diff options
Diffstat (limited to 'Master/texmf-dist/doc/latex/frege/frege.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/frege/frege.tex | 336 |
1 files changed, 336 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/frege/frege.tex b/Master/texmf-dist/doc/latex/frege/frege.tex new file mode 100644 index 00000000000..36b0041286f --- /dev/null +++ b/Master/texmf-dist/doc/latex/frege/frege.tex @@ -0,0 +1,336 @@ +\documentclass[12pt]{article} +\usepackage{frege} +\usepackage{amsmath} + +%% For condensed itemize: +\newcommand{\squishlist}{ + \begin{list}{$\bullet$}{ + \setlength{\itemsep}{0pt} + \setlength{\parsep}{0pt} + \setlength{\topsep}{0pt} + \setlength{\partopsep}{0pt} + \setlength{\leftmargin}{1em} + \setlength{\labelwidth}{1em} + \setlength{\parskip}{0pt} + \setlength{\partopsep}{0pt} + \setlength{\rightmargin}{0pt} + \setlength{\labelsep}{0.5em}}} +\newcommand{\squishlistend}{\end{list}} + +\title{frege.sty \\ A \LaTeXe Package for Typesetting Begriffsschrift} +\author{Quirin Pamp \\ \texttt{Quirin.Pamp.2009@my.bristol.ac.uk}} + +\begin{document} +\maketitle +\section{Background} +\subsection{begriff.sty} + This package is based on begriff.sty released under the GNU General Public + License. + Copyright (C) 2003 by Josh Parsons (josh@coombs.anu.edu.au) with changes made in + October 2004 by Richard Heck (heck@fas.harvard.edu) and minor changes by Josh + Parsons to fix a problem with linespacing made in May 2005. + + While I could not have done so without the aforementioned work, I have reworked the + package from the ground up, to the point where some of the underlying approaches + have changed. On the downside this means there is no simple way of converting + anything typeset using begriff.sty to use this package instead. I felt this was + necessary to achieve a end result I was happy with. + +\subsection{GNU General Public License} + This package and all accompanying documentation is released under the GNU General + Public License. It is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free Software + Foundation; either version 2 of the License, or (at your option) any later version. + + This program is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A + PARTICULAR PURPOSE. See the GNU General Public License for more details. + + You should have received a copy of the GNU General Public License along with this + program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - + Suite 330, Boston, MA 02111, USA. (or just search for it online... Seriously.) + +\subsection{Changes as Compared to begriff.sty} + \squishlist + \item correct relative lengths of the content stroke with respect to other + strokes attached to it; + \item content strokes point at the middle of the followint symbols, rather + than the bottom; + \item greater width for the assertion stroke as compared to the content stroke; + \item a more intuitive structure for the conditional (arguments are now given in + the same order as they appear on the left of a completed formula); + \item the command for the conditional with empty arguments now results in a + vertical line (conditional stroke) on it's own the other strokes are added as + the arguments; + \item the linewidth is properly accounted for so that things remain properly + centered when scaled; + \squishlistend + +\subsection{Changes in Version 1.1} + \squishlist + \item added a optional scale factor to all basic strokes; + \item simplified the code for Fbracket in terms of that for Fbox; + \item rearranged the code in the style file in a more logical way; + \squishlistend + +\subsection{Changes in Version 1.2} + \squishlist + \item added a new command ``Fargument'' for typesetting arguments; + \item added a new command ``Fstrut'' to be used in conjunction with Fargument; + \item changed Fbaselength to be equal to the full length of a basi stroke (20pt); + \item fixed a bug where the scale factor introduced in version 1.1 does not reset + after all uses; + \squishlistend + +\subsection{Changes and Features yet to come} + \squishlist + \item incorporation of other frege related material such as fge.sty so as to put + all frege related material in a single package; + \item a vertical shorthand stroke such as used by Frege for typesetting arguments + in ``Begriffsschrift''; + \squishlistend + +\section{Features and Usage} +\subsection{Commands} +\subsubsection{Basic Commands} + The following is a list of the basic commands provided by this package along with + accompanying output. The conditional is treated sepperately. + \begin{flalign*} + &\mbox{\textbackslash Fcontent[1]} & &\Fcontent & & &\\ + &\mbox{\textbackslash Fncontent[1]} & &\Fncontent\\ + &\mbox{\textbackslash Fnncontent[1]} & &\Fnncontent\\ + &\mbox{\textbackslash Facontent[1]} & &\Facontent\\ + &\mbox{\textbackslash Fancontent[1]} & &\Fancontent\\ + &\mbox{\textbackslash Fanncontent[1]} & &\Fanncontent\\ + &\mbox{\textbackslash Fquant[1]\{a\}} & &\Fquant{a}\\ + &\mbox{\textbackslash Fnquant[1]\{a\}} & &\Fnquant{a}\\ + &\mbox{\textbackslash Fnnquant[1]\{a\}} & &\Fnnquant{a}\\ + &\mbox{\textbackslash Fquantn[1]\{a\}} & &\Fquantn{a}\\ + &\mbox{\textbackslash Fquantnn[1]\{a\}} & &\Fquantnn{a}\\ + &\mbox{\textbackslash Fnquantn[1]\{a\}} & &\Fnquantn{a}\\ + &\mbox{\textbackslash Fnquantnn[1]\{a\}} & &\Fnquantnn{a}\\ + &\mbox{\textbackslash Fnnquantn[1]\{a\}} & &\Fnnquantn{a}\\ + &\mbox{\textbackslash Fnnquantnn[1]\{a\}} & &\Fnnquantnn{a}\\ + &\mbox{\textbackslash Faquant[1]\{a\}} & &\Faquant{a}\\ + &\mbox{\textbackslash Fanquant[1]\{a\}} & &\Fanquant{a}\\ + &\mbox{\textbackslash Fannquant[1]\{a\}} & &\Fannquant{a}\\ + &\mbox{\textbackslash Faquantn[1]\{a\}} & &\Faquantn{a}\\ + &\mbox{\textbackslash Faquantnn[1]\{a\}} & &\Faquantnn{a}\\ + &\mbox{\textbackslash Fanquantn[1]\{a\}} & &\Fanquantn{a}\\ + &\mbox{\textbackslash Fanquantnn[1]\{a\}} & &\Fanquantnn{a}\\ + &\mbox{\textbackslash Fannquantn[1]\{a\}} & &\Fannquantn{a}\\ + &\mbox{\textbackslash Fannquantnn[1]\{a\}} & &\Fannquantnn{a}\\ + \end{flalign*} + This may seem like a daunting list, but there is an exceedingly simple way to think + about it. In a sense there are only two commands \textbackslash Fcontent[1] and + \textbackslash Fquant[1]\{\}. These two commands can be augmented with a + combination of as and ns so as to add assertion and negation strokes respectively. + Any stroke that is asserted (has a fat vertical line at the start) starts with + `\textbackslash Fa'. This may be followed by either one or two or no `n' to add one + or two or no negation strokes (the small vertical lines below the assertion + stroke). Next comes the name of the main command, either `quant' or `content'. + Finally the quantifiers may be followed by either one or two `n' to add one or two + negation strokes to the content stroke after the quantifier's depression. + + Consider also that many of these commands are only really present for completeness + sake. It is difficult to imagine a situation where a twice negated quantifier with + twice negated content would ever be needed. + + Since version 1.1 all basic strokes also have an optional scaling factor. A command + followed by [.5], for example would produce a stroke exactly half the default + length while [2] produces a stroke twice the default length. (The default length + is given by \textbackslash Fbaselength which is set to 20pt. Scaling allows for + greater control in the total length of formula as well as for a shorter syntax. + (We can replace expressions like \textbackslash Facontent \textbackslash Fcontent + with \textbackslash Facontent[2].) Care must be taken not to set a length that is + shorter than what is needed to fit all the parts of some basic stroke. This will + lead to negative lengths and hence unpredictable output. + + All quantifiers also have a mandatory argument that specifies the variable + associated with the quantifier. (Mandatory arguments are contained in a set of + curly brackets \{ and \}). This argument should be a single small letter and + will be typeset above the semi circular depression in the assertion stroke in + mathfrak font which is provided by tha amssymb package. This font can be used in + maths mode by using the command `\textbackslash mathfrak\{\}'. Note that all the + commands provided by this package may be used in both math and text mode. (Though + math mode usually results in better formatting.) + + Finally one may combine the above commands in arbitrary combinations which will + result in gapless longer strokes. (Eg.: $\Faquant[0.6]{a}\Fnquantn[1.4]{b}A$) + which may be roughly translated into english as ``for all $\mathfrak{a}$ there + exists a $\mathfrak{b}$ such that $A$''. (The commands I used for this expression + are \$\textbackslash Faquant\{a\}\textbackslash Fnquantn\{b\}A\$). + +\subsubsection{Conditional} + The conditional is the most important command in this package since it gives + Frege's Begriffsschrift it's two dimensional structure.\\ + The syntax for the Fconditional command is as follows: + + \textbackslash Fconditional[\textless option\textgreater] + \{\textless consequent\textgreater\}\{\textless antecedent\textgreater\}\\ + The arguments may in principle be anything, but you will only get a begriffschrift + formula if the arguments are themselves given by appropriate commands from the list + of basic commands given earlier. As an example, an asserted conjunction between $A$ + and $B$ would be given as follows: + + \$\textbackslash Fconditional[\textbackslash Fancontent]\{\textbackslash Fncontent + A\}\{\textbackslash Fcontent B\}\$ \\ + and produce the following output: + \begin{align*} + \Fbox{\Fconditional[\Fancontent]{\Fncontent A}{\Fcontent B}} + \end{align*} + In addition Fconditional may be nested as it's own argument to arbitrary depth. + Nesting in the option is not recommended. \\ + A conditional with nested consequent may be given as follows: + + \$\textbackslash Fconditional[\textbackslash Facontent]\{\textbackslash + Fcontent\textbackslash Fconditional\{\textbackslash Fcontent A\}\{\textbackslash + Fcontent B\}\}\{\textbackslash Fcontent\textbackslash Fcontent C\}\$\\ + and produces the following output: + \begin{align*} + \Fbox{\Fconditional[\Facontent]{\Fcontent\Fconditional{\Fcontent A} + {\Fcontent B}}{\Fcontent[2] C}} + \end{align*} + A conditional with nested antecedent may be given as follows: + + \$\textbackslash Fconditional[\textbackslash Facontent]\{\textbackslash Fcontent + \textbackslash Fcontent A\}\{\textbackslash Fcontent\textbackslash Fconditional + \{\textbackslash Fcontent B\}\{\textbackslash Fcontent C\}\}\$\\ + and produces the following output: + \begin{align*} + \Fbox{\Fconditional[\Facontent]{\Fcontent[2] A}{\Fcontent\Fconditional% + {\Fcontent B}{\Fcontent C}}} + \end{align*} + Each section of a content stroke may thus be replaced with any of the strokes given + by the list of basic commands. Note that it is up to the user to place the + appropriate number of strokes in each argument to ensure that the content strokes + all line up on the right hand side. + +\subsubsection{Brackets and Boxes} + There are two more commands to be considered: + + \textbackslash Fbracket\{\textless complex expression\textgreater\} + + \textbackslash Fbox\{\textless complex expression\textgreater\}\\ + Both Fbox and Fbracket take what I have called a `complex expression' for their + argument. A `complex expression' is any formula in begriffsschrift that has at + least one conditional in it. It is generally a good idea to put all complex + expressions into either a Fbox or a Fbracket. It is never necessary to place a + complex expressions into both an Fbox and an Fbracket since an Fbox simply is a + Fbracket without the actual brackets. Fbracket exists only for convenience with + the same effect being achieved by \textbackslash left(\textbackslash Fbox\{\} + \textbackslash right). + + The reason why the Fbox is a good idea, is that the baseline is very near the top of + a complex expression of Begriffsschrift, which can make for some odd formatting + effects. In addition to placing the baseline at the middel of a complex expression + an Fbox ensures the expression is treated by LaTeX as a single object and given + enough space. + + Finally a complex expression may not format correctly in some environments (like + the align* environment for example) unless it is placed in an Fbox. In short, + always use an Fbox (or Fbracket). + +\subsection{Arguments and Struts} + Since version 1.2 two arguments have been added that allow for the typesetting of + arguments. The syntax for the argument command is as follows: + + \textbackslash Fargument[\textless absent premise\textgreater]\{\textless premise + 1\textgreater\}\{\textless premise 2\textgreater\}\{\textless conclusion + \textgreater\}\\ + In the following esample the optional argument for the absent premise takes the + value `$X$' the premises are the two formulas above the therfore line and the + conclusion is the formula below the therefore line. The Begriffschrift expressions + in the arguments of the Fargument command do not need to be placed in an Fbox, + since the Fargument command works by boxing it's arguments allready. + \begin{align*} + \Fargument[X] + {\Fconditional[\Facontent] + {\Fcontent[2] A} + {\Fcontent\Fconditional{\Fcontent B}{\Fcontent C}}} + {\Fstrut[2]\Facontent C} + {\Fstrut[2]\Facontent A} + \end{align*} + where $X=\Facontent B$; (this is typeset seperately from the Fargument command); + + The three begriffsschrift formulas above are in fact aligned leftbound. To make + them appear rightbound no matter what the relative lengths of $A$, $B$, and $C$, + the command ``Fstrut'' has been used in front of $\Facontent C$ and $\Facontent A$. + The command \textbackslash Fstrut[1] works exactly like an invisible content + stroke, that is it inserts space of length Fbaselength. Like all basic strokes it + can be scaled via an optional scale factor. + +\subsection{Lengths} + In theory all the dimensions in this package can be changed with the command + \textbackslash setlength\{\textless name of length\textgreater\}\{\textless new + value\textgreater\}, though I have not done a great deal of testing and recommend + sticking to the default values. The following then is a table of all lengths: \\ + \begin{tabular}{|l|l|l|} + \hline + name & default value & description \\ + \hline + \textbackslash Fbaselength & 20pt & the length of the basic strokes \\ + \textbackslash Flinewidth & 0.5pt & the line width \\ + \textbackslash Fspace & 2pt & seperation between lines and text/formula \\ + \textbackslash Fassertwidth & 3\textbackslash Flinewidth & width of assert + stroke \\ + \textbackslash Fraiseheight & 1ex-\textbackslash Flinewidth & height of content + lines above baseline \\ + \textbackslash Fnegsep & 3\textbackslash Flinewidth & seperation between a + double negation \\ + \textbackslash Fnegshort & 2\textbackslash Flinewidth & space between negation + stroke and baseline \\ + \textbackslash Fquantwidth & 6pt & width of the semi-circular quantifier + depression \\ + \hline + \end{tabular} + the height of the conditional stroke is determined by the size of the contents of + the conditionals argument, as well as the baselineskip of the surrounding text. It + cannot be changed manually. + +\subsection{Final Example} + The Geach-Kaplan sentance (with thanks to Marcus Rossberg): + \begin{align*} + \Fbox% + {% + \Fconditional[{\Facontent[.2]\Fnquant{F}\Fcontent[.2]}]% + {% + \Fcontent% + \Fconditional% + {% + \Fcontent[3]% + \Fbox% + {% + f\Fbracket% + {% + \Fconditional[\Faquant{a}]% + {\Fcontent C\mathfrak{(a)}}% + {\Fcontent \mathfrak{F(a)}}% + }% + }% + }% + {\Fcontent\Fnquantn{b}\Fcontent\mathfrak{F(b)}}% + }% + {% + \Fcontent[0.4]% + \Fquant[0.6]{c}% + \Fquant[0.6]{d}% + \Fcontent[0.4]% + \Fconditional% + {% + \Fncontent% + \Fconditional{\Fcontent\mathfrak{c=d}}{\Fcontent\mathfrak{F(d)}}% + }% + {% + \Fncontent% + \Fconditional{\Fncontent\mathfrak{F(c)}}{\Fcontent A\mathfrak{(c,d)}}% + }% + }% + }% + \end{align*} + And that is all. \\ + For comments, suggestions, identified errors, email me at \\ + \textless Q.Pamp.2009 at my.bristol.ac.uk\textgreater. + % don't like storing my full email in a text file on the interneti, + % so I replaced the @ with " at "; +\end{document} |