File:QuantifierScopes.pdf
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QuantifierScopes.pdf (677 × 383 pixels, file size: 20 KB, MIME type: application/pdf)
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Summary
[edit]| 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}
|
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 16:19, 5 June 2019 |  | 677 × 383 (20 KB) | Jochen Burghardt (talk | contribs) | rm image dim markers |
| 16:12, 5 June 2019 | No thumbnail | 0 × 0 (27 KB) | Jochen Burghardt (talk | contribs) | User created page with UploadWizard |
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