File:QuantifierScopes.pdf
Summary
| Description |
English: Syntax tree for the formula . Bound and free variable occurrences are colored in red and green, respectively. The binding scope of each quantifier is indicated by a light red rectangle. Observe that occurs both bound and free in the formula; same for . |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
| Other versions | File:QuantifierScopes_svg.svg |
LaTeX source |
|---|
\documentclass[12pt]{article}
\setlength{\unitlength}{10mm}
\usepackage[pdftex]{color}
\usepackage{amssymb}
\usepackage[paperwidth=11.5\unitlength,paperheight=6.5\unitlength]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{11.5\unitlength}
\setlength{\textheight}{6.5\unitlength}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\pagestyle{empty}
% colors
\definecolor{fQuant} {rgb}{0.50,0.00,0.00}
\definecolor{fBound} {rgb}{0.99,0.00,0.00}
\definecolor{fFree} {rgb}{0.00,0.99,0.00}
\definecolor{bX} {rgb}{0.99,0.90,0.90}
\definecolor{bY} {rgb}{0.99,0.80,0.80}
\newcommand{\tree}[1]{}
\begin{document}
\begin{picture}(11,6)
%\put(0,0){\makebox(0,0){$+$}}
%\put(11,6){\makebox(0,0){$+$}}
\put(0.300,3.200){\makebox(0.000,0.000)[tl]{\textcolor{bX}{\rule{6.5cm}{2.9cm}}}}%
\put(2.300,2.100){\makebox(0.000,0.000)[tl]{\textcolor{bY}{\rule{4.4cm}{1.7cm}}}}%
%!2}textree g fs 1 | texcalc oxy -0.5 0.5
%\tree{$\lor$}
% {\tree{$\forall$}
% {\tree{\textcolor{fQuant}{$x$}}}
% {\tree{$\exists$}
% {\tree{\textcolor{fQuant}{$y$}}}
% {\tree{$B$}
% {\tree{\textcolor{fBound}{$x$}}}
% {\tree{\textcolor{fBound}{$y$}}}
% }
% }
% }
% {\tree{$C$}
% {\tree{\textcolor{fFree}{$y$}}}
% {\tree{\textcolor{fFree}{$x$}}}
% }
\put(0.500,3.100){\makebox(0.000,0.000)[t]{\textcolor{fQuant}{$x$}}}%aa
\put(2.500,1.900){\makebox(0.000,0.000)[t]{\textcolor{fQuant}{$y$}}}%aba
\put(4.500,0.700){\makebox(0.000,0.000)[t]{\textcolor{fBound}{$x$}}}%abba
\put(6.500,0.700){\makebox(0.000,0.000)[t]{\textcolor{fBound}{$y$}}}%abbb
\put(5.500,1.900){\makebox(0.000,0.000)[t]{$B$}}%abb
\put(5.500,1.500){\line(-5,-3){1.000}}%abb-a
\put(5.500,1.500){\line(5,-3){1.000}}%abb-b
\put(4.000,3.100){\makebox(0.000,0.000)[t]{$\exists$}}%ab
\put(4.000,2.700){\line(-5,-2){1.500}}%ab-a
\put(4.000,2.700){\line(5,-2){1.500}}%ab-b
\put(2.250,4.300){\makebox(0.000,0.000)[t]{$\forall$}}%a
\put(2.250,3.900){\line(-3,-1){1.750}}%a-a
\put(2.250,3.900){\line(3,-1){1.750}}%a-b
\put(8.500,3.100){\makebox(0.000,0.000)[t]{\textcolor{fFree}{$y$}}}%ba
\put(10.500,3.100){\makebox(0.000,0.000)[t]{\textcolor{fFree}{$x$}}}%bb
\put(9.500,4.300){\makebox(0.000,0.000)[t]{$C$}}%b
\put(9.500,3.900){\line(-5,-3){1.000}}%b-a
\put(9.500,3.900){\line(5,-3){1.000}}%b-b
\put(5.875,5.500){\makebox(0.000,0.000)[t]{$\lor$}}%
\put(5.875,5.100){\line(-6,-1){3.625}}%-a
\put(5.875,5.100){\line(6,-1){3.625}}%-b
\end{picture}
\end{document}
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