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Bibliography

Published online by Cambridge University Press:  05 June 2012

Merrie Bergmann
Merrie Bergmann
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Smith College, Massachusetts
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An Introduction to Many-Valued and Fuzzy Logic
Semantics, Algebras, and Derivation Systems
 , pp. 321 - 326
Publisher: Cambridge University Press
Print publication year: 2008

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References

Ackermann, Robert. 1967. Introduction to Many-Valued Logics. London: Routledge & Kegan Paul.Google Scholar
Aguzzoli, S., and Ciabattoni, A.. 2000. “Finiteness in Infinite-Valued Łukasiewicz Logic.” Journal of Logic, Language, and Information 9, pp. 5–29.CrossRefGoogle Scholar
Baaz, Matthias. 1996. “Infinite-Valued Gödel Logics with 0–1-Projections and Relativizations.” In ed. Hájek, Petr, Gödel '96: Logical Foundations of Mathematics, Computer Science and Physics – Kurt Gödel's Legacy. New York: Springer, pp. 23–33.CrossRefGoogle Scholar
Baaz, Matthias, Fermüller, Christian G., and Zach, Richard. 1993. “Systematic Construction of Natural Deduction Systems for Many-Valued Logics.” Proceedings of the 23rd International Symposium on Multiple Valued Logic. Los Alamitos, CA: IEEE Computer Society Press, pp. 208–213.Google Scholar
Baaz, Mathias, Hájek, Petr, Kraníček, Jan, and Švejda, David. 1998. “Embedding Logics into Product Logic.” Studia Logica 61, pp. 35–47.CrossRefGoogle Scholar
Baaz, M., and Zach, R.. 1998. “Compact Propositional Gödel Logics.” Proceedings of the 28th International Symposium on Multiple-Valued Logic. Los Alamitos, CA: IEEE Computer Society Press, pp. 108–113.Google Scholar
Balbes, Raymond, and Dwinger, Philip. 1974. Distributive Lattices. Columbia: University of Missouri Press.Google Scholar
Beall, J. C., and Colyvan, Mark. 2001. “Heaps of Gluts and Hyde-ing the Sorities.” Mind 110, pp. 401–408.CrossRefGoogle Scholar
Beall, J. C., and Fraassen, Bas C.. 2003. Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic. New York: Oxford University Press.Google Scholar
Behounek, Libor. “A Model of Higher-Order Vagueness in Higher-Order Fuzzy Logic.” http://atlas-conferences.com/cgi-bin/abstract/casu-34.
Bergmann, Merrie, Moor, James H., and Nelson, Jack. 2004. The Logic Book, 4th ed. New York: McGraw-Hill.Google Scholar
Black, Max. 1937. “Vagueness: An Exercise in Logical Analysis.” Philosophy of Science 4, pp. 427–455.CrossRefGoogle Scholar
Bochvar, D. A. 1937. “Ob odnom Tréhznačnom Isčislénii i égo Priménénii k Analizu Paradoksov Klassičéskogo Rasširénnogo Funkcional'nogo Isčisléniá.” Matématčéskij Sbornik 4 (46), pp. 287–308. (English translation by Merrie Bergmann, “On a Three-Valued Calculus and Its Application to the Analysis of the Paradoxes of the Classical Extended Functional Calculus.” History and Philosophy of Logic 2, 1981, pp. 87–112.)Google Scholar
Bolc, Leonard, and Borowik, Piotr. 1992. Many-Valued Logics. I: Theoretical Foundations. New York: Springer-Verlag.CrossRefGoogle Scholar
Chang, C. C. 1958a. “Proof of an Axiom of Łukasiewicz.” Transactions of the American Mathematical Society 87, 55–56.Google Scholar
Chang, C. C. 1958b. “Algebraic Analysis of Many Valued Logics.” Transactions of the American Mathematical Society 88, pp. 476–490.CrossRefGoogle Scholar
Chang, C. C. 1959. “A New Proof of the Completeness of the Łukasiewicz Axioms.” Transactions of the American Mathematical Society 93, pp. 74–80.Google Scholar
Church, Alonzo. 1936. “A Note on the Entscheidungsproblem.” Journal of Symbolic Logic 1, pp. 40–41.CrossRefGoogle Scholar
Cignoli, Roberto L. O., D'Ottaviano, Itala M. L., and Mundici, Daniele. 2000. Algebraic Foundations of Many-Valued Reasoning. Boston: Kluwer.CrossRefGoogle Scholar
Delong, Howard. 1970. A Profile of Mathematical Logic. Reading, MA: Addison-Wesley.Google Scholar
Dilworth, R. P., and Ward, M.. 1939. “Residuated Lattices.” Transactions of the American Mathematical Society 45, pp. 335–354.Google Scholar
Dunn, J. Michael, and Hardegree, Gary M.. 2001. Algebraic Methods in Philosophical Logic. New York: Oxford University Press.Google Scholar
Edgington, Dorothy. 1999. “Vagueness by Degrees.” In eds. Keefe, Rosanna and Smith, Peter, Vagueness: A Reader. Cambridge, MA: MIT Press, pp. 294–316.Google Scholar
Esteva, Francesc, Godo, Lluis, Hájek, Petr, and Navara, Mirko. 2000. “Residuated Fuzzy Logics with an Involutive Negation.” Archive for Mathematical Logic 39, pp. 103–124.CrossRefGoogle Scholar
Esteva, Francesc, Godo, Lluis, and Montagna, Franco. 2001. “The ŁΠ and ŁΠ½ Logics: Two Complete Fuzzy Systems Joining Lukasiewicz and Product Logics.” Archive for Mathematical Logic 40, pp. 39–67.CrossRefGoogle Scholar
Fine, Kit. 1975. “Vagueness, Truth and Logic.” Synthese 30, pp. 265–300.CrossRefGoogle Scholar
Frege, Gottlob. 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: Verlag von Louis Nebert.Google Scholar
Gödel, Kurt. 1932. “Zum Intuitionistischen Aussagenkalkül.” Anzeiger der Akademie der Wissenschaften Wien, mathematisch, naturwissenschaftliche Klasse 69, pp. 65–66.Google Scholar
Goguen, Joseph A. 1967. “L-Fuzzy Sets.” Journal of Mathematical Analysis and Applications 18, pp. 145–174.CrossRefGoogle Scholar
Goguen, Joseph A. 1968–1969. “The Logic of Inexact Concepts.” Synthese 19, pp. 325–373.CrossRefGoogle Scholar
Goldberg, H., LeBlanc, H., and Weaver, G.. 1974. “A Strong Completeness Theorem.” Notre Dame Journal of Formal Logic 15 (2), pp. 325–331.CrossRefGoogle Scholar
Gottwald, Siegfried. 2001. A Treatise on Many-Valued Logics. Philadelphia: Research Studies Press.Google Scholar
Gottwald, Siegfried, and Petr Hájek. 2005. “Triangular Norm-based Mathematical Fuzzy Logics.” In eds. Klement, E. P. and Mesiar, R., Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Numbers. New York: Elsevier, pp. 275–299.Google Scholar
Haack, Susan. 1979. “Do We Need Fuzzy Logic?” International Journal of Man-Machine Studies 11, pp. 437–445.CrossRefGoogle Scholar
Hájek, Petr. 1995a. “Fuzzy Logic and Arithmetical Hierarchy.” Fuzzy Sets and Systems 73 (3), pp. 359–363.CrossRefGoogle Scholar
Hájek, Petr. 1995b. “Fuzzy Logic from the Logical Point of View.” In eds. Bartošek, M., Staudek, J., and Wiedermann, J., SOFSEM '95: Theory and Practice of Informatics; Lecture Notes in Computer Science 1012. New York: Springer-Verlag, pp. 31–49.Google Scholar
Hájek, Petr. 1997. “Fuzzy Logic and Arithmetical Hierarchy II.” Studia Logica 58, pp. 129–141.CrossRefGoogle Scholar
Hájek, Petr. 1998a. “Basic Fuzzy Logic and BL-algebras.” Soft Computing 2, pp. 124–128.Google Scholar
Hájek, Petr. 1998b. Metamathematics of Fuzzy Logic. Boston: Kluwer.CrossRefGoogle Scholar
Hájek, Petr. 2001. “On Very True.” Fuzzy Sets and Systems 124, pp. 329–333.CrossRefGoogle Scholar
Hájek, Petr, Paris, Jeff, and Shepherdson, John. 2000. “Rational Pavelka Predicate Logic Is a Conservative Extension of Łukasiewicz Predicate Logic.” The Journal of Symbolic Logic 65 (2), pp. 669–682.CrossRefGoogle Scholar
Heck, Richard G. 1993. “A Note on the Logic of (Higher-Order) Vagueness.” Analysis 53, pp. 201–208.CrossRefGoogle Scholar
Hirota, K., ed. 1993. Industrial Applications of Fuzzy Technology (translated by H. Solomon). New York: Springer-Verlag.CrossRefGoogle Scholar
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Kearns, John T. 1979. “The Strong Completeness of a System for Kleene's Three-Valued Logic.” Zeitschrift für mathematische Logik und Grundlagen der Mathematik 25, pp. 61–68.CrossRefGoogle Scholar
Keefe, Rosanna, and Smith, Peter, eds. 1997. Vagueness: A Reader. Cambridge, MA: MIT Press.Google Scholar
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Lakoff, George. 1973. “Hedges: A Study in Meaning Criteria,” Journal of Philosophical Logic 2, pp. 459–508.CrossRefGoogle Scholar
LeBlanc, Hugues. 1977. “A Strong Completeness Theorem for 3-Valued Logic: Part II.” Notre Dame Journal of Formal Logic 18 (1), pp. 107–116.CrossRefGoogle Scholar
Lee, R. C. T., and Chang, C.-L.. 1971. “Some Properties of Fuzzy Logic.” Information and Control 19, pp. 417–431.CrossRefGoogle Scholar
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Beall, J. C., and Fraassen, Bas C.. 2003. Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic. New York: Oxford University Press.Google Scholar
Behounek, Libor. “A Model of Higher-Order Vagueness in Higher-Order Fuzzy Logic.” http://atlas-conferences.com/cgi-bin/abstract/casu-34.
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Black, Max. 1937. “Vagueness: An Exercise in Logical Analysis.” Philosophy of Science 4, pp. 427–455.CrossRefGoogle Scholar
Bochvar, D. A. 1937. “Ob odnom Tréhznačnom Isčislénii i égo Priménénii k Analizu Paradoksov Klassičéskogo Rasširénnogo Funkcional'nogo Isčisléniá.” Matématčéskij Sbornik 4 (46), pp. 287–308. (English translation by Merrie Bergmann, “On a Three-Valued Calculus and Its Application to the Analysis of the Paradoxes of the Classical Extended Functional Calculus.” History and Philosophy of Logic 2, 1981, pp. 87–112.)Google Scholar
Bolc, Leonard, and Borowik, Piotr. 1992. Many-Valued Logics. I: Theoretical Foundations. New York: Springer-Verlag.CrossRefGoogle Scholar
Chang, C. C. 1958a. “Proof of an Axiom of Łukasiewicz.” Transactions of the American Mathematical Society 87, 55–56.Google Scholar
Chang, C. C. 1958b. “Algebraic Analysis of Many Valued Logics.” Transactions of the American Mathematical Society 88, pp. 476–490.CrossRefGoogle Scholar
Chang, C. C. 1959. “A New Proof of the Completeness of the Łukasiewicz Axioms.” Transactions of the American Mathematical Society 93, pp. 74–80.Google Scholar
Church, Alonzo. 1936. “A Note on the Entscheidungsproblem.” Journal of Symbolic Logic 1, pp. 40–41.CrossRefGoogle Scholar
Cignoli, Roberto L. O., D'Ottaviano, Itala M. L., and Mundici, Daniele. 2000. Algebraic Foundations of Many-Valued Reasoning. Boston: Kluwer.CrossRefGoogle Scholar
Delong, Howard. 1970. A Profile of Mathematical Logic. Reading, MA: Addison-Wesley.Google Scholar
Dilworth, R. P., and Ward, M.. 1939. “Residuated Lattices.” Transactions of the American Mathematical Society 45, pp. 335–354.Google Scholar
Dunn, J. Michael, and Hardegree, Gary M.. 2001. Algebraic Methods in Philosophical Logic. New York: Oxford University Press.Google Scholar
Edgington, Dorothy. 1999. “Vagueness by Degrees.” In eds. Keefe, Rosanna and Smith, Peter, Vagueness: A Reader. Cambridge, MA: MIT Press, pp. 294–316.Google Scholar
Esteva, Francesc, Godo, Lluis, Hájek, Petr, and Navara, Mirko. 2000. “Residuated Fuzzy Logics with an Involutive Negation.” Archive for Mathematical Logic 39, pp. 103–124.CrossRefGoogle Scholar
Esteva, Francesc, Godo, Lluis, and Montagna, Franco. 2001. “The ŁΠ and ŁΠ½ Logics: Two Complete Fuzzy Systems Joining Lukasiewicz and Product Logics.” Archive for Mathematical Logic 40, pp. 39–67.CrossRefGoogle Scholar
Fine, Kit. 1975. “Vagueness, Truth and Logic.” Synthese 30, pp. 265–300.CrossRefGoogle Scholar
Frege, Gottlob. 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: Verlag von Louis Nebert.Google Scholar
Gödel, Kurt. 1932. “Zum Intuitionistischen Aussagenkalkül.” Anzeiger der Akademie der Wissenschaften Wien, mathematisch, naturwissenschaftliche Klasse 69, pp. 65–66.Google Scholar
Goguen, Joseph A. 1967. “L-Fuzzy Sets.” Journal of Mathematical Analysis and Applications 18, pp. 145–174.CrossRefGoogle Scholar
Goguen, Joseph A. 1968–1969. “The Logic of Inexact Concepts.” Synthese 19, pp. 325–373.CrossRefGoogle Scholar
Goldberg, H., LeBlanc, H., and Weaver, G.. 1974. “A Strong Completeness Theorem.” Notre Dame Journal of Formal Logic 15 (2), pp. 325–331.CrossRefGoogle Scholar
Gottwald, Siegfried. 2001. A Treatise on Many-Valued Logics. Philadelphia: Research Studies Press.Google Scholar
Gottwald, Siegfried, and Petr Hájek. 2005. “Triangular Norm-based Mathematical Fuzzy Logics.” In eds. Klement, E. P. and Mesiar, R., Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Numbers. New York: Elsevier, pp. 275–299.Google Scholar
Haack, Susan. 1979. “Do We Need Fuzzy Logic?” International Journal of Man-Machine Studies 11, pp. 437–445.CrossRefGoogle Scholar
Hájek, Petr. 1995a. “Fuzzy Logic and Arithmetical Hierarchy.” Fuzzy Sets and Systems 73 (3), pp. 359–363.CrossRefGoogle Scholar
Hájek, Petr. 1995b. “Fuzzy Logic from the Logical Point of View.” In eds. Bartošek, M., Staudek, J., and Wiedermann, J., SOFSEM '95: Theory and Practice of Informatics; Lecture Notes in Computer Science 1012. New York: Springer-Verlag, pp. 31–49.Google Scholar
Hájek, Petr. 1997. “Fuzzy Logic and Arithmetical Hierarchy II.” Studia Logica 58, pp. 129–141.CrossRefGoogle Scholar
Hájek, Petr. 1998a. “Basic Fuzzy Logic and BL-algebras.” Soft Computing 2, pp. 124–128.Google Scholar
Hájek, Petr. 1998b. Metamathematics of Fuzzy Logic. Boston: Kluwer.CrossRefGoogle Scholar
Hájek, Petr. 2001. “On Very True.” Fuzzy Sets and Systems 124, pp. 329–333.CrossRefGoogle Scholar
Hájek, Petr, Paris, Jeff, and Shepherdson, John. 2000. “Rational Pavelka Predicate Logic Is a Conservative Extension of Łukasiewicz Predicate Logic.” The Journal of Symbolic Logic 65 (2), pp. 669–682.CrossRefGoogle Scholar
Heck, Richard G. 1993. “A Note on the Logic of (Higher-Order) Vagueness.” Analysis 53, pp. 201–208.CrossRefGoogle Scholar
Hirota, K., ed. 1993. Industrial Applications of Fuzzy Technology (translated by H. Solomon). New York: Springer-Verlag.CrossRefGoogle Scholar
Hunter, Geoffrey. 1971. Metalogic: An Introduction to the Metatheory of Standard First-Order Logic. Los Angeles: University of California Press.CrossRefGoogle Scholar
Hyde, Dominic. 1997. “From Heaps and Gaps to Heaps of Gluts.” Mind N. S. 106, pp. 641–660CrossRefGoogle Scholar
Kearns, John T. 1979. “The Strong Completeness of a System for Kleene's Three-Valued Logic.” Zeitschrift für mathematische Logik und Grundlagen der Mathematik 25, pp. 61–68.CrossRefGoogle Scholar
Keefe, Rosanna, and Smith, Peter, eds. 1997. Vagueness: A Reader. Cambridge, MA: MIT Press.Google Scholar
Kleene, Stephen C. 1938. “On a Notation for Ordinal Numbers.” The Journal of Symbolic Logic 3, pp. 150–155.CrossRefGoogle Scholar
Klir, George J., and Yuan, Bo. 1995. Fuzzy Sets and Fuzzy Logic: Theory and Applications. Saddle River, NJ: Prentice Hall.Google Scholar
Lakoff, George. 1973. “Hedges: A Study in Meaning Criteria,” Journal of Philosophical Logic 2, pp. 459–508.CrossRefGoogle Scholar
LeBlanc, Hugues. 1977. “A Strong Completeness Theorem for 3-Valued Logic: Part II.” Notre Dame Journal of Formal Logic 18 (1), pp. 107–116.CrossRefGoogle Scholar
Lee, R. C. T., and Chang, C.-L.. 1971. “Some Properties of Fuzzy Logic.” Information and Control 19, pp. 417–431.CrossRefGoogle Scholar
Łukasiewicz, Jan. 1930. “Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls.” Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie 23, ⅽⅼ. ⅲ, pp. 51–77. (English translation by H. Weber, “Philosophical Remarks on Many-Valued Systems of Propositional Logic.” In ed. Storrs McCall, Polish Logic: 1920–1939, New York: Oxford University Press, 1967, pp. 40–65.)Google Scholar
Łukasiewicz, Jan. 1934. “Z historii logiki zdań.” Przeglad Filozoficzny 37, pp. 417–437. (English translation by Storrs McCall, “On the History of the Logic of Propositions.” In ed. Storrs McCall, Polish Logic 1920–1939, New York: Oxford University Press, 1967, pp. 66–87.)Google Scholar
Łukasiewicz, J., and Tarski, A.. 1930. “Untersuchungen über den Aussagenkalkül.” Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie 23, ⅽⅼ. ⅲ, pp. 39–50. (English translation by J. H. Woodger, “Investigations into the Sentential Calculus.” In Alfred Tarski, Logic, Semantics, Metamathematics: Papers from 1923 to 1938, 2nd ed., Indianapolis: Hackett Publishing Co., 1983, pp. 38–59.Google Scholar
Machina, Kenton F. 1976. “Truth, Belief, and Vagueness.” Journal of Philosophical Logic 5, pp. 47–78.CrossRefGoogle Scholar
MacLane, Saunders, and Birkhoff, Garrett. 1999. Algebra, 3rd ed. Providence, RI: American Mathematical Society.Google Scholar
Mangani, P. 1973. “Su Certe Algebre Connesse con Logiche a Piú Valori (On Certain Algebras Related to Many-Valued Logics).” Bollettino dell'Unione Matematica Italiana (Series 4) 8, pp. 68–78.Google Scholar
Martin, Robert L., ed. 1970. Paradox of the Liar. New Haven, CT: Yale University Press.Google Scholar
Martin, Robert L., ed. 1984. Recent Essays on Truth and the Liar Paradox. New York: Oxford University Press.Google Scholar
McNaughton, Robert. 1951. “A Theorem about Infinite-Valued Sentential Logic.” Journal of Symbolic Logic 16, pp. 1–13.CrossRefGoogle Scholar
Menger, K. 1942. “Statistical Metrics.” Proceedings of the National Academy of Sciences in the USA 8, pp. 535–537.CrossRefGoogle Scholar
Meredith, C. A. 1928. “The Dependence of an Axiom of Łukasiewicz.” Transactions of the American Mathematical Society 87, p. 54.Google Scholar
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  • Bibliography
  • Merrie Bergmann, Smith College, Massachusetts
  • Book: An Introduction to Many-Valued and Fuzzy Logic
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511801129.020
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  • Bibliography
  • Merrie Bergmann, Smith College, Massachusetts
  • Book: An Introduction to Many-Valued and Fuzzy Logic
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511801129.020
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  • Bibliography
  • Merrie Bergmann, Smith College, Massachusetts
  • Book: An Introduction to Many-Valued and Fuzzy Logic
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511801129.020
Available formats
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