This is a bibliography for N-valued logics and their applications.
[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 in Categories, Higher Dimensional Algebra and
Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic
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 American Mathematical Society 93, 74-80.
[14] 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.
[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, Soft Computing 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 University Press, 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 Logic 16, 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. Functional Analysis 65, 15-63.
[35] Rose, A.: 1956, Formalisation du calcul propositionnel implicatif à ℵ0 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 American Mathematical 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 ℵ0–Valued Łukasiewicz Propositional
Calculi’. J. Symbolic Logic, 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.