“BibliographyOfManyvaluedLogicsAndApplications”的概念、定义、习题解题方法及翻译-数学辞典

1 Awodey, S. & Butz, C., 2000, Topological Completeness for Higher Order Logic., Journal of Symbolic Logic, 65, 3, 1168–1182.

2 Awodey, S. & Reck, E. R., 2002, Completeness and Categoricity II. Twentieth-Century Metalogic to Twenty-first-Century Semantics, History and Philosophy of Logic, 23, (2): 77–94.

3 Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective,Philosophia Mathematica, 3: 209–237.

4 Baez, J., 1997, An Introduction to n-Categories, in Category Theory and Computer Science, Lecture Notes in Computer Science, 1290, Berlin: Springer-Verlag, 1–33.

5 Baez, J. & Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes,in: Advances in Mathematics, 135, 145–206.

6 Baianu, I. C., R. Brown , G. Georgescu and J. F. Glazebrook: 2006, Complex Nonlinear Biodynamics inCategories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic andNeoplastic Networks., Axiomathes,, 16: 82-165.

7 Baianu, I. C.: 1977, A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non–linear Theory,Bull. of Math. Biol. 39, 249–258.

8 M. Barr and C. Wells. Toposes, Triples and Theories. Montreal: McGill University, 2000.

9 Barr, M. & Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag.

10 Birkhoff, G.: 1948, Lattice Theory, Amer. Math. Soc., New York.

11 Boicescu, V., A. Filipoiu, G. Georgescu, and S. Rudeanu.: 1991, Łukasiewicz-Moisil Algebras,North-Holland, Amsterdam.

12 Chang, C. C.: 1958, Algebraic analysis of many valued logics. Trans. Amer. Math. Soc., 88,467–490.

13 Chang, C. C.: 1959, A new proof of the completeness of the Łukasiewicz axioms, Transactions AmericanMathematical Society 93, 74-80.

14 Cignoli, R., Esteva, F., Godo, L. and Torrens, A. : 2000, Basic Fuzzy Logic is the logic of continuous t-normsand their residua, Soft Computing 4, 106-112.

15 Cignoli, R.: Moisil algebras, Notas de Logica Matematica, Inst. Mat., Univ. Nacional del Sur,Bahia-Blanca, No. 27.

16 Bourbaki, N. : 1964. Eléments de Mathématique, Livre II, Algèbre, 4, Hermann, Editor,Paris.

17 Carnap, R.: 1938, The Logical Syntax of Language, Harcourt, Brace and Co., New York.

18 Ehresmann, C.: 1965, Catégories et Structures, Dunod, Paris.

19 Eilenberg, S. and S. MacLane: 1945, The General Theory of Natural Equivalences, Trans. Amer. Math. Soc.58, 231–294.

20 Georgescu, G. and D. Popescu: 1968, On Algebraic Categories, Rev. Roum. Math. Pures et Appl.13, 337–342.

21 Georgescu, G., and C. Vraciu.: 1970. On the characterization of centered Łukasiewicz algebras.J. Algebra 16, 486-495.

22 Georgescu, G., and I. Leuştean.: 2000. Towards a probability theory based on Moisil logic, SoftComputing 4, 19-26.

23 Grigolia, R.S.: 1977. Algebraic analysis of Łukasiewicz-Tarski’s logical systems, in Wójcicki, R.,Malinowski, G. (Eds), Selected Papers on Łukasiewicz Sentential Calculi, Osolineum, Wroclaw, pp. 81-92.

24 Hilbert, D. and W. Ackerman: 1927, Grunduge der Theoretischen Logik, Springer, Berlin.

25 Kan, D.M.: 1958, Adjoint Functors, Trans Amer. Math. Soc. 87, 294-329.

26 Lambek J. and P. J. Scott: 1986, Introduction to Higher Order Categorical Logic, Cambridge UniversityPress, Cambridge, UK, 1986.

27 Lawvere, F.W.: 1963, Functorial Semantics of Algebraic Theories, Proc. Natl. Acad. Sci. USA.50, 869–872.

28 Löfgren, L.: 1968, An Axiomatic Explanation of Complete Self-Reproduction, Bull. Math. Biophys.30, 317–348.

29 Łukasiewicz, J.: 1970, Selected Works, (ed.: L. Borkowski), North-Holland Publ. Co., Amsterdam and PWN,Warsaw.

30 MacLane, S. and I. Moerdijk: 1992, Sheaves in Geometry and Logic - A first Introduction to Topos Theory,Springer Verlag, New York.

31 McCulloch, W. and W. Pitts: 1943, ‘A Logical Calculus of Ideas Immanent in Nervous Activity’, Bull. Math.Biophys. 5, 115–133.

32 McNaughton, R.: 1951, A theorem about infinite-valued sentential logic, Journal Symbolic Logic16, 1-13.

33 Moisil, Gr. C.: 1972, Essai sur les logiques non-chrysippiennes. Ed. Academiei, Bucharest.

34 Mundici, D.: 1986, Interpretation of AF C*-algebras in Łukasiewicz sentential calculus, J. FunctionalAnalysis 65, 15-63.

35 Rose, A.: 1956, Formalisation du calcul propositionnel implicatif à

\\aleph_{0}

valeurs de Łukasiewicz,C. R. Acad. Sci. Paris 243,1183-1185.

36 Rose, A. and Rosser, J.B.: 1958, Fragments of many-valued statement calculi, Transactions AmericanMathematical Society 87, 1-53.

37 Rose, A.: 1962, Extensions of Some Theorems of Anderson and Belnap, J. Symbolic Logic, 27,(4), 423–425.

38 Rose, A.: 1978, ‘Formalisations of Further

\\aleph_{0}

–Valued Łukasiewicz Propositional Calculi’. J. SymbolicLogic, 43(2): 207-210

39 Rosen, R.: 1958a, A Relational Theory of Biological Systems, Bull. Math. Biophys. 20,245–260.

40 Rosen, R.: 1958b, “The Representation of Biological Systems from the Standpoint of the Theory of Categories.”,Bull. Math. Biophys. 20, 317-341.

41 Rosen, R.: 1991, Life Itself, Columbia University Press, New York.

42 Rosen, R.: 1999, Essays on Life Itself, Columbia University Press, New York.

43 Rosenbloom, Paul.: 1950, The Elements of Mathematical Logic, Dover, New York.

44 Rosenbloom, Paul.:1962, ibid., Prentice Hall, Englewood Cliffs, N.J.

45 Rosser, J.B. and Turquette, A.R.: 1952, Many-Valued Logics. North-Holland Publ. Co., Amsterdam.

单词	BibliographyOfManyvaluedLogicsAndApplications
释义	bibliography of many-valued logics and applications \\xyoption curve 0.1 A list of references for N-valued logics and their applications References 1 Awodey, S. & Butz, C., 2000, Topological Completeness for Higher Order Logic., Journal of Symbolic Logic, 65, 3, 1168–1182. 2 Awodey, S. & Reck, E. R., 2002, Completeness and Categoricity II. Twentieth-Century Metalogic to Twenty-first-Century Semantics, History and Philosophy of Logic, 23, (2): 77–94. 3 Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective,Philosophia Mathematica, 3: 209–237. 4 Baez, J., 1997, An Introduction to n-Categories, in Category Theory and Computer Science, Lecture Notes in Computer Science, 1290, Berlin: Springer-Verlag, 1–33. 5 Baez, J. & Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes,in: Advances in Mathematics, 135, 145–206. 6 Baianu, I. C., R. Brown , G. Georgescu and J. F. Glazebrook: 2006, Complex Nonlinear Biodynamics inCategories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic andNeoplastic Networks., Axiomathes,, 16: 82-165. 7 Baianu, I. C.: 1977, A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non–linear Theory,Bull. of Math. Biol. 39, 249–258. 8 M. Barr and C. Wells. Toposes, Triples and Theories. Montreal: McGill University, 2000. 9 Barr, M. & Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag. 10 Birkhoff, G.: 1948, Lattice Theory, Amer. Math. Soc., New York. 11 Boicescu, V., A. Filipoiu, G. Georgescu, and S. Rudeanu.: 1991, Łukasiewicz-Moisil Algebras,North-Holland, Amsterdam. 12 Chang, C. C.: 1958, Algebraic analysis of many valued logics. Trans. Amer. Math. Soc., 88,467–490. 13 Chang, C. C.: 1959, A new proof of the completeness of the Łukasiewicz axioms, Transactions AmericanMathematical Society 93, 74-80. 14 Cignoli, R., Esteva, F., Godo, L. and Torrens, A. : 2000, Basic Fuzzy Logic is the logic of continuous t-normsand their residua, Soft Computing 4, 106-112. 15 Cignoli, R.: Moisil algebras, Notas de Logica Matematica, Inst. Mat., Univ. Nacional del Sur,Bahia-Blanca, No. 27. 16 Bourbaki, N. : 1964. Eléments de Mathématique, Livre II, Algèbre, 4, Hermann, Editor,Paris. 17 Carnap, R.: 1938, The Logical Syntax of Language, Harcourt, Brace and Co., New York. 18 Ehresmann, C.: 1965, Catégories et Structures, Dunod, Paris. 19 Eilenberg, S. and S. MacLane: 1945, The General Theory of Natural Equivalences, Trans. Amer. Math. Soc.58, 231–294. 20 Georgescu, G. and D. Popescu: 1968, On Algebraic Categories, Rev. Roum. Math. Pures et Appl.13, 337–342. 21 Georgescu, G., and C. Vraciu.: 1970. On the characterization of centered Łukasiewicz algebras.J. Algebra 16, 486-495. 22 Georgescu, G., and I. Leuştean.: 2000. Towards a probability theory based on Moisil logic, SoftComputing 4, 19-26. 23 Grigolia, R.S.: 1977. Algebraic analysis of Łukasiewicz-Tarski’s logical systems, in Wójcicki, R.,Malinowski, G. (Eds), Selected Papers on Łukasiewicz Sentential Calculi, Osolineum, Wroclaw, pp. 81-92. 24 Hilbert, D. and W. Ackerman: 1927, Grunduge der Theoretischen Logik, Springer, Berlin. 25 Kan, D.M.: 1958, Adjoint Functors, Trans Amer. Math. Soc. 87, 294-329. 26 Lambek J. and P. J. Scott: 1986, Introduction to Higher Order Categorical Logic, Cambridge UniversityPress, Cambridge, UK, 1986. 27 Lawvere, F.W.: 1963, Functorial Semantics of Algebraic Theories, Proc. Natl. Acad. Sci. USA.50, 869–872. 28 Löfgren, L.: 1968, An Axiomatic Explanation of Complete Self-Reproduction, Bull. Math. Biophys.30, 317–348. 29 Łukasiewicz, J.: 1970, Selected Works, (ed.: L. Borkowski), North-Holland Publ. Co., Amsterdam and PWN,Warsaw. 30 MacLane, S. and I. Moerdijk: 1992, Sheaves in Geometry and Logic - A first Introduction to Topos Theory,Springer Verlag, New York. 31 McCulloch, W. and W. Pitts: 1943, ‘A Logical Calculus of Ideas Immanent in Nervous Activity’, Bull. Math.Biophys. 5, 115–133. 32 McNaughton, R.: 1951, A theorem about infinite-valued sentential logic, Journal Symbolic Logic16, 1-13. 33 Moisil, Gr. C.: 1972, Essai sur les logiques non-chrysippiennes. Ed. Academiei, Bucharest. 34 Mundici, D.: 1986, Interpretation of AF C-algebras in Łukasiewicz sentential calculus, J. FunctionalAnalysis* 65, 15-63. 35 Rose, A.: 1956, Formalisation du calcul propositionnel implicatif à $\\aleph_{0}$ valeurs de Łukasiewicz,C. R. Acad. Sci. Paris 243,1183-1185. 36 Rose, A. and Rosser, J.B.: 1958, Fragments of many-valued statement calculi, Transactions AmericanMathematical Society 87, 1-53. 37 Rose, A.: 1962, Extensions of Some Theorems of Anderson and Belnap, J. Symbolic Logic, 27,(4), 423–425. 38 Rose, A.: 1978, ‘Formalisations of Further $\\aleph_{0}$ –Valued Łukasiewicz Propositional Calculi’. J. SymbolicLogic, 43(2): 207-210 39 Rosen, R.: 1958a, A Relational Theory of Biological Systems, Bull. Math. Biophys. 20,245–260. 40 Rosen, R.: 1958b, “The Representation of Biological Systems from the Standpoint of the Theory of Categories.”,Bull. Math. Biophys. 20, 317-341. 41 Rosen, R.: 1991, Life Itself, Columbia University Press, New York. 42 Rosen, R.: 1999, Essays on Life Itself, Columbia University Press, New York. 43 Rosenbloom, Paul.: 1950, The Elements of Mathematical Logic, Dover, New York. 44 Rosenbloom, Paul.:1962, ibid., Prentice Hall, Englewood Cliffs, N.J. 45 Rosser, J.B. and Turquette, A.R.: 1952, Many-Valued Logics. North-Holland Publ. Co., Amsterdam.
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bibliography of many-valued logics and applications

0.1 A list of references for N-valued logics and their applications

References