An introduction to many-valued and fuzzy logic: Semantics, algebras, and derivation systems

An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems

Volumn , Issue , 2008, Pages 1-329

  Bergmann, Merrie ^a  

^a NONE

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EID: 84924717453     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511801129     Document Type: Book

References (95)

1. Ackermann, Robert. 1967. Introduction to Many-Valued Logics. London: Routledge & Kegan Paul.
2. Aguzzoli, S., and A. Ciabattoni. 2000. “Finiteness in Infinite-ValuedŁukasiewicz Logic.” Journal of Logic, Language, and Information9, pp. 5-29.
3. Baaz, Matthias. 1996. “Infinite-Valued Gödel Logics with 0-1-Projections and Relativizations.” In ed. Petr Hájek, Gödel ’96: Logical Foundations of Mathematics, Computer Science and Physics—Kurt Gödel’s Legacy. New York: Springer, pp. 23-33.
4. Baaz, Matthias, Christian G. Fermüller, and Richard Zach. 1993. “Systematic Construction ofNaturalDeduction Systems forMany-Valued Logics.” Proceedings of the 23rd International Symposium on Multiple Valued Logic. Los Alamitos, CA: IEEE Computer Society Press, pp. 208-213.
5. Baaz, Mathias, Petr Hájek, Jan Kraníček, and David Švejda. 1998. “Embedding Logics into Product Logic.” Studia Logica61, pp. 35-47.
6. Baaz, M., and R. Zach. 1998. “Compact PropositionalGödel Logics.” Proceedings of the 28th International Symposium on Multiple-Valued Logic. Los Alamitos, CA: IEEE Computer Society Press, pp. 108-113.
7. Balbes, Raymond, and Philip Dwinger. 1974. Distributive Lattices. Columbia:University of Missouri Press.
8. Beall, J. C., and Mark Colyvan. 2001. “Heaps of Gluts and Hyde-ing the Sorities.” Mind110, pp. 401-408.
9. Beall, J. C., and Bas C. van Fraassen. 2003. Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic. New York: Oxford University Press.
10. Behounek, Libor. “A Model of Higher-Order Vagueness in Higher-Order Fuzzy Logic.” http://atlas-conferences.com/cgi-bin/abstract/casu-34.
11. Bergmann, Merrie, James H. Moor, and Jack Nelson. 2004. The Logic Book, 4th ed. New York: McGraw-Hill.
12. Black, Max. 1937. “Vagueness: An Exercise in Logical Analysis.” Philosophy of Science4, pp. 427-455.
13. 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.)
14. Bolc, Leonard, and Piotr Borowik. 1992. Many-Valued Logics. I: Theoretical Foundations. NewYork: Springer-Verlag.
15. Chang, C. C. 1958a. “Proof of an Axiom ofŁukasiewicz.” Transactions of the American Mathematical Society87, 55-56.
16. Chang, C. C. 1958b. “Algebraic Analysis ofMany Valued Logics.” Transactions of the American Mathematical Society88, pp. 476-490.
17. Chang, C. C. 1959. “A New Proof of the Completeness of theŁukasiewicz Axioms.” Transactions of the American Mathematical Society93, pp. 74-80.
18. Church, Alonzo. 1936. “A Note on the Entscheidungsproblem.” Journal of Symbolic Logic1, pp. 40-41.
19. Cignoli, Roberto L.O., Itala M., L. D’Ottaviano, and Daniele Mundici. 2000. Algebraic Foundations of Many-Valued Reasoning. Boston: Kluwer.
20. Delong, Howard. 1970. A Profile of Mathematical Logic. Reading, MA: Addison-Wesley.
21. Dilworth, R. P., and M. Ward. 1939. “Residuated Lattices.” Transactions of the American Mathematical Society45, pp. 335-354.
22. Dunn, J.Michael, and Gary M. Hardegree. 2001. Algebraic Methods in Philosophical Logic. NewYork: Oxford University Press.
23. Edgington, Dorothy. 1999. “VaguenessbyDegrees.” In eds.RosannaKeefe andPeter Smith, Vagueness: A Reader. Cambridge, MA: MIT Press, pp. 294-316.
24. Esteva, Francesc, Lluis Godo, Petr Hájek, and Mirko Navara. 2000. “Residuated Fuzzy Logics with an Involutive Negation.” Archive for Mathematical Logic39, pp. 103-124.
25. Esteva, Francesc, Lluis Godo, and Franco Montagna. 2001. “TheŁπ and Łπ1/2 Logics: Two Complete Fuzzy Systems Joining Lukasiewicz and Product Logics.” Archive for Mathematical Logic40, pp. 39-67.
26. Fine, Kit. 1975. “Vagueness, Truth and Logic.” Synthese30, pp. 265-300.
27. Frege, Gottlob. 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: Verlag von Louis Nebert.
28. Gödel, Kurt. 1932. “Zum Intuitionistischen Aussagenkalkül.” Anzeiger der Akademie der Wissenschaften Wien, mathematisch, naturwissenschaftliche Klasse 69, pp. 65-66.
29. Goguen, Joseph A. 1967. “L-Fuzzy Sets.” Journal of Mathematical AnalysisandApplications18, pp. 145-174.
30. Goguen, Joseph A. 1968-1969. “The Logic of Inexact Concepts.” Synthese 19, pp. 325-373.
31. Goldberg, H., H. LeBlanc, and G. Weaver. 1974. “A Strong Completeness Theorem.” Notre Dame Journal of Formal Logic15 (2), pp. 325-331.
32. Gottwald, Siegfried. 2001. A Treatise on Many-Valued Logics. Philadelphia: Research Studies Press.
33. Gottwald, Siegfried, and Petr Hájek. 2005. “Triangular Norm-based Mathematical Fuzzy Logics.” Ineds.E.P. KlementandR.Mesiar, Logical, Algebraic, Analytic, andProbabilistic Aspects of Triangular Numbers. New York: Elsevier, pp. 275-299.
34. Haack, Susan. 1979. “Do We Need Fuzzy Logic?” International Journal of Man-Machine Studies11, pp. 437-445.
35. Hájek, Petr. 1995a. “Fuzzy Logic and Arithmetical Hierarchy.” Fuzzy Sets and Systems73 (3), pp. 359-363.
36. Hájek, Petr. 1995b. “Fuzzy Logic from the Logical Point of View.” In eds. M. BartoŠek, J. Staudek, and J. Wiedermann, SOFSEM ’95: Theory and Practice of Informatics; Lecture Notes in Computer Science 1012. New York: Springer-Verlag, pp. 31-49.
37. Hájek, Petr. 1997. “Fuzzy Logic and Arithmetical Hierarchy II.” Studia Logica58, pp. 129-141.
38. Hájek, Petr. 1998a. “Basic Fuzzy Logic and BL-algebras.” Soft Computing2, pp. 124-128.
39. Hájek, Petr. 1998b. Metamathematics of Fuzzy Logic. Boston: Kluwer.
40. Hájek, Petr. 2001. “On Very True.” Fuzzy Sets and Systems124, pp. 329-333.
41. Hájek, Petr, Jeff Paris, and John Shepherdson. 2000. “Rational Pavelka Predicate Logic Is a Conservative Extension ofŁukasiewicz Predicate Logic.” The Journal of Symbolic Logic65 (2), pp. 669-682.
42. Heck, Richard G. 1993. “A Note on the Logic of (Higher-Order) Vagueness.” Analysis53, pp. 201-208.
43. Hirota, K., ed. 1993. Industrial Applications ofFuzzyTechnology(translatedbyH.Solomon). NewYork: Springer-Verlag.
44. Hunter, Geoffrey. 1971. Metalogic: An Introduction to the Metatheory of Standard First-Order Logic. Los Angeles: University of California Press.
45. Hyde, Dominic. 1997. “FromHeaps and Gaps to Heaps of Gluts.” Mind N. S. 106, pp. 641-660.
46. Kearns, John T. 1979. “The Strong Completeness of a System for Kleene’s Three-Valued Logic.” Zeitschrift f ür mathematische Logik und Grundlagen der Mathematik25, pp. 61-68.
47. Keefe, Rosanna, and Peter Smith, eds. 1997. Vagueness: A Reader. Cambridge, MA: MIT Press.
48. Kleene, Stephen C. 1938. “On a Notation for Ordinal Numbers.” The Journal of Symbolic Logic3, pp. 150-155.
49. Klir, George J., and Bo Yuan. 1995. Fuzzy Sets and Fuzzy Logic: Theory and Applications. Saddle River, NJ: Prentice Hall.
50. Lakoff, George. 1973. “Hedges: A Study inMeaningCriteria,” Journal of Philosophical Logic 2, pp. 459-508.
51. LeBlanc, Hugues. 1977.“AStrongCompletenessTheoremfor 3-Valued Logic:Part II.” Notre Dame Journal of Formal Logic 18 (1), pp. 107-116.
52. Lee, R. C.T., and C.-L. Chang. 1971. “Some Properties of Fuzzy Logic.” Information and Control19, pp. 417-431.
53. 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.)
54. Łukasiewicz, Jan. 1934. “Z historii logiki zdán.” Przeglad Filozoficzny 37, pp. 417-437.
55. 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.
56. Łukasiewicz, J., and A. Tarski. 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.
57. 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.
58. Machina, Kenton F. 1976. “Truth, Belief, and Vagueness.” Journal of Philosophical Logic5, pp. 47-78.
59. MacLane, Saunders, and Garrett Birkhoff. 1999. Algebra, 3rd ed. Providence, RI: American Mathematical Society.
60. Mangani, P. 1973. “Su Certe Algebre Connesse con Logiche a Pi ´u Valori (On Certain Algebras Related to Many-Valued Logics).” Bollettino dell’Unione Matematica Italiana (Series 4)8, pp. 68-78.
61. Martin, Robert L., ed. 1970. Paradox of the Liar. New Haven, CT: Yale University Press.
62. Martin, Robert L., ed. 1984. Recent Essays on Truth and the Liar Paradox. New York: Oxford University Press.
63. McNaughton, Robert. 1951. “A Theorem about Infinite-Valued Sentential Logic.” Journal of Symbolic Logic 16, pp. 1-13.
64. Menger, K. 1942. “Statistical Metrics.” Proceedings of the National Academy of Sciences in the USA8, pp. 535-537.
65. Meredith, C. A. 1928. “The Dependence of an Axiom ofŁukasiewicz.” Transactions of the American Mathematical Society87, p. 54.
66. Minari, Pierluigi. 2003. “ANote onŁukasiewicz’s Three-Valued Logic.” http://eprints.unifi.it/archive/00001106/02/08Minari.pdf.
67. Morgan, Charles G., and Francis J. Pelletier. 1977. “SomeNotes Concerning Fuzzy Logics.” Linguistics and Philosophy1, pp. 79-97.
68. Novák, Vilém. 1990. “On the Syntactico-Semantical Completeness of First-Order Fuzzy Logic” (Parts I and II). Kybernetika 26, pp. 47-66, 134-154.
69. Novák, Vilém. 2001. “Antonyms and Linguistic Quantifiers in Fuzzy Logic.” Fuzzy Sets and Systems124, pp. 335-351.
70. Novák, Vilém, Irina Perfilieva, and Jiří Močkoř. 1999. Mathematical Principles of Fuzzy Logic. Boston: Kluwer.
71. Pavelka, J. M. 1979. “On Fuzzy Logic” (Parts I, II, and III). Zeitschrift f ür mathematische Logik und Grundlagen der Mathematik 25, pp. 45-52, 119-134, 447-464.
72. Pedrycz, Witold, and Fernando Gomide. 1998. An Introduction to Fuzzy Sets: Analysis and Design. Cambridge, MA: MIT Press.
73. Pogorzelski, W. A. 1964. “The Deduction Theorem forŁukasiewicz Many-Valued Propositional Calculi.” Studia Logica15, pp. 7-23.
74. Priest, Graham. 2001. An Introduction to Non-Classical Logic. Cambridge: CambridgeUniversity Press, p. 215.
75. Quine, W. V. O. 1960. Word and Object. Cambridge, MA: MIT Press.
76. Rescher, Nicholas. 1969. Many-Valued Logic. New York:McGraw-Hill.
77. Robinson, J. A. 1965. “A Machine-Oriented Logic Based on the Resolution Principle.” Journal of the Association for Computational Machinery12, pp. 23-41.
78. Rose, Alan, and J. Barkley Rosser. 1958. “Fragments of Many-Valued Statement Calculi.” Transactions of the American Mathematical Society87 (1), pp. 1-53.
79. Ruspini, Enrique H., Piero P. Bonissone, and Witold Predrycz, eds. 1998. Handbook of Fuzzy Computation. Philadelphia: Institute of Physics Publishing.
80. Russell, Bertrand. 1923. “Vagueness.” Australasian Journal of Philosophy1, pp. 84-92.
81. Scarpellini, B. 1962. “Die Nichtaxiomatisierbarkeit des undenlichwertigen Pr¨adikatenkalk üls vonŁukasiewicz.” Journal of Symbolic Logic27, pp. 159-170.
82. SŁupecki, Jerzy. 1936. “Der volle dreivertige Aussagenkalkül.” Comptes rendus des séances de la Société des sciences et des lettres de Varsovie 3 (29), pp. 9-11.
83. English translation by Storrs McCall, “The Full Three-Valued Propositional Calculus.” In ed. Storrs McCall, Polish Logic: 1920-1939. New York: Oxford University Press, 1967, pp. 335-337.
84. Smullyan, Raymond M. 1968. First-Order Logic. New York: Springer-Verlag.
85. Stoll, Robert R. 1961. Set Theory and Logic. San Francisco:W. H. Freeman.
86. Takeuti, Gaisi, and Satoko Titani. 1984. “Intuitionistic Fuzzy Logic and Intuitionistic Fuzzy Set Theory.” The Journal of Symbolic Logic 49, pp. 851-866.
87. Tarski, Alfred. 1936. “DerWahrheitsbegriff in den formalisierten Sprachen.” Studia Philosophica1, pp. 261-405.
88. Turksen, I.B. 1991.“Measurement ofMembership Functions and TheirAcquisition.” Fuzzy Sets and Systems 40, pp. 5-38.
89. Van Fraassen, Bas C. 1966. “Singular Terms, Truth-Value Gaps, and Free Logic.” Journal of Philosophy 63, pp. 481-495.
90. Wajsberg, Mordchaj. 1931. “Aksjomatyzacja trójwarto´sciowego rachunku zdán.” Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie 24, cl. iii, pp. 126-145.
91. English translation by B. Gruchman and S. McCall, “Axiomatization of the Three-Valued Propositional Calculus.” In ed. StorrsMcCall, Polish Logic: 1920-1939. New York: Oxford University Press, 1967, pp. 264-284.
92. Wright, Crispin. 1987. “Further Reflections on the Sorites Paradox.” Philosophical Topics15, pp. 227-290.
93. Wu, Olivia. 2003. “Rice Goes Digital Cooked the Fuzzy LogicWay: Side-by-Side Tests Show ApplianceMakes a Difference.” San Francisco Chronicle, December 10, p. E1.
94. Zadeh, Lotfi A. 1965. “Fuzzy Sets.” Information and Control8, pp. 338-353.
95. Zadeh, Lotfi A. 1975. “Fuzzy Logic and Approximate Reasoning.” Synthese30, pp. 407-428.