Linked bibliography for the SEP article "Many-Valued Logic" by Siegfried Gottwald

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Monographs and Survey Papers

  • Ackermann, R., 1967, An Introduction to Many-Valued Logics, London: Routledge and Kegan Paul. (Scholar)
  • Bolc, L. and Borowik, P., 1992, Many-Valued Logics (1. Theoretical Foundations), Berlin: Springer. (Scholar)
  • –––, 2003, Many-Valued Logics (2. Automated Reasoning and Practical Applications), Berlin: Springer. (Scholar)
  • Cignoli, R., d’Ottaviano, I. and Mundici, D., 2000, Algebraic Foundations of Many-Valued Reasoning, Dordrecht: Kluwer. (Scholar)
  • Cintula, P. and Hájek, P., 2010, Triangular norm based predicate fuzzy logics, Fuzzy Sets and Systems, 161 (3): 311–346. (Scholar)
  • Cintula, P., Hájek, P. and Noguera Ch. (eds.), 2011, Handbook of Mathematical Fuzzy Logic (Studies in Logic, Volumes 37–38), College Publications: London. (Scholar)
  • Epstein G., 1993, Multiple-Valued Logic Design, Bristol: Institute of Physics Publishing. (Scholar)
  • Fitting, M. and Orlowska, E. (eds.), 2003, Beyond Two, Heidelberg: Physica Verlag. (Scholar)
  • Gottwald, S., 1999, Many-valued logic and fuzzy set theory, in U. Höhle, S.E. Rodabaugh (eds.) Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory (The Handbooks of Fuzzy Sets Series), Boston: Kluwer, 5–89. (Scholar)
  • –––, 2001, A Treatise on Many-Valued Logics (Studies in Logic and Computation, vol. 9), Baldock: Research Studies Press Ltd.. (Scholar)
  • –––, 2007, Many-valued logics, in D. Jacquette (ed.) Philosophy of Logic (Handbook of the Philosophy of Science Series), Amsterdam: North-Holland, 675–722. (Scholar)
  • –––, 2008, Mathematical fuzzy logics, Bulletin Symbolic Logic, 14: 210–239. (Scholar)
  • Gottwald, S. and Hájek, P., 2005, T-norm based mathematical fuzzy logics, in E.-P. Klement, R. Mesiar (eds.), Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, Dordrecht: Elsevier, 275–299.
  • Hähnle, R., 1993, Automated Deduction in Multiple-Valued Logics, Oxford : Clarendon Press. (Scholar)
  • –––, 1999, Tableaux for many-valued logics, in M. d’Agostino et al. (eds.) Handbook of Tableau Methods, Dordrecht: Kluwer, 529–580. (Scholar)
  • –––, 2001, Advanced many-valued logics, in D. Gabbay, F. Guenthner (eds.), Handbook of Philosophical Logic (Volume 2), 2nd ed., Dordrecht: Kluwer, 297–395. (Scholar)
  • Hájek, P., 1998, Metamathematics of Fuzzy Logic, Dordrecht: Kluwer. (Scholar)
  • Karpenko, A.S., 1997, Mnogoznacnye Logiki (Logika i Kompjuter, vol. 4), Moscow: Nauka. (Scholar)
  • Malinowski, G., 1993, Many-Valued Logics, Oxford: Clarendon Press. (Scholar)
  • Metcalfe, G., Olivetti, N. and Gabbay, D., 2009, Proof Theory for Fuzzy Logics, New York: Springer. (Scholar)
  • Montagna, F. (ed.), 2015, Petr Hájek on Mathematical Fuzzy Logic (Outstanding Contributions to Logic, vol. 6), Cham etc.:Springer. (Scholar)
  • Novák, V., Perfilieva, I. and Močkoř, J., 1999, Mathematical Principles of Fuzzy Logic, Boston: Kluwer. (Scholar)
  • Panti, G., 1998, Multi-valued logics, in P. Smets (ed.) Quantified Representation of Uncertainty and Imprecision (Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 1), Dordrecht: Kluwer, 25–74. (Scholar)
  • Rescher, N., 1969, Many-Valued Logic, New York: McGraw Hill. (Scholar)
  • Rine, D.C. (ed.), 1977, Computer Science and Multiple Valued Logic, Amsterdam : North-Holland [2nd rev. ed. 1984]. (Scholar)
  • Rosser, J.B. and Turquette, A.R., 1952, Many-Valued Logics, Amsterdam: North-Holland. (Scholar)
  • Shramko, Y. and Wansing H., 2011, Truth and Falsehood. An Inquiry into Generalized Logical Values (Trends in Logic: Volume 36), Dordrecht etc.: Springer. (Scholar)
  • Urquhart, A., 2001, Basic many-valued logic, in D. Gabbay, F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. 2 (2d edition), Dordrecht: Kluwer, 249–295. (Scholar)
  • Wojcicki, R. and Malinowski, G. (eds.), 1977, Selected Papers on Łukasiewicz Sentential Calculi, Wroclaw: Ossolineum. (Scholar)
  • Wolf, R.G., 1977, A survey of many-valued logic (1966–1974), in J.M. Dunn, G. Epstein (eds.), Modern Uses of Multiple-Valued Logic, Dordrecht: Reidel, 167–323.
  • Zinovev, A.A., 1963, Philosophical Problems of Many-Valued Logic, Dordrecht: Reidel. (Scholar)

Other Works Cited

  • Belluce, L.P. and Chang, C.C., 1963, A weak completeness theorem for infinite valued first-order logic, Journal Symbolic Logic, 28: 43–50. (Scholar)
  • Belnap, N.D., 1977, How a computer should think, in G. Ryle (ed.), Contemporary Aspects of Philosophy, Stockfield: Oriel Press, 30–56. (Scholar)
  • –––, 1977, A useful four-valued logic, in J.M. Dunn, G. Epstein (eds.), Modern Uses of Multiple-Valued Logic, Dordrecht: Reidel, 8–37.
  • Blau, U., 1978, Die dreiwertige Logik der Sprache: ihre Syntax, Semantik und Anwendung in der Sprachanalyse, Berlin: de Gruyter. (Scholar)
  • Bochvar, D.A., 1938, Ob odnom trechznacnom iscislenii i ego primenenii k analizu paradoksov klassiceskogo rassirennogo funkcional’nogo iscislenija, Matematiceskij Sbornik, 4 (46): 287–308. [English translation: Bochvar, D.A., On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus, History and Philosophy of Logic, 2: 87–112.] (Scholar)
  • Chang, C.C., 1958, Algebraic analysis of many valued logics, Transactions American Mathematical Society, 88: 476–490. (Scholar)
  • –––, 1959, A new proof of the completeness of the Łukasiewicz axioms, Transactions American Mathematical Society, 93: 74–80. (Scholar)
  • Cignoli, R., Esteva, F., Godo, L. and Torrens, A., 2000, Basic Fuzzy Logic is the logic of continuous t-norms and their residua, Soft Computing, 4: 106–112. (Scholar)
  • Dummett, M., 1959, A propositional calculus with denumerable matrix, Journal Symbolic Logic, 24: 97–106. (Scholar)
  • Dunn, J.M., 1976, Intuitive semantics for first-degree entailments and ‘coupled trees’, Philosophical Studies, 29: 149–168. (Scholar)
  • Esteva, F. and Godo, L., 2001, Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy Sets and Systems, 124: 271–288. (Scholar)
  • Esteva, F., Godo, L. and Montagna, F., 2004, Equational characterization of the subvarieties of BL generated by t-norm algebras, Studia Logica, 76: 161–200. (Scholar)
  • Fermüller, C.G., 2008, Dialogue games for many-valued logics–an overview, Studia Logica, 90: 43–68. (Scholar)
  • Fermüller, C.G. and Metcalfe, G., 2009, Giles’s game and the proof theory of Łukasiewicz logic, Studia Logica, 92: 27–61. (Scholar)
  • Fermüller, C.G. and Roschger, C., 2014, From games to truth functions: a generalization of Giles’s game, Studia Logica, 102: 389–410. (Scholar)
  • Fitting, M.C., 1991/92, Many-valued modal logics (I,II), Fundamenta Informaticae, 15: 235–254; 17: 55–73. (Scholar)
  • Giles, R., 1974, A non-classical logic for physics, Studia Logica, 33: 397–415. (Scholar)
  • –––, 1975. Łukasiewicz logic and fuzzy set theory. In: Proceedings 1975 Internat. Symposium Multiple-Valued Logic (Indiana Univ., Bloomington/IN)}, Long Beach/CA: IEEE Computer Soc., 197–211.
  • –––, 1976, Łukasiewicz logic and fuzzy set theory. Internat. Journ. Man-Machine Studies, 8: 313–327.
  • –––, 1979, A formal system for fuzzy reasoning. Fuzzy Sets and Systems, 2: 233–257.
  • Giles, R., 1988, The concept of grade of membership. Fuzzy Sets and Systems, 25: 297–323. (Scholar)
  • Gödel, K., 1932, Zum intuitionistischen Aussagenkalkül, Anzeiger Akademie der Wissenschaften Wien (Math.-naturwiss. Klasse), 69: 65–66; – reprinted: (1933), Ergebnisse eines mathematischen Kolloquiums, 4: 40. (Scholar)
  • Goguen, J.A., 1968–69, The logic of inexact concepts, Synthese, 19: 325–373. (Scholar)
  • Hájek, P., 2005, Making fuzzy description logic more general, Fuzzy Sets and Systems, 154: 1–15. (Scholar)
  • Hájek, P. and Zach, R., 1994, Review of Many-Valued Logics 1: Theoretical Foundations, by Leonard Bolc and Piotr Borowik, Journal of Applied Non-Classical Logics, 4 (2): 215–220. (Scholar)
  • Hay, L.S., 1963, Axiomatization of the infinite-valued predicate calculus, Journal Symbolic Logic, 28: 77–86. (Scholar)
  • Jaskowski, S., 1936, Recherches sur le système de la logique intuitioniste, in Actes du Congrès Internationale de Philosophie Scientifique 1936, vol. 6, Paris, 58–61. [English translation: Studia Logica, 34 (1975): 117–120.] (Scholar)
  • Jenei, S., 2004, How to construct left-continuous triangular norms – state of the art, Fuzzy Sets and Systems, 143: 27–45. (Scholar)
  • Jenei, S. and Montagna, F., 2002, A proof of standard completeness of Esteva and Godo’s logic MTL, Studia Logica, 70: 183–192. (Scholar)
  • Kleene, S.C., 1938, On notation for ordinal numbers, Journal Symbolic Logic, 3: 150–155. (Scholar)
  • Kripke, S.A., 1975, Outline of a theory of truth, Journal of Philosophy, 72: 690–716. (Scholar)
  • Łukasiewicz, J., 1920, O logice trojwartosciowej, Ruch Filozoficny, 5: 170–171. [English translation in: Łukasiewicz (1970).] (Scholar)
  • –––, 1970, Selected Works, L. Borkowski (ed.), Amsterdam: North-Holland and Warsaw: PWN. (Scholar)
  • McNaughton, R., 1951, A theorem about infinite-valued sentential logic, Journal Symbolic Logic, 16: 1–13. (Scholar)
  • Mundici, D., 1986, Interpretation of AF C*-algebras in Łukasiewicz sentential calculus, J. Functional Analysis, 65: 15–63. (Scholar)
  • –––, 1992, The logic of Ulam’s game with lies, in: C. Bicchieri and M.L. dalla Chiara (eds.) Knowledge, belief, and strategic interaction, Cambridge: Cambridge Univ. Press, 275–284. (Scholar)
  • Novák, V., 2008, A formal theory of intermediate quantifiers, Fuzzy Sets and Systems, 159: 1229–1246. (Scholar)
  • Odintsov, S.P., 2009, On axiomatizing Shramko-Wansing’s Logic, Studia Logica, 91: 407–428. (Scholar)
  • Post, E. L., 1920, Determination of all closed systems of truth tables, Bulletin American Mathematical Society, 26: 437. (Scholar)
  • –––, 1921, Introduction to a general theory of elementary propositions, American Journal Mathematics, 43: 163–185. (Scholar)
  • Ragaz, M., 1983, Die Unentscheidbarkeit der einstelligen unendlichwertigen Prädikatenlogik, Archiv mathematische Logik Grundlagenforschung, 23: 129–139. (Scholar)
  • Rose, A. and Rosser, J.B., 1958, Fragments of many-valued statement calculi, Transactions American Mathematical Society, 87: 1–53. (Scholar)
  • Scarpellini, B., 1962, Die Nichtaxiomatisierbarkeit des unendlichwertigen Prädikatenkalküls von Łukasiewicz, Journal Symbolic Logic, 27: 159–170. (Scholar)
  • Shramko, Y. and Wansing H., 2005, Some useful 16-valued logics. How a computer network should think, Journal Philosophical Logic, 34: 121–153. (Scholar)
  • Skolem, Th., 1957, Bemerkungen zum Komprehensionsaxiom, Zeitschrift mathematische Logik Grundlagen Mathematik, 3: 1–17. (Scholar)
  • Stoilos, G. Stamou, G., Pan, J.Z., Tzouvaras, V., and Horrocks, I., 2007, Reasoning with very expressive fuzzy description logics, J. Artificial Intelligence Res, 30: 273–320. (Scholar)
  • Straccia, U. (2001), Reasoning within fuzzy description logics, J. Artificial Intelligence Res, 14: 137–166. (Scholar)
  • White, R.B., 1979, The consistency of the axiom of comprehension in the infinite-valued predicate logic of Łukasiewicz, J. Philosophical Logic, 8: 509–534. (Scholar)
  • Wronski, A., 1987, Remarks on a survey article on many valued logic by A. Urquhart, Studia Logica, 46: 275–278. (Scholar)
  • Zadeh, L.A., 1965, Fuzzy sets, Information and Control, 8: 338–353. (Scholar)
  • –––, 1975, Fuzzy logic and approximate reasoning, Synthese, 30: 407–428. (Scholar)
  • –––, 1978, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1: 3–28. (Scholar)
  • –––, 1979, A theory of approximate reasoning, in J.E. Hayes, D. Michie, L.I. Mikulich (eds.), Machine Intelligence 9. New York: Halstead Press, 149–194.

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