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PlanetPhysics/Bibliography for N Valued Logics and Their Applications

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

\begin{thebibliography} {99}

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  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 \L ukasiewicz--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 \L{}ukasiewicz 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, \L{ ukasiewicz-Moisil Algebras}, North-Holland, Amsterdam.
  12. ↑ Chang, C. C.: 1958, Algebraic analysis of many valued logics. Trans. Amer. Math. Soc ., 88 , 467--490. \bibitem {cha:alg59} Chang, C. C.: 1959, A new proof of the completeness of the \L{}ukasiewicz axioms, \emph{Transactions American Mathematical Society} 93 , 74-80.
  13. ↑ 13.0 13.1 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. Cite error: Invalid <ref> tag; name "cig:moi" defined multiple times with different content
  14. ↑ Bourbaki, N. : 1964. El\'ements de Math\'ematique, Livre II, Alg\`ebre , 4 , Hermann, Editor, Paris.
  15. ↑ Carnap, R.: 1938, The Logical Syntax of Language , Harcourt, Brace and Co., New York.
  16. ↑ Ehresmann, C.: 1965, Cat\'egories et Structures , Dunod, Paris.
  17. ↑ Eilenberg, S. and S. MacLane: 1945, The General Theory of Natural Equivalences, Trans. Amer. Math. Soc. 58 , 231--294.
  18. ↑ Georgescu, G. and D. Popescu: 1968, On Algebraic Categories, Rev. Roum. Math. Pures et Appl. 13 , 337--342.
  19. ↑ Georgescu, G., and C. Vraciu.: 1970. On the characterization of centered \L{}ukasiewicz algebras. J. Algebra 16 , 486-495.
  20. ↑ Georgescu, G., and I. Leu\c stean.: 2000. Towards a probability theory based on Moisil logic, \emph{Soft Computing} 4 , 19-26.
  21. ↑ Grigolia, R.S.: 1977. Algebraic analysis of \L ukasiewicz-Tarski's logical systems, in W\'{o}jcicki, R., Malinowski, G. (Eds), Selected Papers on \L ukasiewicz Sentential Calculi , Osolineum, Wroclaw, pp. 81-92.
  22. ↑ Hilbert, D. and W. Ackerman: 1927, Grunduge der Theoretischen Logik , Springer, Berlin.
  23. ↑ Kan, D.M.: 1958, Adjoint Functors, Trans Amer. Math. Soc. 87 , 294-329.
  24. ↑ Lambek J. and P. J. Scott: 1986, Introduction to Higher Order Categorical Logic , Cambridge University Press, Cambridge, UK, 1986.
  25. ↑ Lawvere, F.W.: 1963, Functorial Semantics of Algebraic Theories, Proc. Natl. Acad. Sci. USA. 50 , 869--872.
  26. ↑ L\"{o}fgren, L.: 1968, An Axiomatic Explanation of Complete Self-Reproduction, Bull. Math. Biophys. 30 , 317--348.
  27. ↑ \L{}ukasiewicz, J.: 1970, Selected Works , (ed.: L. Borkowski), North-Holland Publ. Co., Amsterdam and PWN, Warsaw.
  28. ↑ MacLane, S. and I. Moerdijk: 1992, Sheaves in Geometry and Logic - A first Introduction to Topos Theory , Springer Verlag, New York.
  29. ↑ McCulloch, W. and W. Pitts: 1943, `A Logical Calculus of Ideas Immanent in Nervous Activity', \emph{Bull. Math. Biophys}. 5 , 115--133.
  30. ↑ McNaughton, R.: 1951, A theorem about infinite-valued sentential logic, Journal Symbolic Logic 16 , 1-13.
  31. ↑ Moisil, Gr. C.: 1972, Essai sur les logiques non-chrysippiennes . Ed. Academiei, Bucharest.
  32. ↑ Mundici, D.: 1986, Interpretation of AF C*-algebras in \L{}ukasiewicz sentential calculus, \emph{J. Functional Analysis} 65 , 15-63.
  33. ↑ Rose, A.: 1956, Formalisation du calcul propositionnel implicatif \`a valeurs de \L{}ukasiewicz, C. R. Acad. Sci. Paris 243 ,1183-1185.
  34. ↑ Rose, A. and Rosser, J.B.: 1958, Fragments of many-valued statement calculi, \emph{Transactions American Mathematical Society} 87 , 1-53.
  35. ↑ Rose, A.: 1962, Extensions of Some Theorems of Anderson and Belnap, J. Symbolic Logic , 27 , (4), 423--425.
  36. ↑ Rose, A.: 1978, `Formalisations of Further --Valued \L{}ukasiewicz Propositional Calculi'. \emph{J. Symbolic Logic}, 43 (2): 207-210
  37. ↑ Rosen, R.: 1958a, A Relational Theory of Biological Systems, Bull. Math. Biophys. 20 , 245--260.
  38. ↑ Rosen, R.: 1958b, "The Representation of Biological Systems from the Standpoint of the Theory of Categories.", Bull. Math. Biophys. 20 , 317-341. \bibitem {RR91} Rosen, R.: 1991, Life Itself , Columbia University Press, New York.
  39. ↑ Rosen, R.: 1999, Essays on Life Itself , Columbia University Press, New York.
  40. ↑ Rosenbloom, Paul.: 1950, The Elements of Mathematical Logic , Dover, New York.
  41. ↑ Rosenbloom, Paul.:1962, ibid. , Prentice Hall, Englewood Cliffs, N.J.
  42. ↑ Rosser, J.B. and Turquette, A.R.: 1952, Many-Valued Logics . North-Holland Publ. Co., Amsterdam.
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