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%                                                                      %
%  logik.sty -- Datum 10. April 1994                                   %
%  Definiert Theoreme, bold math italic, logische Zeichen und          %
%  jede Menge Modaloperatoren                                          %
%                                                                      %
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%
% BoldMathItalic
%
\newfont{\bmi}{cmbxti10 scaled 1200}
%
%  Theorem Umgebungen
%
\newtheorem{thm}{Theorem}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{defn}[thm]{Definition}
\newtheorem{claim}[thm]{Claim}
\newtheorem{prop}[thm]{Proposition}
\newtheorem{cor}[thm]{Corollary}
\newtheorem{crit}[thm]{Criterion}
\newcommand{\proofend}{Q.~E.~D.}
\newcommand{\proofbeg}{{\bf Proof. }}
% \newcommand{\proofbeg}{\begin{proof}}
% \newcommand{\proofend}{\end{proof}}
\newcommand{\pseudoproofend}{$(\Diamond)$}
%
% Die Booleschen Symbole
%
\newcommand{\pf}{\rightarrow}
\newcommand{\dpf}{\leftrightarrow}
\newcommand{\und}{\wedge}
\newcommand{\oder}{\vee}
\newcommand{\nicht}{\neg}
\newcommand{\gund}{\bigwedge}
\newcommand{\goder}{\bigvee}
%
% Verbandsoperationen (VerbandsUnd,GrossesVerbandsUnd,
% VerbandsOder, GrossesVerbandsOder)
%
\newcommand{\vund}{\sqcap}
\newcommand{\voder}{\sqcup}
\newcommand{\gvund}{\raisebox{-.2em}{\begin{picture}(1,1)
                        \thicklines
                        \put(0.1,0){\line(0,1){0.9}}
                        \put(0.8,0){\line(0,1){0.9}}
                        \put(0.1,0.9){\line(1,0){0.7}}
                        \end{picture}}}
\newcommand{\gvoder}{\raisebox{-.2em}{\begin{picture}(1,1)
                        \thicklines
                        \put(0.1,0){\line(0,1){0.9}}
                        \put(0.8,0){\line(0,1){0.9}}
                        \put(0.1,0){\line(1,0){0.7}}
                        \end{picture}}}
%
% Zeichenhilfen: Klammern, Ueberstreichungen etc.
%
\newcommand{\auf}{\langle}
\newcommand{\zu}{\rangle}
\newcommand{\upp}[1]{{\uparrow\! #1}}
\newcommand{\low}[1]{{\downarrow\! #1}}
\newcommand{\Pf}{\Rightarrow}
\newcommand{\epi}{\twoheadrightarrow}
\newcommand{\mono}{\rightarrowtail}
\newcommand{\Dpf}{\Leftrightarrow}
\newcommand{\tlm}{\subseteq}
\newcommand{\dfgl}{\leftrightharpoons}
\newcommand{\wht}[1]{\widehat{#1}}
\newcommand{\oli}[1]{\overline{#1}}
\newcommand{\uli}[1]{\underline{#1}}
\newcommand{\wit}[1]{\widetilde{#1}}
\newcommand{\nmodels}{\nvDash}
%%
%%  Modalitaeten: Orientierungsmodalitaeten
%%
\newcommand{\oben}{\begin{picture}(.8,.8)
                \put(.4,.17){\makebox(0,0){$\Diamond$}}
                \put(.4,.29){\line(0,1){.3}}
                   \end{picture}}
\newcommand{\unten}{\begin{picture}(.8,.8)
                \put(.4,.17){\makebox(0,0){$\Diamond$}}
                \put(.4,.29){\line(0,-1){.3}}
                   \end{picture}}
\newcommand{\links}{\begin{picture}(.8,.8)
                \put(.4,.17){\makebox(0,0){$\Diamond$}}
                \put(.4,.29){\line(-1,0){.3}}
                   \end{picture}}
\newcommand{\rechts}{\begin{picture}(.8,.8)
                \put(.4,.17){\makebox(0,0){$\Diamond$}}
                \put(.4,.29){\line(1,0){.3}}
                   \end{picture}}
\newcommand{\qoben}{\begin{picture}(.8,.8)
                \put(.4,.17){\makebox(0,0){$\Box$}}
                \put(.4,.29){\line(0,1){.3}}
                   \end{picture}}
\newcommand{\qunten}{\begin{picture}(.8,.8)
                \put(.4,.17){\makebox(0,0){$\Box$}}
                \put(.4,.29){\line(0,-1){.3}}
                   \end{picture}}
\newcommand{\qlinks}{\begin{picture}(.8,.8)
                \put(.4,.17){\makebox(0,0){$\Box$}}
                \put(.4,.29){\line(-1,0){.3}}
                   \end{picture}}
\newcommand{\qrechts}{\begin{picture}(.8,.8)
                \put(.4,.17){\makebox(0,0){$\Box$}}
                \put(.4,.29){\line(1,0){.3}}
                   \end{picture}}
%
% Ensprechende Algebra-Operationen
%
\newcommand{\soben}{\begin{picture}(1,.8)
                \put(.5,.32){\makebox(0,0){$\blacklozenge$}}
                \put(.5,.33){\line(0,1){.45}}
                   \end{picture}}
\newcommand{\sunten}{\begin{picture}(1,.8)
                \put(.5,.32){\makebox(0,0){$\blacklozenge$}}
                \put(.5,.33){\line(0,-1){.45}}
                   \end{picture}}
\newcommand{\slinks}{\begin{picture}(1,.8)
                \put(.5,.32){\makebox(0,0){$\blacklozenge$}}
                \put(.5,.33){\line(-1,0){.4}}
                   \end{picture}}
\newcommand{\srechts}{\begin{picture}(1,.9)
                \put(.5,.32){\makebox(0,0){$\blacklozenge$}}
                \put(.5,.33){\line(1,0){.4}}
                   \end{picture}}
\newcommand{\sqoben}{\begin{picture}(.8,.8)
                \put(.5,.32){\makebox(0,0){$\blacksquare$}}
                \put(.5,.33){\line(0,1){.45}}
                   \end{picture}}
\newcommand{\squnten}{\begin{picture}(.8,.8)
                \put(.5,.32){\makebox(0,0){$\blacksquare$}}
                \put(.5,.33){\line(0,-1){.45}}
                   \end{picture}}
\newcommand{\sqlinks}{\begin{picture}(1.1,.8)
                \put(.55,.32){\makebox(0,0){$\blacksquare$}}
                \put(.55,.33){\line(-1,0){.5}}
                   \end{picture}}
\newcommand{\sqrechts}{\begin{picture}(1.2,.9)
                \put(.5,.32){\makebox(0,0){$\blacksquare$}}
                \put(.5,.33){\line(1,0){.5}}
                   \end{picture}}
%
% Die Weisse Relation      
%
\newcommand{\wD}{\lozenge}
\newcommand{\wq}{\square}
\newcommand{\whd}{\lhd}
\newcommand{\rwhd}{\rhd}
\newcommand{\nhd}{\ntriangleleft}
\newcommand{\nwhd}{\ntriangleleft}
\newcommand{\raute}{\lozenge}             
\newcommand{\qu}{\square}
\newcommand{\quadrat}{\square}
%
% Schwarze Relation
%
\newcommand{\sD}{\blacklozenge}
\newcommand{\sq}{\blacksquare}
\newcommand{\shd}{\blacktriangleleft}
\newcommand{\rshd}{\blacktriangleright}
%
% Simulierende Relation
%
\newcommand{\oD}{\onelozenge}
\newcommand{\oq}{\boxminus}
\newcommand{\ohd}{\leqslant}
\newcommand{\rohd}{\geqslant}
\newcommand{\nohd}{\nleqslant}
\newcommand{\onelozenge}{\begin{picture}(.8,1)
                                \put(.4,.3){\makebox(0,0){$\lozenge$}}
                                \put(.15,.3){\line(1,0){.4}}
                         \end{picture}}
%
%
%
\newcommand{\schq}{\begin{picture}(.8,.9)
                \put(.4,.17){\makebox(0,0){$\Box$}}
                \put(.1,.58){\line(1,-1){.5}}
                   \end{picture}}
\newcommand{\schD}{\begin{picture}(.8,.8)
                \put(.4,.17){\makebox(0,0){$\Diamond$}}
                \put(.2,.33){\line(1,-1){.5}}
                   \end{picture}}




