<?xml version="1.0" encoding="UTF-8"?>

<record version="1" id="705">
 <title>generalized toposes with many-valued logic subobject classifiers</title>
 <name>GeneralizedToposesWithManyValuedLogicSubobjectClassifiers</name>
 <created>2009-05-01 00:22:17</created>
 <modified>2009-05-01 00:22:17</modified>
 <type>Topic</type>
 <creator id="441" name="bci1"/>
 <modifier id="441" name="bci1"/>
 <author id="441" name="bci1"/>
 <classification>
	<category scheme="msc" code="00."/>
	<category scheme="msc" code="02."/>
	<category scheme="msc" code="03."/>
	<category scheme="msc" code="03.65.Fd"/>
 </classification>
 <defines>
	<concept>generalized toposes</concept>
	<concept>many-valued logic subobject classifiers</concept>
 </defines>
 <synonyms>
	<synonym concept="generalized toposes with many-valued logic subobject classifiers" alias="quantum logic candidates"/>
 </synonyms>
 <keywords>
	<term>generalized toposes</term>
 </keywords>
 <preamble></preamble>
 <content>\subsection{Introduction}

 \emph{Generalized topoi (toposes) with many-valued algebraic logic subobject classifiers}
are specified by the associated categories of algebraic logics previously defined as $LM_n$, that is, {\em non-commutative} lattices with $n$ logical values, where $n$ can also be chosen to be any cardinal, including infinity, etc.

\subsection{Axioms defining generalized topoi:}
\begin{itemize}
\item XY
\item YZ
\end{itemize}

\subsection{Applications of generalized topoi:}
\begin{itemize}
\item XY
\item YZ
\end{itemize}

\subsection{Generalized logic `spaces' defined by LMn.}

\begin{itemize}
\item XY
\item YZ
\end{itemize}

\begin{thebibliography}{9}

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\bibitem{GG2k6}
Georgescu, G. 2006, N-valued Logics and \L ukasiewicz-Moisil Algebras, \emph{Axiomathes}, \textbf{16} (1-2): 123-136.

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

\bibitem{ICB2004a}
Baianu, I.C.: 2004a. \L{}ukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models (2004). Eprint. Cogprints--Sussex Univ.

\bibitem{ICB04b}
Baianu, I.C.: 2004b \L{}ukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamics). CERN Preprint EXT-2004-059. \textit{Health Physics and Radiation Effects} (June 29, 2004).

\bibitem{Bgg2}
Baianu, I. C., Glazebrook, J. F. and G. Georgescu: 2004, Categories of Quantum Automata and N-Valued \L ukasiewicz Algebras in Relation to Dynamic Bionetworks, \textbf{(M,R)}--Systems and Their Higher Dimensional Algebra,
\PMlinkexternal{Abstract and Preprint of Report in PDF}{http://www.ag.uiuc.edu/fs401/QAuto.pdf} .

\bibitem{BBGG1}
Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006b, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and \L{}ukasiewicz--Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks., \emph{Axiomathes}, \textbf{16} Nos. 1--2: 65--122.

\end{thebibliography}</content>
</record>
