
diff -r 345dd18f020e -r 907b1fff5637 Prover/G4ip.tex
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Prover/G4ip.tex	Thu Mar 15 10:07:28 2012 +0000
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+\documentclass[11pt]{article}
+\usepackage{dina4}
+\usepackage{my}
+\usepackage{latexsym,amssymb}
+%\usepackage[final]{graphics}
+
+
+\newcommand{\FN}[1]{FN(#1)} % free name
+\newcommand{\FC}[1]{FC(#1)} % free co-name
+\renewcommand{\refname}{\-}
+
+\begin{document}
+\section*{Inference Rules of G4ip (LJT)}
+
+\begin{figure}[h]
+  \begin{center}
+  \begin{FramedTitled}{\-}
+  \centering
+  \def\arraystretch{3.0}
+  \begin{tabular}{cc}
+
+   \infer[Axiom]{\sequ{A,\Gamm}{A}}{} &
+
+   \infer[${\em false}-L$]{\sequ{\mbox{\em false},\Gamm}{G}}{}\\[-8mm]
+
+   ($A$ being atomic) \\
+
+   \infer[\&$-L$]{\sequ{B \& C,\Gamm}{G}}
+                 {\sequ{B,C,\Gamm}{G}} &
+
+   \infer[\&$-R$]{\sequ{\Gamm}{B \& C}}
+                 {  \sequ{\Gamm}{B}
+                  & \sequ{\Gamm}{C}}\\
+
+   \infer[\OR$-L$]
+              {\sequ{B\OR C,\Gamm}{G}}
+              { \sequ{B,\Gamm}{G}
+               &\sequ{C,\Gamm}{G}} &
+
+   \infer[\OR$-R$_1]
+              {\sequ{\Gamm}{B\OR C}}
+              {\sequ{\Gamm}{B}}\hspace{3mm}
+   \infer[\OR$-R$_2]
+              {\sequ{\Gamm}{B\OR C}}
+              {\sequ{\Gamm}{C}}\\
+
+   \infer[\mbox{\tt ->}$-L$_1]
+                    {\sequ{A\mbox{\tt ->} B,A,\Gamm}{G}}
+                    {\sequ{B,A,\Gamm}{G}} &
+
+   \infer[\mbox{\tt ->}$-R$]
+                 {\sequ{\Gamm}{B\mbox{\tt ->} C}}
+                 {  \sequ{B,\Gamm}{C}}\\[-8mm]
+      
+   ($A$ being atomic)\\           
+       
+   \multicolumn{2}{c}{
+   \infer[\mbox{\tt ->}$-L$_2]
+              {\sequ{(C \& D)\mbox{\tt ->} B,\Gamm}{G}}
+              {\sequ{C \mbox{\tt ->} (D \mbox{\tt ->} B)\Gamm}{G}}} \\
+
+   \multicolumn{2}{c}{
+   \infer[\mbox{\tt ->}$-L$_3]
+              {\sequ{(C\OR D)\mbox{\tt ->} B\Gamm}{G}}
+              {\sequ{C\mbox{\tt ->}B,D\mbox{\tt ->}B,\Gamm}{G}}}\\
+
+   \multicolumn{2}{c}{
+   \infer[\mbox{\tt ->}$-L$_4]
+              {\sequ{(C\mbox{\tt ->} D)\mbox{\tt ->} B\Gamm}{G}}
+              {\sequ{D\mbox{\tt ->}B,\Gamm}{C\mbox{\tt ->} D} &
+               \sequ{B,\Gamm}{G}} }\\
+
+   %\infer[\mbox{\tt <->}$-L$]
+   %                 {\sequ{B\mbox{\tt <->} C,\Gamm}{G}}
+   %                 {\sequ{B\mbox{\tt ->} C, C\mbox{\tt ->} B,\Gamm}{G} 
+   %                 } &
+
+   %\infer[\mbox{\tt <->}$-R$]
+   %              {\sequ{\Gamm}{B\mbox{\tt <->} C}}
+   %              {  \sequ{\Gamm}{B\mbox{\tt ->} C} &
+   %                 \sequ{\Gamm}{C\mbox{\tt ->} B} }\\
+
+   \multicolumn{2}{c}
+     { $B\mbox{\tt <->}C$ is defined as $B\mbox{\tt ->}C \& C\mbox{\tt ->}B$
+     }           
+  \end{tabular}
+  \end{FramedTitled}
+  \caption{Inference rules for G4ip; see for example \cite{Dyckhoff92}.}
+  \label{fig:CL}
+  \end{center}
+\end{figure}
+
+\bibliography{/home/cu200/tex/bib/all}
+\bibliographystyle{fullnames}
+
+
+\end{document}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "G4ip.tex"
+%%% End:
+
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