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author | Karl Berry <karl@freefriends.org> | 2008-10-03 23:11:35 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2008-10-03 23:11:35 +0000 |
commit | 15da3ecbe72e81cfbf2201f260a8f69dd84bde83 (patch) | |
tree | c712d16e5f998d9d95286b66750bc442a34380a9 /Master/texmf-dist/doc/latex/logic | |
parent | 425881b562f2bbf12c3d8fd24db155db11aabad1 (diff) |
update logic, without gene-logic files (cfrees 3 Oct 2008 00:10:49)
git-svn-id: svn://tug.org/texlive/trunk@10848 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/logic')
-rw-r--r-- | Master/texmf-dist/doc/latex/logic/gn-logic14.dvi | bin | 19712 -> 0 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/latex/logic/gn-logic14.tex | 394 |
2 files changed, 0 insertions, 394 deletions
diff --git a/Master/texmf-dist/doc/latex/logic/gn-logic14.dvi b/Master/texmf-dist/doc/latex/logic/gn-logic14.dvi Binary files differdeleted file mode 100644 index aced3dee685..00000000000 --- a/Master/texmf-dist/doc/latex/logic/gn-logic14.dvi +++ /dev/null diff --git a/Master/texmf-dist/doc/latex/logic/gn-logic14.tex b/Master/texmf-dist/doc/latex/logic/gn-logic14.tex deleted file mode 100644 index 1ad9ff0e158..00000000000 --- a/Master/texmf-dist/doc/latex/logic/gn-logic14.tex +++ /dev/null @@ -1,394 +0,0 @@ -%*****************************************************************************/ -%* */ -%* Version: 1.00 Date: 21/04/92 File: gn-logic14.tex */ -%* Last Version: File: */ -%* Changes: */ -%* 30/12/90 First version of documentation. */ -%* 21/04/92 new properties */ -%* */ -%* Title: */ -%* Author: Gerd Neugebauer */ -%* */ -%* Usage: latex gn-logic14.tex */ -%* */ -%*****************************************************************************/ - -\documentstyle[11pt,dina4,gn-logic14]{article} - -\setlength{\unitlength}{1pt} - - -\begin{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\newlength{\Width} \Width=\textwidth \advance\Width by -1.5em \divide\Width by 2 - -\section{The {\tt gn-logic} style option} -Description of Version 1.4 (5/95) by Gerd Neugebauer \bigskip - -The {\tt gn-logic} style option provides a facility to typeset logical -formulas of a certain kind. This style option provides an environment like -\verb|eqnarray|, an extended {\tt newtheorem} environment and several macros. - - - -\subsection{Mathematical Symbols} - -The following marcos provide better usage of the junctors and quantifiers. -Especially the spacing is improved. - - -\noindent\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}*{4}{l}} -\multicolumn{1}{c}{\small Symbol} - & \multicolumn{1}{c}{\small Macro} - & \multicolumn{2}{c}{\small Example} \\ - & & & \\ -$\AND$ & \verb|\AND| & \verb$A\AND B$ & $A\AND B$ \\ -$\OR$ & \verb|\OR| & \verb$A\OR B$ & $A\OR B$ \\ -$\XOR$ & \verb|\XOR| & \verb$A\XOR B$ & $A\XOR B$ \\ -$\IMPLIES$ & \verb|\IMPLIES| & \verb$A\IMPLIES B$ & $A\IMPLIES B$ \\ -$\IMPL$ & \verb|\IMPL| & \verb$A\IMPL B$ & $A\IMPL B$ \\ -$\IF$ & \verb|\IF| & \verb$A\IF B$ & $A\IF B$ \\ -$\IFF$ & \verb|\IFF| & \verb$A\IFF B$ & $A\IFF B$ \\ -$\IFFdef$ & \verb|\IFFdef| & \verb$A\IFFdef B$ & $A\IFFdef B$ \\ -$\ANDdots$ & \verb|\ANDdots| & \verb$A_1\ANDdots A_n$ & $A_1\ANDdots A_n$ \\ -$\ORdots$ & \verb|\ORdots| & \verb$A_1\ORdots A_n$ & $A_1\ORdots A_n$ \\ -$\is$ & \verb|\is| & \verb$x\is y$ & $x\is y$ \\ -$\Nat$ & \verb|\Nat| & \verb$n\in\Nat$ & $n\in\Nat$ \\ -$\Forall$ & \verb|\Forall| & \verb$\Forall x P(x)$ & $\Forall x P(x)$ \\ -$\Exists$ & \verb|\Exists| & \verb$\Exists y P(x)$ & $\Exists y P(x)$ \\ -\end{tabular*} - - -\newcommand{\bs}{{\tt\char"5C}} -\newcommand{\mac}[1]{The {\tt\char92 #1} Macro} -\newcommand{\macs}[2]{The {\tt\char92 #1} and the {\tt\char92 #2} Macros} -\newenvironment{compare}% -{\noindent\begin{center}% - \begin{tabular}{@{}l@{\hspace*{1.5em}produces\hspace*{1.5em}}l@{}}}% -{\end{tabular}\end{center}} - -\subsubsection*{\mac{AND}} -This macro can be used for the logical conjunction. In addition to the -\verb|\wedge| macro it adds more space and the formulas tend to be better -readable. Compare - -\begin{compare} -\verb$x=1\AND y=x$ & $x=1\AND y=x$ \\ -\verb$x=1\wedge y=x$ & $x=1\wedge y=x$ \\ -\verb$x=1\land y=x$ & $x=1\land y=x$ -\end{compare} - -\subsubsection*{\mac{OR}} -This macro can be used for the logical disjunction. In addition to the -\verb|\vee| macro it adds more space. Compare - -\begin{compare} -\verb$x=1\OR y=x$ & $x=1\OR y=x$ \\ -\verb$x=1\vee y=x$ & $x=1\vee y=x$ \\ -\verb$x=1\lor y=x$ & $x=1\lor y=x$ -\end{compare} - - -\subsubsection*{\mac{XOR}} -This macro can be used for the exclusive disjunction. It has no common -counterpart. The spacing is like in in all junctor macros. - -\begin{compare} -\verb$x=1\XOR y=x$ & $x=1\XOR y=x$ -\end{compare} - - -\subsubsection*{\macs{IMPL}{IMPLIES}} -These macros can be used for the logical implication. In addition to the -\verb|\rightarrow| macro it adds more space. Compare - -\begin{compare} -\verb$x=1\IMPL y=x$ & $x=1\IMPL y=x$ \\ -\verb$x=1\IMPLIES y=x$ & $x=1\IMPLIES y=x$ \\ -\verb$x=1\rightarrow y=x$ & $x=1\rightarrow y=x$ -\end{compare} - - -\subsubsection*{\mac{IF}} - This macro can be used for the logical implication written in reverse order. -In addition to the \verb|\leftarrow| macro it adds more space. Compare - -\begin{compare} -\verb$x=1\IF y=x$ & $x=1\IF y=x$ \\ -\verb$x=1\lefttarrow y=x$ & $x=1\leftarrow y=x$ -\end{compare} - -\subsubsection*{\mac{IFF}} - This macro can be used for the logical equivalence. -In addition to the \verb|\leftrightarrow| macro it adds more space. Compare - -\begin{compare} -\verb$x=1\IFF y=x$ & $x=1\IFF y=x$ \\ -\verb$x=1\leftrighttarrow y=x$ & $x=1\leftrightarrow y=x$ -\end{compare} - -\subsubsection*{\mac{IFFdef}} - Like above but with a small ``def'' above the arrow. - -\begin{compare} -\verb$x=1\IFFdef y=x$ & $x=1\IFFdef y=x$ -\end{compare} - -\subsubsection*{\mac{is}} - This macro is for typesetting unifiers. In this case the predefined -\verb|\setminus| produces to much space. - -\begin{compare} -\verb$\{y\setminus x, z\setminus 4\}$ & $\{y\setminus x, z\setminus 4\}$ \\ -\verb$\{y\is x, z\is 4\}$ & $\{y\is x, z\is 4\}$ \\ -\verb$\{y\backslash x, z\backslash 4P}$ & $\{y\backslash x, z\backslash 4\}$ -\end{compare} - -\ifx\AmSTeX\undefined -\def\AmSTeX{$\cal A$\kern-.1667em\lower.5ex\hbox - {$\cal M$}\kern-.125em$\cal S$-\kern-.1em\TeX} -\fi - -\subsubsection*{The Number Macros} -This are macros for those who have no access to the \AmSTeX{} fonts. It makes -the symbols for the natural numbers, integers, rationals, reals and complex -numbers. The usual magnification commands apply to it aswell. - - -\def\BB#1{\csname bb#1\endcsname} -\def\Line#1{\LINE{#1}\(\BB{#1}_{\BB{#1}}\)} -\def\LINE#1{{\tt \char92bb#1}&% - {\tiny\BB{#1}}&% - {\scriptsize\BB{#1}}&% - {\footnotesize\BB{#1}}&% - {\small\BB{#1}}&% - {\normalsize\BB{#1}}&% - {\large\BB{#1}}&% - {\Large\BB{#1}}&% - {\LARGE\BB{#1}}&% - {\huge\BB{#1}}&% - {\Huge\BB{#1}}&% - } -\begin{center} - \begin{tabular}{c|cccccccccc|c} - &\multicolumn{10}{|c|}{{\tt \char92tiny \hfill...\hfill\char92normalsize \hfill...\hfill\char92Huge}}&\verb|X_X| - \\\hline - \Line B\\ - \verb|\Complex|\Line C\\ - \Line D\\ - \Line E\\ - \Line F\\ - \Line G\\ - \Line H\\ - \Line I\\ - \Line J\\ - \Line K\\ - \Line L\\ - \Line M\\ - \verb|\Nat| \Line N\\ - \Line O\\ - \Line P\\ - \verb|\Rat| \Line Q\\ - \verb|\Real| \Line R\\ - \verb|\Int| \Line Z\\ - \Line{One} - \end{tabular} -\end{center} - -Unfortunately the macros \verb|\bbC|, \verb|\bbG|, \verb|\bbO|, and -\verb|\bbQ| do not scale properly when used in subscripts or superscripts of -formulae. The following examples shows how the sizing can be achieved manually - -\noindent\begin{compare} -\verb$\bbQ_{\mbox{\scriptsize \bbQ}}$ & $\bbQ_{\mbox{\scriptsize \bbQ}}$ -\end{compare} - - - -\subsubsection*{\macs{Forall}{Exists}} - The general problem with quantifies is that after the quantified variable the -following formula is not automatically seperated with a small space. This can -be overcome by the following macros. - -The \verb|\Forall| and the \verb|\Exists| macros take one argument. They -typeset the respective quantifier followed by the argument (i.e.\ the variable) -and finally a small space. As usual the argument has to be enclosed in braces -if it consists of more than one character. Otherwise the braces can be omitted. -This allows a elegant notation of short quantified formulas. - -\noindent\begin{compare} -\verb$\Forall x P(x)$ & $\Forall x P(x)$\\ -\verb$\Forall{x_1,\ldots,x_n}P(x_1,\ldots,x_n)$% -&$\Forall{x_1,\ldots,x_n}P(x_1,\ldots,x_n)$\\ -\verb$\Exists x P(x)$ & $\Exists x P(x)$\\ -\verb$\Exists{x_1,\ldots,x_n}P(x_1,\ldots,x_n)$% -& $\Exists{x_1,\ldots,x_n}P(x_1,\ldots,x_n)$ -\end{compare} - - - -\subsection{The {\tt Formula} Environment} - -This environment allows to typeset logical formulas. The main problem with the -\verb|eqnarray| environment was the numbering. In multiline formulas my -intention was to have the number in the middle of the formula. Inside this -environment several macros are valid. - -\begin{description} - \item[{\tt\bs begin\{Formula\}[{\em label}] \bs end\{Formula\}}] \ \\ - Start the list of formulas. Optionally a label can be given. This label - is used to reference the first formula. - \item[{\tt\bs =}] \ \\ - Start a new line. - \item[{\tt\bs >}{\em level}] \ \\ - Start a new line and indent to the given {\em level}. This indentation - is done in quantities of \verb|\FormulaIndent| which can be set with - the \verb|\setlength| command. The default value is {\tt 3em}. - \item[{\tt\bs Form[{\em label}]}] \ \\ - Start a new formula. Optionally a {\em label} can be given. This {\em - label} can be used to reference to the formula (see \verb|\ref|). -\end{description} - -Now lets have a look at some examples. First, we see a single two-line formula. -Note that the number at the right side is centered between the two lines. -\medskip - -\noindent -\begin{minipage}{\Width} -\small\begin{verbatim} -\begin{Formula} - P(X) \IMPL -\= Q(X) \IFF R_1(X) \OR R_2(X) -\end{Formula} -\end{verbatim} -\end{minipage} -\hfill -\begin{minipage}{\Width} -\begin{Formula} - P(X) \IMPL -\= Q(X) \IFF R_1(X) \OR R_2(X) -\end{Formula} -\end{minipage}\medskip - -Next we will see an example of several formulas. The first formula is split to -three lines and the third line is indented to level 1. Remark: \verb|\=| is in -reality an abbrevation for \verb|\>0|. -\medskip - -\noindent -\begin{minipage}{\Width} -\small\begin{verbatim} -\begin{Formula}[form:1] - P(X) \IMPL -\= Q(X) \IFF R_1(X) -\>1 \OR R_2(X) -\Form[form:2] - S(X) \IMPL -\= \neg Q(X) \IFF R_1(X) \OR R_2(X) -\end{Formula} -\end{verbatim} -\end{minipage} -\hfill -\begin{minipage}{\Width} -\begin{Formula}[form:1] - P(X) \IMPL -\= Q(X) \IFF R_1(X) -\>1 \OR R_2(X) -\Form[form:2] - S(X) \IMPL -\= \neg Q(X) \IFF R_1(X) \OR R_2(X) -\end{Formula} -\end{minipage}\medskip - - -\subsection{The {\tt NewTheorem} Environment} - -My experience with the {\tt newtheorem} environment was that I had a certain -scheme to use it. First, every theorem got a label. Thus, every {\em theorem} -was followed by a {\tt label} command. Optionally a {\em theorem} may have a -name. This name is typeset right after the number. The body of the {\em - theorem} allways started in the next line. This let to the definition of an -extended {\tt NewTheorem} environment. The arguments are the same as those of -the {\tt newtheorem} environment. But the environment defined by this extended -command take two optional arguments. The first optional argument is a label to -be assigned to the {\em theorem}. This argument has to be enclosed in -parentheses. The second type of optional argument has to be enclosed in -brakets. It is typeset in \verb|\small| after the title text. The third -optional argument is enclosed in \verb|<>|. It is typeset in \verb|\small\bf| -and surrounded by parentheses. -\medskip - -\noindent\begin{minipage}{\Width} -\small\begin{verbatim} - -\NewTheorem{guess}{Conjecture} - -\begin{guess}[Fermat](thm:fermat) - There do not exist integers $n>2$, - $x$, $y$, and $z$ such that - $x^n+y^n=z^n$. -\end{guess} -\end{verbatim} -\end{minipage} -\hfill -\begin{minipage}{\Width} -\NewTheorem{guess}{Conjecture} - -\begin{guess}[Fermat](thm:fermat) - There do not exist integers $n>2$, - $x$, $y$, and $z$ such that - $x^n+y^n=z^n$. -\end{guess} -\end{minipage} -\medskip - -The commands used to typeset some of the optional argument can be customized -in the following way. The macros \verb|\TheoremTitle| and \verb|\TheoremName| -are used to typeset their argument in \verb|\small| and \verb|\small\bf| and -enclosed in parentheses respectively. This macros can be redefined using -\verb|\renewcommand| as shown in the following example: -\medskip - -\noindent\begin{minipage}{\Width} -\footnotesize\begin{verbatim} -\NewTheorem{theorem}{Theorem} -\renewcommand{\TheoremTitle}[1]{{\sf [#1]}} -\renewcommand{\TheoremName}[1]{{\small(#1)}} -\begin{theorem}[Fermat]<conjecture>(thm:f2) - There do not exist integers ... -\end{theorem} -\end{verbatim} -\end{minipage} -\hfill -\begin{minipage}{\Width} -\NewTheorem{theorem}{Theorem} -\renewcommand{\TheoremTitle}[1]{{\sf #1}} -\renewcommand{\TheoremName}[1]{{\small(#1)}} -\begin{theorem}[Fermat]<conjecture>(thm:f2) - There do not exist integers $n>2$, - $x$, $y$, and $z$ such that - $x^n+y^n=z^n$. -\end{theorem} -\end{minipage} - -\end{document} - - - -\newcommand{\ENTRY}[1]{{#1 \Nat}& {#1 \Int}& {#1 \Rat}&{#1 \Real}& {#1 \Complex}} - -\begin{center} -\begin{tabular}{l|ccccc} -&\verb|\Nat|&\verb|\Int|&\verb|\Rat|&\verb|\Real|&\verb|\Complex|\\ -&&\\\hline&&\\ -\verb$\tiny$ & \ENTRY{\tiny} \\ -\verb$\scriptsize$ & \ENTRY{\scriptsize} \\ -\verb$\footnotesize$ & \ENTRY{\footnotesize} \\ -\verb$\small$ & \ENTRY{\small} \\ -\verb$\normalsize$ & \ENTRY{\normalsize} \\ -\verb$\large$ & \ENTRY{\large} \\ -\verb$\Large$ & \ENTRY{\Large} \\ -\verb$\LARGE$ & \ENTRY{\LARGE} \\ -\verb$\huge$ & \ENTRY{\huge} \\ -\verb$\Huge$ & \ENTRY{\Huge} -\end{tabular}\end{center} |