This is a bibliography for N-valued logics and their applications.

Bibliography

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.

14

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

15

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

16

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

17

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

18

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

19

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

20

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

21

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

22

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

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

24

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

25

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

26

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

27

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

28

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

29

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

30

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

31

McNaughton, R.: 1951, A theorem about infinite-valued sentential logic, Journal Symbolic Logic 16, 1-13.

32

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

33

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

34

Rose, A.: 1956, Formalisation du calcul propositionnel implicatif à valeurs de Łukasiewicz, C. R. Acad. Sci. Paris 243,1183-1185.

35

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

36

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

37

Rose, A.: 1978, `Formalisations of Further –Valued Łukasiewicz Propositional Calculi'. J. Symbolic Logic, 43(2): 207-210

38

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

39

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

40

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

41

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

42

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

43

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

44

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