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'bibliography of many-valued logics and applications'
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| Title of object: |
bibliography of many-valued logics and applications |
| Canonical Name: |
BibliographyOfManyValuedLogicsAndApplications |
| Type: |
Bibliography |
| Created on: |
2008-08-16 13:05:01 |
| Modified on: |
2008-08-16 13:25:53 |
| Classification: |
msc:03-00, msc:03G20, msc:03G10, msc:03G12, msc:03G30 |
| Keywords: |
bibliography of many-valued logics and their applications in Quantum theories, quantum logic, categorical ontology, foundations of mathematics and mathematical biology |
| Synonyms: |
bibliography of many-valued logics and applications=many-valued logic
bibliography of many-valued logics and applications=nonstandard logics
bibliography of many-valued logics and applications=N-valued logic |
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Content:
\textbf{A bibliography for N-Valued Logics and Their Applications}
\begin{thebibliography} {99}
\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{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:cen}70
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 [\protect\citeauthoryear{McCulloch -- Pitts}{1943}] {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 [\protect\citeauthoryear{McNaughton}{1951}] {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 $N_0$--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{RRs58}
Rosser, J.B. and Turquette, A.R.: 1952, \emph{Many-Valued Logics}. North-Holland Publ. Co., Amsterdam.
\end{thebibliography}
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