View source for PlanetPhysics/Bibliography for N Valued Logics and Their Applications

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

\begin{thebibliography} {99}

</ref><ref name='AS-BC2k'>
Awodey, S. \& Butz, C., 2000, Topological Completeness for Higher Order Logic., Journal of Symbolic Logic, 65, 3, 1168--1182.

</ref><ref name='AS-RER2k2'>
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.

</ref><ref name='AS96'>
Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective,
''Philosophia Mathematica'' , 3: 209--237.

</ref><ref name='BAJ-DJ97'>
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.

</ref><ref name='BAJ-DJ98a'>
Baez, J. \& Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes,
in: ''Advances in Mathematics'' , 135, 145--206.

</ref><ref name='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., ''Axiomathes,'' , 16: 82-165.

</ref><ref name='ICB77'>
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.

</ref><ref name='Ba-We2k'>
M.~Barr and C.~Wells. ''Toposes, Triples and Theories'' . Montreal: McGill University, 2000.

</ref><ref name='Ba-We85'>
Barr, M. \& Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag.

</ref><ref name='Birkhoff48'>
Birkhoff, G.: 1948, Lattice Theory, ''Amer. Math. Soc.'' , New York.

</ref><ref name='bfgr:luk'>
Boicescu, V., A. Filipoiu, G. Georgescu, and S. Rudeanu.: 1991, ''\L{'' ukasiewicz-Moisil Algebras},
North-Holland, Amsterdam.

</ref><ref name='cha:alg58'>
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.

</ref><ref name='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, ''Soft Computing''  '''4''' , 106-112.

</ref><ref name='cig:moi'>
Cignoli, R.: Moisil algebras, ''Notas de Logica Matematica'' , Inst. Mat., Univ. Nacional del Sur,
Bahia-Blanca, No. 27.

</ref><ref name='NB64'>
Bourbaki, N. : 1964. ''El\'ements de Math\'ematique, Livre II, Alg\`ebre'' , '''4''' , Hermann, Editor,
Paris.

</ref><ref name='CR638'>
Carnap, R.: 1938, ''The Logical Syntax of Language'' , Harcourt, Brace and Co., New York.

</ref><ref name='Ehresmann65'>
Ehresmann, C.: 1965, ''Cat\'egories et Structures'' , Dunod, Paris.

</ref><ref name='EM45'>
Eilenberg, S. and S. MacLane: 1945, The General Theory of Natural Equivalences, ''Trans. Amer. Math. Soc.''
'''58''' , 231--294.

</ref><ref name='GGDP68'>
Georgescu, G. and D. Popescu: 1968, On Algebraic Categories, ''Rev. Roum. Math. Pures et Appl.''
'''13''' , 337--342.

</ref><ref name='geo:cen70'>
Georgescu, G., and C. Vraciu.: 1970. On the characterization of centered \L{}ukasiewicz algebras.
''J. Algebra''  '''16''' , 486-495.

</ref><ref name='geo:tow2k'>
Georgescu, G., and I. Leu\c stean.: 2000. Towards a probability theory based on Moisil logic, \emph{Soft
Computing} '''4''' , 19-26.

</ref><ref name='grig77'>
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.

</ref><ref name='Hilbert-Ack27'>
Hilbert, D. and W. Ackerman: 1927, ''Grunduge der Theoretischen Logik'' , Springer, Berlin.

</ref><ref name='Kan'>
Kan, D.M.: 1958, Adjoint Functors, ''Trans Amer. Math. Soc.''  '''87''' , 294-329.

</ref><ref name='lambek-scott86'>
Lambek J. and P. J. Scott: 1986, ''Introduction to Higher Order Categorical Logic'' , Cambridge University
Press, Cambridge, UK, 1986.

</ref><ref name='Lawvere'>
Lawvere, F.W.: 1963, Functorial Semantics of Algebraic Theories, ''Proc. Natl. Acad. Sci. USA.''
'''50''' , 869--872.

</ref><ref name='Lof'>
L\"{o}fgren, L.: 1968, An Axiomatic Explanation of Complete Self-Reproduction,'' Bull. Math. Biophys.''
'''30''' , 317--348.

</ref><ref name='Luk70'>
\L{}ukasiewicz, J.: 1970, ''Selected Works'' , (ed.: L. Borkowski), North-Holland Publ. Co., Amsterdam and PWN,
Warsaw.

</ref><ref name='MM'>
MacLane, S. and I. Moerdijk: 1992, ''Sheaves in Geometry and Logic - A first Introduction to Topos Theory'' ,
Springer Verlag, New York.

</ref><ref name='MP43'>
McCulloch, W. and W. Pitts: 1943, `A Logical Calculus of Ideas Immanent in Nervous Activity', \emph{Bull. Math.
Biophys}. '''5''' , 115--133.

</ref><ref name='Mn51'>
McNaughton, R.: 1951, A theorem about infinite-valued sentential logic, ''Journal Symbolic Logic''
'''16''' , 1-13.

</ref><ref name='moi:ess'>
Moisil, Gr. C.: 1972, ''Essai sur les logiques non-chrysippiennes'' . Ed. Academiei, Bucharest.

</ref><ref name='mundici86'>
Mundici, D.: 1986, Interpretation of AF C*-algebras in \L{}ukasiewicz sentential calculus, \emph{J. Functional
Analysis} '''65''' , 15-63.

</ref><ref name='Rose56'>
Rose, A.: 1956, Formalisation du calcul propositionnel implicatif \`a <math>\aleph_0</math> valeurs de \L{}ukasiewicz,
''C. R. Acad. Sci. Paris''  '''243''' ,1183-1185.

</ref><ref name='RRs58'>
Rose, A. and Rosser, J.B.: 1958, Fragments of many-valued statement calculi, \emph{Transactions American
Mathematical Society} '''87''' , 1-53.

</ref><ref name='Rose62'>
Rose, A.: 1962, Extensions of Some Theorems of Anderson and Belnap, ''J. Symbolic Logic'' , '''27''' ,
(4), 423--425.

</ref><ref name='Rose78'>
Rose, A.: 1978, `Formalisations of Further <math>\aleph_0</math>--Valued \L{}ukasiewicz Propositional Calculi'. \emph{J. Symbolic
Logic}, '''43''' (2): 207-210

</ref><ref name='RR58A'>
Rosen, R.: 1958a, A Relational Theory of Biological Systems, ''Bull. Math. Biophys.''  '''20''' ,
245--260.

</ref><ref name='RR58B'>
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.

</ref><ref name='RR99'>
Rosen, R.: 1999, ''Essays on Life Itself'' , Columbia University Press, New York.

</ref><ref name='RP50'>
Rosenbloom, Paul.: 1950, ''The Elements of Mathematical Logic'' , Dover, New York.

</ref><ref name='RP62'>
Rosenbloom, Paul.:1962, ''ibid.'' , Prentice Hall, Englewood Cliffs, N.J.

</ref><ref name='RJTA52'>
Rosser, J.B. and Turquette, A.R.: 1952, ''Many-Valued Logics'' . North-Holland Publ. Co., Amsterdam.

</ref></references>

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