% ********************************************************************
% LOGIC.sty  14 August 1991
% Royal Octavo format: 100%
% ********************************************************************
\typeout{ }
\typeout{* Document Style `LOGIC'*}
\typeout{   * * Version 1.4 * * }
\typeout{ }

% *************
% Error message
% *************
\def\@logicerr#1%
	{\errhelp{This standard LaTeX command is not used in LOGIC.STY.
		ªªJTry pressing return, and it'll probably be ignored.}%
	\typeout{Style error. \space See `Typesetting your chapter....}%
	\errmessage{#1}}

% **************************************
% Page dimensions, lineskips, type sizes
% **************************************
\lineskip 1pt \normallineskip 1pt
\def\baselinestretch{1}

\@twosidetrue     % Left and right pages
\@mparswitchtrue  % Marginal notes in the outside margin

\def\@normalsize{\@setsize\normalsize{12pt}\xpt\@xpt
	\abovedisplayskip 12pt minus3pt
	\belowdisplayskip\abovedisplayskip
	\abovedisplayshortskip \z@ plus3pt
	\belowdisplayshortskip 6.5pt plus3.5pt minus3pt
	\let\@listi\@listI}
\def\small{\@setsize\small{10pt}\ixpt\@ixpt
	\abovedisplayskip 11pt minus3pt
	\belowdisplayskip\abovedisplayskip
	\abovedisplayshortskip \z@ plus2pt
	\belowdisplayshortskip 4pt plus2pt minus2pt
	\def\@listi{\parsep 4.5pt plus 2pt minus 1pt
	\itemsep \parsep
	\topsep 9pt plus 3pt minus 5pt}}
\def\footnotesize{\@setsize\footnotesize{9pt}\viiipt\@viiipt
	\abovedisplayskip 6pt minus3pt
	\belowdisplayskip \abovedisplayskip
	\abovedisplayshortskip \z@ plus1pt
	\belowdisplayshortskip 3pt plus1pt minus2pt
	\def\@listi{\leftmargin\leftmargini
	\topsep 4pt plus 2pt minus 2pt
	\parsep 2pt plus 1pt minus 1pt
	\itemsep \parsep}}
\def\scriptsize{\@setsize\scriptsize{9pt}\viiipt\@viiipt}
\def\tiny{\@setsize\tiny{7pt}\vipt\@vipt}
\def\large{\@setsize\large{14pt}\xiipt\@xiipt}   % B
\def\Large{\@setsize\Large{16pt}\xivpt\@xivpt}   % A
\def\LARGE{\@setsize\LARGE{22pt}\xxpt\@xxpt}     % Chap
\def\huge{\@setsize\huge{30pt}\xxvpt\@xxvpt}
\let\Huge=\huge
\def\em{\it}
\def\sl{\it}
\normalsize

% **********************

\oddsidemargin 6.25pc
\evensidemargin 6.25pc
\marginparwidth 85pt

\marginparsep 10pt
\topmargin 27pt
\headheight 8pt
\headsep 18pt
\footskip 30pt
\topskip 10pt

\textheight = 37\baselineskip       % 37 lines on a page
\advance\textheight by \topskip     %
\textwidth 27pc                     % 4.5 in
\columnsep 2pc
\columnseprule 0pt

\footnotesep 8.4pt
\skip\footins 10.8pt plus 4pt minus 2pt
\marginparpush 7pt

\parskip 0pt
\parindent .3in
\partopsep 3pt plus 2pt minus 2pt
\def\chapstrut{\hrule width0pt height24pt depth0pt}
\def\afterchapstrut{\hrule width0pt height12pt depth0pt}
%\thispagestyle{plain}


% Penalties
\binoppenalty=2000
\relpenalty=1500
\@lowpenalty 51 \@medpenalty 151 \@highpenalty 301
\@beginparpenalty -\@lowpenalty
\@endparpenalty -\@lowpenalty
\@itempenalty -\@lowpenalty
\clubpenalty 2500
\widowpenalty 2500
\displaywidowpenalty 1500
\predisplaypenalty 500
\postdisplaypenalty 500
\interlinepenalty 0
\brokenpenalty 2000

\@beginparpenalty=\predisplaypenalty
\@endparpenalty=\postdisplaypenalty
\@itempenalty=500

\def\@ptsize{0}
\@namedef{ds@11pt}{\@logicerr{Only 10 point is available}}
\@namedef{ds@12pt}{\@logicerr{Only 10 point is available}}
\def\ds@twoside{}
\def\ds@draft{\overfullrule 5pt}
\@options
\relax

% *******************
% Sectioning commands
% *******************
% Counters
\newcounter {chapter}
\newcounter {section}[chapter]
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]

% Form of the numbers
\def\thechapter{\arabic{chapter}}
\def\thesection{\thechapter.\arabic{section}}
\def\thesubsection{\thesection.\arabic{subsection}}
%\def\thesubsubsection{\thesubsection .\arabic{subsubsection}}
%\def\theparagraph{\thesubsubsection.\arabic{paragraph}}
%\def\thesubparagraph{\theparagraph.\arabic{subparagraph}}

% Section macros
\def\chapter{\par
	\thispagestyle{plain} \@afterindentfalse
	\secdef\@chapter\@schapter}
\def\@chapter[#1]#2#3{
	\markboth{#3}{#1}
	\refstepcounter{chapter}
	\null\chapstrut
	{\raggedright
	\LARGE\bf #2\par
	\vskip 6pt \LARGE\bf #3\par}
	\chapstrut
	\hrule depth 0.5pt \afterchapstrut
	%\tableofcontents
	\chapstrut
	\@afterheading}
\def\@schapter#1{
	\markboth{#1}{#1}
	\null\chapstrut
	{\raggedright
	\LARGE\bf #1\par}
	\chapstrut\@afterheading }
\def\section
	{\@ifstar{\@sectionstar}{\@sectionnostar}}
\def\@sectionstar
	{\@startsection
	{section}{1}{\z@}{-12pt plus -1ex minus -3pt}{4pt minus 2pt}{\Large\bf}*}
\def\@sectionnostar
	{\@ifnextchar[{\@sectionopt}{\@sectionnoopt}}
\def\@sectionopt[#1]#2%
	{\sectionmark{#1}
	\@startsection
	{section}{1}{\z@}{-12pt plus -1ex minus -3pt}
	{4pt minus 2pt}{\Large\bf}[#1]{\Large\bf #2}
	\addcontentsline{toc}{section}
	{\protect\numberline{\thesection}#2}}
\def\@sectionnoopt#1
	{\sectionmark{#1}
	\@startsection
	{section}{1}{\z@}{-12pt plus -1ex minus -3pt}
	{4pt minus 2pt}{\Large\bf}[#1]{\Large\bf #1}}
\def\subsection%
	{\@ifstar{\@subsectionstar}{\@subsectionnostar}}
\def\@subsectionnostar{\@startsection{subsection}{2}{\z@}
	{-9pt minus -2pt}{4pt minus 2pt}{\large\bf}}
\def\@subsectionstar{\@startsection{subsection}{2}{\z@}
	{-9pt minus -2pt}{4pt minus 2pt}{\large\bf}*}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}
	{-9pt minus -2pt}{4pt minus 2pt}{\normalsize\bf}}
\def\paragraph{\@startsection{paragraph}{4}{\z@}
	{6pt minus 2pt}{-1em}{\normalsize\it}}
\def\subparagraph{\@startsection{subparagraph}{4}{\parindent}
	{6pt minus 2pt}{-1em}{\normalsize\it}}

\setcounter{secnumdepth}{3}

% Running headlines
\mark{{}{}}

\def\ps@headings
	{\let\@mkboth\markboth
	\def\@oddfoot{}%
	\def\@evenfoot{}%
	\def\@evenhead{\bf\thepage\hfil\it\leftmark\hfil\hbox{}}%
	\def\@oddhead{\hbox{}\hfil\it\rightmark\hfil\bf\thepage}%
	\def\sectionmark##1{\markright{##1}}%
	\def\chaptermark##1{\markboth{##1}{##1}}%
	\def\subsectionmark##1{}}

\def\ps@myheadings
	{\@logicerr{The page style `myheadings' is not available.}}

% Figures and tables
\long\def\@makecaption#1#2{%
	\vskip 6pt
	\setbox\@tempboxa\hbox{\bf #1.\ \rm #2}
	\ifdim \wd\@tempboxa >\hsize \bf #1.\ \rm #2\par
		\else \hbox to\hsize{\hfil\box\@tempboxa\hfil}
	\fi }

\long\def\@tablecaption#1#2{%
	\setbox\@tempboxa\hbox{\bf #1.\ \rm #2}
	\ifdim \wd\@tempboxa >\hsize \bf #1.\ \rm #2\par
		\else \hbox to\hsize{\hfil\box\@tempboxa\hfil}
	\fi \vskip 6pt}

\newcounter{figure}[chapter]
\def\thefigure{\@arabic\c@figure}
\def\fps@figure{tbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{Fig. \thefigure}
\def\figure{\@float{figure}}
\let\endfigure\end@float
\@namedef{figure*}{\@dblfloat{figure}}
\@namedef{endfigure*}{\end@dblfloat}
\newcounter{table}[chapter]
\def\thetable{\@arabic\c@table}
\def\fps@table{tbp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{Table \thetable}
\def\table{\let\@makecaption\@tablecaption \@float{table}}
\let\endtable\end@float
\@namedef{table*}{\@dblfloat{table}}
\@namedef{endtable*}{\end@dblfloat}


% Modifications to the equation environment
\@addtoreset{equation}{section}
\def\theequation{\thesection.\arabic{equation}}
\arraycolsep 5pt \tabcolsep 6pt \arrayrulewidth .4pt \doublerulesep 2pt
\tabbingsep \labelsep

% New theorem-like environments
\@addtoreset{definition}{section}
\newtheorem{definition}{Definition}[subsection]
\newtheorem{theorem}[definition]{Theorem}
\newtheorem{lemma}[definition]{Lemma}
\newtheorem{algorithm}[definition]{Algorithm}
\newtheorem{example}[definition]{Example}
\newtheorem{examples}[definition]{Examples}
\newtheorem{fact}[definition]{Fact}
\newtheorem{observation}[definition]{Observation}
\newtheorem{conjecture}[definition]{Conjecture}
\newtheorem{convention}[definition]{Convention}
\newtheorem{comment}[definition]{Comment}
\newtheorem{proposition}[definition]{Proposition}
\newtheorem{characterization}[definition]{Characterization}
\newtheorem{corollary}[definition]{Corollary}
\newtheorem{thesis}[definition]{Thesis}
\newtheorem{notation}[definition]{Notation}
\newtheorem{note}[definition]{Note}
\newtheorem{remark}[definition]{Remark}
\newtheorem{remarks}[definition]{Remarks}
\newtheorem{puzzle}[definition]{Puzzle}
\newtheorem{problem}[definition]{Problem}
\newtheorem{application}[definition]{Application}
\newtheorem{zexercise}[definition]{Exercise}
\newtheorem{zexercises}[definition]{Exercises}
\def\setthmfont{%
	\def\theoremtest{theorem}
	\def\proptest{proposition}
	\def\lemmatest{lemma}
	\def\coroltest{corollary}
	\ifx\@currenvir\theoremtest	\def\@thmfont{\it}\else
	\ifx\@currenvir\proptest	\def\@thmfont{\it}\else
	\ifx\@currenvir\lemmatest	\def\@thmfont{\it}\else
	\ifx\@currenvir\coroltest	\def\@thmfont{\it}\else
	\def\@thmfont{\rm}\fi\fi\fi\fi
	}
\def\@begintheorem#1#2{%
	\setthmfont
	\par\addvspace{4pt}\noindent
	{\bf #1\ #2.}\ignorespaces
	\hskip 0.5pc\@thmfont}
\def\@opargbegintheorem#1#2#3{%
	\setthmfont
	\par\addvspace{4pt}\noindent
	{\bf #1\ #2\ (#3).}\ignorespaces
	\hskip 0.5pc\@thmfont}
\def\@endtheorem{\rm\vskip 4pt}


%	END OF PROOF BOX

\def\pushright#1{{%            % set up
	\parfillskip=0pt           % so \par doesn't push \square to left
	\widowpenalty=10000        % so the page is not broken before \square
	\displaywidowpenalty=10000  % ditto
	\finalhyphendemerits=0      % TeXbook exercise 14.32
  %
  %                 horizontal
	\leavevmode                 % \nobreak means lines not pages
	\unskip                     % remove previous space or glue
	\nobreak                    % don't break lines
	\hfil                       % ragged right if we spill over
	\penalty50                  % discouragement to do so
	\hskip.2em                  % ensure some space
	\null                       % anchor following \hfill
	\hfill                      % push \square to right
	{#1}                        % the end-of-proof mark (or whatever)
  %
  %                   vertical
	\par}}                      % build paragraph

\def\proof{%
	\followon{Proof}%
	}
\def\endproof{%
	\ifSuppressEndOfProof
	\global\SuppressEndOfProoffalse
		\else
		\xqed
	\fi
	\endfollowon
	}
\def\qed{\xqed\global\SuppressEndOfProoftrue}
\newif\ifSuppressEndOfProof\SuppressEndOfProoffalse
\def\xqed{\pushright\markendofproof}
\def\markendofproof{\rule{2mm}{3mm}}
\def\followon#1{\trivlist\item[\hskip\labelsep{\bf#1.}]}
\def\endfollowon{\endtrivlist}
\def\@beginexercises{%
	\subsection*{Exercises}
	\small
	\enumerate}
\def\@opargbeginexercises[#1]{%
	\subsection*{Exercises\ (#1)}
	\small
	\enumerate}
\def\@beginexercise{%
	\subsection*{Exercise}
	\small
	\leftskip 1pc
	\rightskip\leftskip}
\def\@opargbeginexercise[#1]{%
	\subsection*{Exercise\ (#1)}
	\small
	\leftskip 1pc
	\rightskip\leftskip}
\newenvironment{exercise}%
{\begin{zexercise}\small}%
{\end{zexercise}}
\newenvironment{exercises}%
{\begin{zexercises}\small\begin{itemize}}%
{\end{itemize}\end{zexercises}}

% List numbering and lettering
\def\labelenumi{{\rm\arabic{enumi}.}}
\def\theenumi{\arabic{enumi}}
\def\labelenumii{{\rm(\alph{enumii})}}
\def\theenumii{\alph{enumii}}
\def\p@enumii{\theenumi}
\def\labelenumiii{{\rm\roman{enumiii}.}}
\def\theenumiii{\roman{enumiii}}
\def\p@enumiii{\theenumi(\theenumii)}
\def\labelenumiv{{\rm\Alph{enumiv}.}}
\def\theenumiv{\Alph{enumiv}}
\def\p@enumiv{\p@enumiii\theenumiii}

\def\labelitemi{$\bullet$}
\def\labelitemii{$\ast$}
\def\labelitemiii{$\circ$}
\def\labelitemiv{\bf --}

\def\descriptionlabel#1{\hspace\labelsep \bf #1}
\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin
	\let\makelabel\descriptionlabel}}
\let\enddescription\endlist

\leftmargini 2.5em
\leftmarginii 2.2em \leftmarginiii 1.87em \leftmarginiv 1.7em
\leftmarginv 1em
\leftmarginvi 1em
\leftmargin\leftmargini
\labelsep .5em
\labelwidth\leftmargini\advance\labelwidth-\labelsep
\def\@listI{\leftmargin\leftmargini \parsep \z@
	\topsep 3pt plus .5pt \itemsep 1pt plus .5pt}
\let\@listi\@listI
\@listi
\def\@listii{\leftmargin\leftmarginii
	\labelwidth\leftmarginii\advance\labelwidth-\labelsep
	\topsep 1pt plus .5pt
	\parsep \z@
	\itemsep .5pt}
\def\@listiii{\leftmargin\leftmarginiii
	\labelwidth\leftmarginiii\advance\labelwidth-\labelsep
	\topsep \z@
	\parsep \z@ \partopsep 1pt plus 0pt minus 1pt
	\itemsep \topsep}
\def\@listiv{\leftmargin\leftmarginiv
	\labelwidth\leftmarginiv\advance\labelwidth-\labelsep}
\def\@listv{\leftmargin\leftmarginv
	\labelwidth\leftmarginv\advance\labelwidth-\labelsep}
\def\@listvi{\leftmargin\leftmarginvi
	\labelwidth\leftmarginvi\advance\labelwidth-\labelsep}

% Verse, quotation, and quote environments
\def\verse{\let\\=\@centercr
	\list{}{\itemsep\z@ \itemindent -1.5em \listparindent\itemindent
	\rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
\let\endverse\endlist
\def\quotation{\list{}{\listparindent 1.5em
	\itemindent\listparindent
	\rightmargin\leftmargin \parsep 0pt plus 1pt}\item[]}
\let\endquotation=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\skip\@mpfootins = \skip\footins
\fboxsep = 3pt \fboxrule = .4pt

% Table of contents
\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{2} % i.e. down to subsection only
\def\tableofcontents{\section*{}
	\@starttoc{toc}}
\def\l@chapter#1#2{\addpenalty{\@secpenalty}
	\addvspace{2.25em plus 1pt} \begingroup
	\@tempdima 3em
	\parindent \z@
	\rightskip \@pnumwidth
	\parfillskip -\@pnumwidth
	{\large \bf \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}}\par
	\nobreak \endgroup}
\def\l@section{\@dottedtocline{1}{0em}{1.5em}}
\def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
\def\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
\def\listoffigures{\section*{List of Figures\@mkboth
	{List of Figures}{List of Figures}}\@starttoc{lof}}
\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\def\listoftables{\section*{List of Tables\@mkboth
	{List of Tables}{List of Tables}}\@starttoc{lot}}
\let\l@table\l@figure

% Bibliography
\def\thebibliography#1{%
	\section*{Bibliography\@mkboth{Bibliography}{Bibliography}}
	\list{[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}
	\leftmargin\labelwidth
	\advance\leftmargin\labelsep
	\usecounter{enumi}}
	\def\newblock{\hskip .11em plus .33em minus .07em}
	\sloppy\clubpenalty4000\widowpenalty4000
	\sfcode`\.=1000\relax}
\let\endthebibliography=\endlist

% *****
% Index
% *****
\def\makeindex{%
			\if@filesw
			\newwrite\@subindexfile\immediate\openout\@subindexfile=\jobname.sbj
			\newwrite\@auindexfile\immediate\openout\@auindexfile=\jobname.aut
			\newwrite\@notindexfile\immediate\openout\@notindexfile=\jobname.not
	\def\subind{\@bsphack\begingroup
			\def\protect####1{\string####1\space}\@sanitize
			\@wrindex\@subindexfile}
			\typeout{Writing the subject index file: \jobname.sbj }
	\def\auind{\@bsphack\begingroup
			\def\protect####1{\string####1\space}\@sanitize
			\@wrindex\@auindexfile}
			\typeout{Writing the author index file:	\jobname.aut }
	\def\notind{\@bsphack\begingroup
			\def\protect####1{\string####1\space}\@sanitize
			\@wrindex\@notindexfile}
			\typeout{Writing the notation index file: \jobname.not }
			\fi}

\def\@wrindex#1#2{\let\thepage\relax
	\xdef\@gtempa{\write#1{\string\indexentry{#2}{\thepage}}}
	\endgroup\@gtempa
	\if@nobreak \ifvmode\nobreak\fi\fi\@esphack}

\def\subind{\@bsphack\begingroup \@sanitize\@index}
\def\auind{\@bsphack\begingroup \@sanitize\@index}
\def\notind{\@bsphack\begingroup \@sanitize\@index}

\def\@index#1{\endgroup\@esphack}

\newif\if@restonecol
\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
	\columnseprule \z@
	\columnsep 35pt\twocolumn[\chapter*{Index}]
	\@mkboth{Index}{Index}\thispagestyle{plain}\parindent\z@
	\parskip\z@ plus .3pt\relax\let\item\@idxitem}
\def\@idxitem{\par\hangindent 40pt}
\def\subitem{\par\hangindent 40pt \hspace*{20pt}}
\def\subsubitem{\par\hangindent 40pt \hspace*{30pt}}
\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}
\def\indexspace{\par \vskip 10pt plus 5pt minus 3pt\relax}

\def\see#1#2{{\em see\/} #1}
\def\printindex{\@input{\jobname.ind}}


% Footnotes
\def\footnoterule{\kern-3\p@
	\hrule width .4\columnwidth
	\kern 2.6\p@}

\long\def\@makefntext#1{\parindent 1em\noindent
	\hbox to 1.8em{\hss$^{\@thefnmark}$}#1}

% Floats
\setcounter{topnumber}{2}
\def\topfraction{.9}
\setcounter{bottomnumber}{2}
\def\bottomfraction{.9}
\setcounter{totalnumber}{3}
\def\textfraction{.1}
\def\floatpagefraction{.9}
\setcounter{dbltopnumber}{2}
\def\dbltopfraction{.7}
\def\dblfloatpagefraction{.5}


\def\abstract{%
	\if@twocolumn
	\section*{Abstract}
		\else \small
		\begin{center}
		{\bf Abstract\vspace{-.5em}\vspace{0pt}}
		\end{center}
		\quotation
	\fi}
\def\endabstract{\if@twocolumn\else\endquotation\fi}

% Date
\def\today{\ifcase\month\or
	January\or February\or March\or April\or May\or June\or
	July\or August\or September\or October\or November\or December\fi
	\space\number\day, \number\year}

% Appendix
\def\appendix{\par
	\setcounter{section}{0}
	\setcounter{subsection}{0}
	\def\thesection{\Alph{section}}}

\ps@headings
\pagenumbering{arabic}
\onecolumn
\flushbottom

%%%%%%%%%%
\floatsep 0pt%6pt
\textfloatsep 12pt
\intextsep 12pt
\@maxsep 12pt%20pt
\dblfloatsep 12pt
\dbltextfloatsep 14pt
\@dblmaxsep 20pt
\@fptop 0pt plus 1fil
\@fpsep 10pt plus 2fil
\@fpbot 0pt plus 1fil
\@dblfptop 0pt plus 1fil
\@dblfpsep 10pt plus 2fil
\@dblfpbot 0pt plus 1fil