Talk:PlanetPhysics/Bibliography for N Valued Logics and Their Applications

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\begin{document}

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

\begin{thebibliography} {99}

\bibitem{AS-BC2k}
Awodey, S. \& Butz, C., 2000, Topological Completeness for Higher Order Logic., Journal of Symbolic Logic, 65, 3, 1168--1182.

\bibitem{AS-RER2k2}
Awodey, S. \& Reck, E. R., 2002, Completeness and Categoricity II. Twentieth-Century Metalogic to Twenty-first-Century Semantics, \emph{History and Philosophy of Logic}, 23, (2): 77--94.

\bibitem{AS96}
Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective,
\emph{Philosophia Mathematica}, 3: 209--237.

\bibitem{BAJ-DJ97}
Baez, J., 1997, An Introduction to n-Categories, in \emph{Category Theory and Computer Science, Lecture Notes in Computer Science}, 1290, Berlin: Springer-Verlag, 1--33.

\bibitem{BAJ-DJ98a}
Baez, J. \& Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes,
in: \emph{Advances in Mathematics}, 135, 145--206.

\bibitem{IBRGB05}
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., \emph{Axiomathes,}, 16: 82-165.

\bibitem{ICB77}
Baianu, I. C.: 1977, A Logical Model of Genetic Activities in \L{}ukasiewicz Algebras: The Non--linear Theory,
\emph{Bull. of Math. Biol}. \textbf{39}, 249--258.

\bibitem{Ba-We2k}
M.~Barr and C.~Wells. {\em Toposes, Triples and Theories}. Montreal: McGill University, 2000.

\bibitem{Ba-We85}
Barr, M. \& Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag.

\bibitem{Birkhoff48}
Birkhoff, G.: 1948, Lattice Theory, {\em Amer. Math. Soc.}, New York.

\bibitem{bfgr:luk}
Boicescu, V., A. Filipoiu, G. Georgescu, and S. Rudeanu.: 1991, \emph{\L{}ukasiewicz-Moisil Algebras},
North-Holland, Amsterdam.

\bibitem{cha:alg58}
Chang, C. C.: 1958, Algebraic analysis of many valued logics. \emph{Trans. Amer. Math. Soc}., \textbf{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} \textbf{93}, 74-80.

\bibitem{cig:moi}
Cignoli, R., Esteva, F., Godo, L. and Torrens, A. : 2000, Basic Fuzzy Logic is the logic of continuous t-norms
and their residua, \emph{Soft Computing} \textbf{4}, 106-112.

\bibitem{cig:moi}
Cignoli, R.: Moisil algebras, \emph{Notas de Logica Matematica}, Inst. Mat., Univ. Nacional del Sur,
Bahia-Blanca, No. 27.

\bibitem{NB64}
Bourbaki, N. : 1964. \emph{El\'ements de Math\'ematique, Livre II, Alg\`ebre}, \textbf{4}, Hermann, Editor,
Paris.

\bibitem{CR638}
Carnap, R.: 1938, \emph{The Logical Syntax of Language}, Harcourt, Brace and Co., New York.

\bibitem{Ehresmann65}
Ehresmann, C.: 1965, \emph{Cat\'egories et Structures}, Dunod, Paris.

\bibitem{EM45}
Eilenberg, S. and S. MacLane: 1945, The General Theory of Natural Equivalences, \emph{Trans. Amer. Math. Soc.}
\textbf{58}, 231--294.

\bibitem{GGDP68}
Georgescu, G. and D. Popescu: 1968, On Algebraic Categories, \emph{Rev. Roum. Math. Pures et Appl.}
\textbf{13}, 337--342.

\bibitem{geo:cen70}
Georgescu, G., and C. Vraciu.: 1970. On the characterization of centered \L{}ukasiewicz algebras.
\emph{J. Algebra} \textbf{16}, 486-495.

\bibitem{geo:tow2k}
Georgescu, G., and I. Leu\c stean.: 2000. Towards a probability theory based on Moisil logic, \emph{Soft
Computing} \textbf{4}, 19-26.

\bibitem{grig77}
Grigolia, R.S.: 1977. Algebraic analysis of \L ukasiewicz-Tarski's logical systems, in W\'{o}jcicki, R.,
Malinowski, G. (Eds), \emph{Selected Papers on \L ukasiewicz Sentential Calculi}, Osolineum, Wroclaw, pp. 81-92.

\bibitem{Hilbert-Ack27}
Hilbert, D. and W. Ackerman: 1927, \emph{Grunduge der Theoretischen Logik}, Springer, Berlin.

\bibitem{Kan}
Kan, D.M.: 1958, Adjoint Functors, \emph{Trans Amer. Math. Soc.} \textbf{87}, 294-329.

\bibitem{lambek-scott86}
Lambek J. and P. J. Scott: 1986, \emph{Introduction to Higher Order Categorical Logic}, Cambridge University
Press, Cambridge, UK, 1986.

\bibitem{Lawvere}
Lawvere, F.W.: 1963, Functorial Semantics of Algebraic Theories, \emph{Proc. Natl. Acad. Sci. USA.}
\textbf{50}, 869--872.

\bibitem{Lof}
L\"{o}fgren, L.: 1968, An Axiomatic Explanation of Complete Self-Reproduction,\emph{ Bull. Math. Biophys.}
\textbf{30}, 317--348.

\bibitem{Luk70}
\L{}ukasiewicz, J.: 1970, \emph{Selected Works}, (ed.: L. Borkowski), North-Holland Publ. Co., Amsterdam and PWN,
Warsaw.

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

\bibitem{MP43}
McCulloch, W. and W. Pitts: 1943, `A Logical Calculus of Ideas Immanent in Nervous Activity', \emph{Bull. Math.
Biophys}. \textbf{5}, 115--133.

\bibitem{Mn51}
McNaughton, R.: 1951, A theorem about infinite-valued sentential logic, \emph{Journal Symbolic Logic}
\textbf{16}, 1-13.

\bibitem{moi:ess}
Moisil, Gr. C.: 1972, \emph{Essai sur les logiques non-chrysippiennes}. Ed. Academiei, Bucharest.

\bibitem{mundici86}
Mundici, D.: 1986, Interpretation of AF C*-algebras in \L{}ukasiewicz sentential calculus, \emph{J. Functional
Analysis} \textbf{65}, 15-63.

\bibitem{Rose56}
Rose, A.: 1956, Formalisation du calcul propositionnel implicatif \`a $\aleph_0$ valeurs de \L{}ukasiewicz,
\emph{C. R. Acad. Sci. Paris} \textbf{243},1183-1185.

\bibitem{RRs58}
Rose, A. and Rosser, J.B.: 1958, Fragments of many-valued statement calculi, \emph{Transactions American
Mathematical Society} \textbf{87}, 1-53.

\bibitem{Rose62}
Rose, A.: 1962, Extensions of Some Theorems of Anderson and Belnap, \emph{J. Symbolic Logic}, \textbf{27},
(4), 423--425.

\bibitem{Rose78}
Rose, A.: 1978, `Formalisations of Further $\aleph_0$--Valued \L{}ukasiewicz Propositional Calculi'. \emph{J. Symbolic
Logic}, \textbf{43}(2): 207-210

\bibitem{RR58A}
Rosen, R.: 1958a, A Relational Theory of Biological Systems, \emph{Bull. Math. Biophys.} \textbf{20},
245--260.

\bibitem{RR58B}
Rosen, R.: 1958b, ``The Representation of Biological Systems from the Standpoint of the Theory of Categories.'',
\emph{Bull. Math. Biophys.} \textbf{20}, 317-341.

\bibitem {RR91}
Rosen, R.: 1991, \emph{Life Itself}, Columbia University Press, New York.

\bibitem{RR99}
Rosen, R.: 1999, \emph{Essays on Life Itself}, Columbia University Press, New York.

\bibitem{RP50}
Rosenbloom, Paul.: 1950, \emph{The Elements of Mathematical Logic}, Dover, New York.

\bibitem{RP62}
Rosenbloom, Paul.:1962, \emph{ibid.}, Prentice Hall, Englewood Cliffs, N.J.

\bibitem{RJTA52}
Rosser, J.B. and Turquette, A.R.: 1952, \emph{Many-Valued Logics}. North-Holland Publ. Co., Amsterdam.

\end{thebibliography} 

\end{document}