexity of T-Tautologies”, Annals of Pure and Applied Logic, 113(1–3): 3–11.
• Hájek, Petr, Franco Montagna, and Carles Noguera, 2011, “Arithmetical Complexity of First-Order Fuzzy Logics”, in Cintula, Petr, Petr Hájek, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 2, (Mathematical Logic and Foundations, Volume 38), London: College Publications, pages 853–908.
• Haniková, Zuzana, 2011, “Computational Complexity of Propositional Fuzzy Logics”, in Cintula, Petr, Petr Hájek, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 2, (Mathematical Logic and Foundations, Volume 38), London: College Publications, pages 793–851.
• Montagna, Franco, 2001, “Three Complexity Problems in Quantified Fuzzy Logic”, Studia Logica, 68(1): 143–152. doi:10.1023/A:1011958407631
• Montagna, Franco and Carles Noguera, 2010, “Arithmetical Complexity of First-Order Predicate Fuzzy Logics Over Distinguished Semantics”, Journal of Logic and Computation, 20(2): 399–424. doi:10.1093/logcom/exp052
• Mundici, Daniele, 1987, “Satisfiability in Many-Valued Sentential Logic is NP-Complete”, Theoretical Computer Science, 52(1–2): 145–153.
• Ragaz, Matthias Emil, 1981, Arithmetische Klassifikation von Formelmengen der unendlichwertigen Logik (PhD thesis). Swiss Federal Institute of Technology, Zürich. doi:10.3929/ethz-a-000226207
• Scarpellini, Bruno, 1962, “Die Nichtaxiomatisierbarkeit des unendlichwertigen Prädikatenkalküls von Łukasiewicz”, Journal of Symbolic Logic, 27(2): 159–170. doi:10.2307/2964111

M. Proof theory for fuzzy logics

• Avron, Arnon, 1991, “Hypersequents, Logical Consequence and Intermediate Logics for Concurrency”, Annals of Mathematics and Artificial Intelligence, 4(3–4): 225–248. doi:10.1007/BF01531058
• Ciabattoni, Agata, Nikolaos Galatos, and Kazushige Terui, 2012, “Algebraic Proof Theory for Substructural Logics: Cut-Elimination and Completions”, Annals of Pure and Applied Logic, 163(3): 266–290.
• Fermüller, Christian G. and George Metcalfe, 2009, “Giles’s Game and Proof Theory for Łukasiewicz Logic”, Studia Logica, 92(1): 27–61. doi:10.1007/s11225-009-9185-2
• Metcalfe, George, 2011, “Proof Theory for Mathematical Fuzzy Logic”, in Cintula, Petr, Petr Hájek, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 1, (Mathematical Logic and Foundations, Volume 37), London: College Publications, pages 209–282.
• Metcalfe, George, Nicola Olivetti, and Dov M. Gabbay, 2008, Proof Theory for Fuzzy Logics,(Applied Logic Series, Volume 36), Dordrecht: Springer Netherlands.

N. Structural completeness and unification in fuzzy logics

• Cintula, Petr and George Metcalfe, 2009, “Structural Completeness in Fuzzy Logics”, Notre Dame Journal of Formal Logic, 50(2): 153–183.
• Jeřábek, Emil, 2010, “Bases of Admissible Rules of Łukasiewicz Logic”, Journal of Logic and Computation, 20(6): 1149–1163.
• Marra, Vincenzo and Luca Spada, 2013, “Duality, Projectivity, and Unification in Łukasiewicz Logic and MV-Algebras”, Annals of Pure and Applied Logic, 164(3): 192–210.

O. Modal fuzzy logics

• Bou, Félix, Francesc Esteva, Lluís Godo, and Ricardo Oscar Rodríguez, 2011, “On the Minimum Many-Valued Modal Logic Over a Finite Residuated Lattice”, Journal of Logic and Computation, 21(5): 739–790.
• Caicedo, Xavier, George Metcalfe, Ricardo Oscar Rodríguez, and Jonas Rogger, 2017, “Decidability of order-based modal logics”, Journal of Computer and System Sciences, 88: 53–74. doi:10.1016/j.jcss.2017.03.012
• Caicedo, Xavier and Ricardo Oscar Rodríguez, 2010, “Standard Gödel Modal Logics”, Studia Logica, 94(2): 189–214.
• –––, 2015, “Bi-modal Gödel logic over [0, 1]-valued Kripke frames”, Journal of Logic and Computation, 25(1): 37–55. doi: 10.1093/logcom/exs036
• Cintula, Petr, Paula Menchón, and Carles Noguera, 2019, “Toward a general frame semantics for modal many-valued logics”, Soft Computing , 23(7): 2233–2241. doi: 10.1007/s00500-018-3369-5
• Hansoul, Georges and Bruno Teheux, 2013, “Extending Łukasiewicz Logics with a Modality: Algebraic Approach to Relational Semantics”, Studia Logica, 101(3): 505–545, doi: 10.1007/s11225-012-9396-9.
• Rodríguez, Ricardo Oscar and Amanda Vidal, 2021, “Axiomatization of Crisp Gödel Modal Logic”, Studia Logica, 109(2): 367–395. doi: 10.1007/s11225-020-09910-5
• Teheux, Bruno, 2016, “Modal definability based on Łukasiewicz validity relations”, Studia Logica, 104(2): 343–363. doi: 10.1007/s11225-015-9643-y
• Vidal, Amanda, 2021, “On transitive modal many-valued logics”, Fuzzy Sets and Systems, 407: 97–114. doi: 10.1016/j.fss.2020.01.011
• Vidal, Amanda, Francesc Esteva, and Lluís Godo, 2017, “On modal extensions of Product fuzzy logic”, Journal of Logic and Computation, 27(1): 299–336. doi: 10.1093/logcom/exv046

P. Description fuzzy logics

• Bobillo, Fernando, Marco Cerami, Francesc Esteva, Àngel García-Cerdaña, Rafael Peñaloza, and Umberto Straccia, 2015, “Fuzzy Description Logics”, in Cintula, Petr, Christian G. Fermüller, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 3, (Mathematical Logic and Foundations, Volume 58), London: College Publications, pages 1105–1181.
• García-Cerdaña, Àngel, Eva Armengol, and Francesc Esteva, 2010, “Fuzzy Description Logics and T-norm Based Fuzzy Logics”, International Journal of Approximate Reasoning, 51(6): 632–655.
• Hájek, Petr, 2005, “Making Fuzzy Description Logic More General”, Fuzzy Sets and Systems, 154(1): 1–15.
• Straccia, Umberto, 1998, “A Fuzzy Description Logic”, in Mostow, Jack and Chuck Rich (eds.), Proceedings of the 15th National Conference on Artificial Intelligence (AAAI 1998), Menlo Park: AAAI Press, pages 594–599.

Q. Probability and fuzzy logics

• Baldi, Paolo, Petr Cintula, and Carles Noguera, 2020, “Classical and Fuzzy Two-Layered Modal Logics for Uncertainty: Translations and Proof Theory”. International Journal of Computational Intelligence Systems, 13(1): 988–1001. doi: 10.2991/ijcis.d.200703.001
• Fedel, Martina, Hykel Hosni, and Franco Montagna, 2011, “A Logical Characterization of Coherence for Imprecise Probabilities”, International Journal of Approximate Reasoning, 52(8): 1147–1170, doi: 10.1016/j.ijar.2011.06.004.
• Flaminio, Tommaso, 2021, “On standard completeness and finite model property for a probabilistic logic on Łukasiewicz events”, International Journal of Approximate Reasoning, 131: 136–150. doi: 10.1016/j.ijar.2020.12.023
• Flaminio, Tommaso, Lluís Godo, and Enrico Marchioni, 2011, “Reasoning About Uncertainty of Fuzzy Events: An Overview”, in Cintula, Petr, Christian G. Fermüller, Lluís Godo, and Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical, and Linguistic Perspectives, (Studies in Logic, Volume 36), London: College Publications, pages 367–400.
• Flaminio, Tommaso, Lluís Godo, and Sara Ugolini, 2018, “Towards a probability theory for product logic: States, integral representation and reasoning”, International Journal of Approximate Reasoning, 93: 199–218. doi: 10.1016/j.ijar.2017.11.003
• Flaminio, Tommaso and Tomáš Kroupa, 2015, “States of MV-Algebras”, in Cintula, Petr, Christian Fermüller, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 3, (Mathematical Logic and Foundations, Volume 58), London: College Publications, pages 1183–1236.
• Godo, Lluís, Francesc Esteva, and Petr Hájek, 2000, “Reasoning About Probability Using Fuzzy Logic”, Neural Network World, 10(5): 811–823.

R. Other approaches to fuzzy logic

• Bělohlávek, Radim and Vilém Vychodil, 2005, Fuzzy Equational Logic, (Studies in Fuzziness and Soft Computing, Volume 186), Berlin and Heidelberg: Springer.
• Gerla, Giangiacomo, 2001, Fuzzy Logic—Mathematical Tool for Approximate Reasoning, (Trends in Logic, Volume 11), New York: Kluwer and Plenum Press.
• Novák, Vilém, 2015, “Fuzzy Logic with Evaluated Syntax”, in Cintula, Petr, Christian Fermüller, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 3, (Mathematical Logic and Foundations, Volume 58), London: College Publications, pages 1063–1104.
• Novák, Vilém, Irina Perfilieva, and Jiří Močkoř, 2000, Mathematical Principles of Fuzzy Logic, Dordrecht: Kluwer.
• Pavelka, Jan, 1979, “On Fuzzy Logic I, II, and III”, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 25: 45–52, 119–134, and 447–464.

S. Vagueness and fuzzy logics

• Běhounek, Libor, 2014, “In Which Sense Is Fuzzy Logic a Logic For Vagueness?”, in Łukasiewicz, Thomas, Rafael Peñaloza, and Anni-Yasmin Turhan (eds.), PRUV 2014: Logics for Reasoning About Preferences, Uncertainty, and Vagueness, (CEUR Workshop Proceedings, Volume 1205), Dresden: CEUR.
• Hájek, Petr and Vilém Novák, 2003, “The Sorites Paradox and Fuzzy Logic”, International Journal of General Systems, 32(4): 373–383. doi:10.1080/0308107031000152522
• Smith, Nicholas J.J., 2005, “Vagueness as Closeness”, Australasian Journal of Philosophy, 83(2): 157–183. doi:10.1080/00048400500110826
• –––, 2008, Vagueness and Degrees of Truth, Oxford: Oxford University Press.
• –––, 2015, “Fuzzy Logics in Theories of Vagueness”, in Cintula, Petr, Christian Fermüller, and Carles Noguera (eds.), Handbook of Mathematical Fuzzy Logic, Volume 3, (Mathematical Logic and Foundations, Volume 58), London: College Publications, pages 1237–1281.