bibliography for N-valued logics and their applications
This is a bibliography for N-valued logics and their applications.
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Awodey, S. & Butz, C., 2000, Topological Completeness for Higher Order Logic., Journal of Symbolic Logic, 65, 3, 1168-1182.
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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.
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Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective,
Philosophia Mathematica, 3: 209-237.
- 4
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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.
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Baez, J. & Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes,
in: Advances in Mathematics, 135, 145-206.
- 6
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Baianu, I. C., R. Brown , G. Georgescu and J. F. Glazebrook: 2006, Complex Nonlinear Biodynamics in
Categories, Higher Dimensional Algebra and Łukasiewicz-Moisil Topos: Transformations of Neuronal, Genetic and
Neoplastic Networks., Axiomathes,, 16: 82-165.
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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
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M. Barr and C. Wells. Toposes, Triples and Theories. Montreal: McGill University, 2000.
- 9
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Barr, M. & Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag.
- 10
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Birkhoff, G.: 1948, Lattice Theory, Amer. Math. Soc., New York.
- 11
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Boicescu, V., A. Filipoiu, G. Georgescu, and S. Rudeanu.: 1991, Łukasiewicz-Moisil Algebras,
North-Holland, Amsterdam.
- 12
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Chang, C. C.: 1958, Algebraic analysis of many valued logics. Trans. Amer. Math. Soc., 88,
467-490.
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Chang, C. C.: 1959, A new proof of the completeness of the Łukasiewicz axioms, Transactions American
Mathematical Society 93, 74-80.
- 14
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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.
- 14
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Cignoli, R.: Moisil algebras, Notas de Logica Matematica, Inst. Mat., Univ. Nacional del Sur,
Bahia-Blanca, No. 27.
- 15
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Bourbaki, N. : 1964. Eléments de Mathématique, Livre II, Algèbre, 4, Hermann, Editor,
Paris.
- 16
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Carnap, R.: 1938, The Logical Syntax of Language, Harcourt, Brace and Co., New York.
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Ehresmann, C.: 1965, Catégories et Structures, Dunod, Paris.
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Eilenberg, S. and S. MacLane: 1945, The General Theory of Natural Equivalences, Trans. Amer. Math. Soc.
58, 231-294.
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Georgescu, G. and D. Popescu: 1968, On Algebraic Categories, Rev. Roum. Math. Pures et Appl.
13, 337-342.
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Georgescu, G., and C. Vraciu.: 1970. On the characterization of centered Łukasiewicz algebras.
J. Algebra 16, 486-495.
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Georgescu, G., and I. Leuştean.: 2000. Towards a probability theory based on Moisil logic, Soft
Computing 4, 19-26.
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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.
- 23
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Hilbert, D. and W. Ackerman: 1927, Grunduge der Theoretischen Logik, Springer, Berlin.
- 24
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Kan, D.M.: 1958, Adjoint Functors, Trans Amer. Math. Soc. 87, 294-329.
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Lambek J. and P. J. Scott: 1986, Introduction to Higher Order Categorical Logic, Cambridge University
Press, Cambridge, UK, 1986.
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Lawvere, F.W.: 1963, Functorial Semantics of Algebraic Theories, Proc. Natl. Acad. Sci. USA.
50, 869-872.
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Löfgren, L.: 1968, An Axiomatic Explanation of Complete Self-Reproduction, Bull. Math. Biophys.
30, 317-348.
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Łukasiewicz, J.: 1970, Selected Works, (ed.: L. Borkowski), North-Holland Publ. Co., Amsterdam and PWN,
Warsaw.
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MacLane, S. and I. Moerdijk: 1992, Sheaves in Geometry and Logic - A first Introduction to Topos Theory,
Springer Verlag, New York.
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McCulloch, W. and W. Pitts: 1943, `A Logical Calculus of Ideas Immanent in Nervous Activity', Bull. Math.
Biophys. 5, 115-133.
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McNaughton, R.: 1951, A theorem about infinite-valued sentential logic, Journal Symbolic Logic
16, 1-13.
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Moisil, Gr. C.: 1972, Essai sur les logiques non-chrysippiennes. Ed. Academiei, Bucharest.
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Mundici, D.: 1986, Interpretation of AF C*-algebras in Łukasiewicz sentential calculus, J. Functional
Analysis 65, 15-63.
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Rose, A.: 1956, Formalisation du calcul propositionnel implicatif à
valeurs de Łukasiewicz,
C. R. Acad. Sci. Paris 243,1183-1185.
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Rose, A. and Rosser, J.B.: 1958, Fragments of many-valued statement calculi, Transactions American
Mathematical Society 87, 1-53.
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Rose, A.: 1962, Extensions of Some Theorems of Anderson and Belnap, J. Symbolic Logic, 27,
(4), 423-425.
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Rose, A.: 1978, `Formalisations of Further
-Valued Łukasiewicz Propositional Calculi'. J. Symbolic
Logic, 43(2): 207-210
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Rosen, R.: 1958a, A Relational Theory of Biological Systems, Bull. Math. Biophys. 20,
245-260.
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Rosen, R.: 1958b, ``The Representation of Biological Systems from the Standpoint of the Theory of Categories.'',
Bull. Math. Biophys. 20, 317-341.
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Rosen, R.: 1991, Life Itself, Columbia University Press, New York.
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Rosen, R.: 1999, Essays on Life Itself, Columbia University Press, New York.
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Rosenbloom, Paul.: 1950, The Elements of Mathematical Logic, Dover, New York.
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Rosenbloom, Paul.:1962, ibid., Prentice Hall, Englewood Cliffs, N.J.
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Rosser, J.B. and Turquette, A.R.: 1952, Many-Valued Logics. North-Holland Publ. Co., Amsterdam.
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