DescriptionHerbrand-model-hasse.png	English: Hasse diagram of the Herbrand interpretations of the Datalog program: e(x, y). e(y, z). p(A, B) :- e(A, B). p(A, C) :- p(A, B), e(B, C). Generated by: % https://tex.stackexchange.com/questions/299005/automatic-page-size-to-fit-arbitrary-content % latex hasse.tex % dvi2ps hasse.dvi % inkscape hasse.ps \documentclass{article} \usepackage{tikz-cd} \newcommand{\eyx}{\mathtt{e(y, x) \newcommand{\exy}{\mathtt{e(x, y)
Source	Own work
Author	This file is lacking author information.

\newcommand{\eyz}{\mathtt{e(y, z)}} \newcommand{\pxy}{\mathtt{p(x, y)}} \newcommand{\pyz}{\mathtt{p(y, z)}} \newcommand{\pxz}{\mathtt{p(x, z)}} \begin{document} \hoffset=-1in \voffset=-1in\newcommand{\exx}{\mathtt{e(x, x)}} \setbox0\hbox{\begin{tikzpicture}

   \matrix (A) [matrix of nodes, row sep=0.8cm, column sep=0cm]
   { 

& $\mathbf{P}(H)$ & \\ $\vdots$ & $\vdots$ & $\vdots$ \\ $M\cup\dots$ & $M\cup\{\exx\}$ & $M \cup\dots$ \\

       & {$M=\{ \exy,  \eyz,\pxy, \pyz, \pxz \}$} \\

$M - \dots$ & $M - \{\pyz\}$ & $M - \dots$ \\

       $\vdots$ & $\vdots$ & $\vdots$ \\
       & $\emptyset$ & \\
   };
   \draw (A-1-2)--(A-2-1);
   \draw (A-1-2)--(A-2-2);
   \draw (A-1-2)--(A-2-3);
   \draw (A-2-1)--(A-3-1);
   \draw (A-2-2)--(A-3-2);
   \draw (A-2-3)--(A-3-3);
   \draw (A-3-1)--(A-4-2);
   \draw (A-3-2)--(A-4-2);
   \draw (A-3-3)--(A-4-2);
   \draw (A-4-2)--(A-5-1);
   \draw (A-4-2)--(A-5-2);
   \draw (A-4-2)--(A-5-3);
   \draw (A-5-1)--(A-6-1);
   \draw (A-5-2)--(A-6-2);
   \draw (A-5-3)--(A-6-3);
   \draw (A-6-1)--(A-7-2);
   \draw (A-6-2)--(A-7-2);
   \draw (A-6-3)--(A-7-2);

\end{tikzpicture}} \pdfpageheight=\dimexpr\ht0+\dp0\relax \pdfpagewidth=\wd0 \shipout\box0 \stop}} |date=2023-03-07 |source=Own work |author=Siddharthist |permission= |other versions= }}

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