1 \documentclass[11pt]{article}

     2 \usepackage{dina4}

     3 \usepackage{my}

     4 \usepackage{latexsym,amssymb}

     5 %\usepackage[final]{graphics}

     6 

     7 

     8 \newcommand{\FN}[1]{FN(#1)} % free name

     9 \newcommand{\FC}[1]{FC(#1)} % free co-name

    10 \renewcommand{\refname}{\-}

    11 

    12 \begin{document}

    13 \section*{Inference Rules of G4ip (LJT)}

    14 

    15 \begin{figure}[h]

    16   \begin{center}

    17   \begin{FramedTitled}{\-}

    18   \centering

    19   \def\arraystretch{3.0}

    20   \begin{tabular}{cc}

    21 

    22    \infer[Axiom]{\sequ{A,\Gamm}{A}}{} &

    23 

    24    \infer[${\em false}-L$]{\sequ{\mbox{\em false},\Gamm}{G}}{}\\[-8mm]

    25 

    26    ($A$ being atomic) \\

    27 

    28    \infer[\&$-L$]{\sequ{B \& C,\Gamm}{G}}

    29                  {\sequ{B,C,\Gamm}{G}} &

    30 

    31    \infer[\&$-R$]{\sequ{\Gamm}{B \& C}}

    32                  {  \sequ{\Gamm}{B}

    33                   & \sequ{\Gamm}{C}}\\

    34 

    35    \infer[\OR$-L$]

    36               {\sequ{B\OR C,\Gamm}{G}}

    37               { \sequ{B,\Gamm}{G}

    38                &\sequ{C,\Gamm}{G}} &

    39 

    40    \infer[\OR$-R$_1]

    41               {\sequ{\Gamm}{B\OR C}}

    42               {\sequ{\Gamm}{B}}\hspace{3mm}

    43    \infer[\OR$-R$_2]

    44               {\sequ{\Gamm}{B\OR C}}

    45               {\sequ{\Gamm}{C}}\\

    46 

    47    \infer[\mbox{\tt ->}$-L$_1]

    48                     {\sequ{A\mbox{\tt ->} B,A,\Gamm}{G}}

    49                     {\sequ{B,A,\Gamm}{G}} &

    50 

    51    \infer[\mbox{\tt ->}$-R$]

    52                  {\sequ{\Gamm}{B\mbox{\tt ->} C}}

    53                  {  \sequ{B,\Gamm}{C}}\\[-8mm]

    54       

    55    ($A$ being atomic)\\           

    56        

    57    \multicolumn{2}{c}{

    58    \infer[\mbox{\tt ->}$-L$_2]

    59               {\sequ{(C \& D)\mbox{\tt ->} B,\Gamm}{G}}

    60               {\sequ{C \mbox{\tt ->} (D \mbox{\tt ->} B)\Gamm}{G}}} \\

    61 

    62    \multicolumn{2}{c}{

    63    \infer[\mbox{\tt ->}$-L$_3]

    64               {\sequ{(C\OR D)\mbox{\tt ->} B\Gamm}{G}}

    65               {\sequ{C\mbox{\tt ->}B,D\mbox{\tt ->}B,\Gamm}{G}}}\\

    66 

    67    \multicolumn{2}{c}{

    68    \infer[\mbox{\tt ->}$-L$_4]

    69               {\sequ{(C\mbox{\tt ->} D)\mbox{\tt ->} B\Gamm}{G}}

    70               {\sequ{D\mbox{\tt ->}B,\Gamm}{C\mbox{\tt ->} D} &

    71                \sequ{B,\Gamm}{G}} }\\

    72 

    73    %\infer[\mbox{\tt <->}$-L$]

    74    %                 {\sequ{B\mbox{\tt <->} C,\Gamm}{G}}

    75    %                 {\sequ{B\mbox{\tt ->} C, C\mbox{\tt ->} B,\Gamm}{G} 

    76    %                 } &

    77 

    78    %\infer[\mbox{\tt <->}$-R$]

    79    %              {\sequ{\Gamm}{B\mbox{\tt <->} C}}

    80    %              {  \sequ{\Gamm}{B\mbox{\tt ->} C} &

    81    %                 \sequ{\Gamm}{C\mbox{\tt ->} B} }\\

    82 

    83    \multicolumn{2}{c}

    84      { $B\mbox{\tt <->}C$ is defined as $B\mbox{\tt ->}C \& C\mbox{\tt ->}B$

    85      }           

    86   \end{tabular}

    87   \end{FramedTitled}

    88   \caption{Inference rules for G4ip; see for example \cite{Dyckhoff92}.}

    89   \label{fig:CL}

    90   \end{center}

    91 \end{figure}

    92 

    93 \bibliography{/home/cu200/tex/bib/all}

    94 \bibliographystyle{fullnames}

    95 

    96 

    97 \end{document}

    98 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    99 %%% Local Variables:

   100 %%% mode: latex

   101 %%% TeX-master: "G4ip.tex"

   102 %%% End:

   103 

   104 

   105 

   106 

   107 

   108 

   109 

   110 

   111 

   112 

   113 

   114 

   115 

   116