% == Definitions of frequently used symbolic terms
% MORE MACROS
% ENVIRONMENTS
\newcounter{proposition}[subsection]
\renewcommand{\theproposition}
{\arabic{section}.\arabic{subsection}:\arabic{proposition}}
\newcounter{dee}[section]
\renewcommand{\thedee}
{\arabic{section}.\arabic{dee}}
\newcounter{definition}
\renewcommand{\thedefinition}
{\arabic{definition}}
\newcounter{theorem}
\renewcommand{\thetheorem}
{\arabic{theorem}}
\newcounter{observation}
\renewcommand{\theobservation}
{\arabic{observation}}
\newcounter{lemma}
\renewcommand{\thelemma}
{\arabic{lemma}}
% short env.s
\newcounter{ShortProp}
\renewcommand{\theShortProp}
{\arabic{ShortProp}}
%\newcommand{\sprop}{\noindent\refstepcounter{ShortProp}\textbf{Proposition\the%ShortProp}. \ }
\newcommand{\sprop}{\noindent\refstepcounter{ShortProp}\textbf{Lemma\theShortProp}. \ }
\newcounter{ShortDef}
\renewcommand{\theShortDef}
{\arabic{ShortDef}}
\newcommand{\propref}[1]{\noindent Lemma \ref{#1}}
\newcommand{\sdef}{\noindent\refstepcounter{ShortDef}\textbf{Definition\theShortDef}. \ }
\newcounter{IntAx}
\renewcommand{\theIntAx}
{\arabic{IntAx}}
\newcommand{\defref}[1]{\noindent Definition \ref{#1}}
\newcommand{\intax}{\noindent\refstepcounter{IntAx}\textbf{A\theIntAx}. \ }
\newcounter{ClAx}
\renewcommand{\theClAx}
{\arabic{ClAx}}
\newcommand{\clax}{\noindent\refstepcounter{ClAx}\textbf{A'\theClAx}. \ }
\newcounter{JAx}
\renewcommand{\theJAx}
{\arabic{JAx}}
%\newcommand{\Jax}{\noindent\refstepcounter{JAx}\textbf{J\theJAx}. \ }
\newcommand{\Jax}{\noindent\refstepcounter{JAx}\textbf{A\theJAx}. \ }
%end short env.s
%\newcounter{corollary}
%\renewcommand{\thecorollary}
%{\arabic{corollary}}
\newenvironment{defn}
{\refstepcounter{definition}%
\begin{description}%
\item[\textbf{Definition}
\thedefinition] \mbox{ }}%
{\end{description}}
\newenvironment{defA}
{\refstepcounter{definition}%
\begin{description}%
\item[\textbf{Def.}
\thedefinition]}%
{\end{description}}
\newenvironment{thmA}
{\refstepcounter{theorem}%
\begin{description}%
\item[\textbf{Theorem}
\thetheorem] \mbox{ }}%
{\end{description}}
\newenvironment{obsA}
{\refstepcounter{observation}%
\begin{description}%
\item[\textbf{Obs.}
\theobservation]}%
{\end{description}}
\newenvironment{lemA}
{\refstepcounter{lemma}%
\begin{description}%
\item[\textbf{Lem.}
\thelemma]}%
{\end{description}}
\newenvironment{jprop}
{\refstepcounter{lemma}%
\begin{description}%
\item[\textbf{Proposition}
\thelemma] \mbox{ }}%
{\end{description}}
\newenvironment{pf}
{\begin{description}%
\item[\textbf{pf: }]}%
{\end{description}}
\newenvironment{Prop}
{\refstepcounter{proposition}%
\begin{description}%
\item[\theproposition]}%
{\end{description}}
\newenvironment{AProp}
{\refstepcounter{proposition}%
\begin{description}%
\item[\textbf{proposition}
\theproposition]}%
{\end{description}}
\newenvironment{BProp}
{\refstepcounter{proposition}%
\begin{description}%
\item[\textbf{definition}
\theproposition]}%
{\end{description}}
\newenvironment{CCProp}
{\refstepcounter{proposition}%
\begin{description}%
\item[\theproposition]}%
{\end{description}}
\newenvironment{CProp}
{\refstepcounter{dee}%
\begin{description}%
\item[\thedee]}%
{\end{description}}
\newenvironment{CdProp}
{\refstepcounter{dee}%
\begin{description}%
\item[\thedee \ \textbf{D}]}%
{\end{description}}
\newenvironment{DProp}[1]
{\refstepcounter{proposition}%
\begin{description}%
\item[\text{#1} \ ]}%
{\end{description}}
\newenvironment{FProp}[1]
{\refstepcounter{proposition}%
\begin{description}%
\item[\textbf{#1} \theproposition]}%
{\end{description}}
\newcounter{Pproposition}
\newenvironment{PProp}
{\refstepcounter{Pproposition}%
\begin{description}%
\item[\thePproposition]}%
{\end{description}}
\newtheorem{prop}{Proposition}
\newtheorem{definit}[prop]{Definition}
\newtheorem{corol}[prop]{Corollary}
% COMMANDS
\newcommand{\escmathcom}[3]{ \newcommand{#1}[#2]{\mbox{#3}}}
% OTHER MACROS
% Set theory
%\escmathcom{\eq}{0}{$\ \equiv \ $}
\escmathcom{\eq}{0}{$ \ = \ $}
\escmathcom{\tset}{1}{$\mathcal{#1}$} % short version
\escmathcom{\tindset}{2}{${\mathcal{#2}}_{#1}$}
\escmathcom{\tindtop}{2}{${\mathcal{#1}}_{\mathcal{#2}}$}
\escmathcom{\powerset}{1}{$\wp (#1)$}
\escmathcom{\mi}{1}{$\mathit{#1}$}
\escmathcom{\ms}{1}{$\mathsf{#1}$}
\escmathcom{\wt}{1}{$\mathtt{#1}$}
\escmathcom{\mcal}{1}{$\mathcal{#1}$}
\escmathcom{\mr}{1}{$\mathcal{#1}$}
% Models and Structures
\escmathcom{\Struct}{1}{$\mathcal{#1}$}
\escmathcom{\AStruct}{1}{$\mathfrak{#1}$}
\escmathcom{\BStruct}{1}{$\mathfrak{#1}_{\rho}$}
% Lattice theory
\escmathcom{\true}{0}{$\top$}
\escmathcom{\false}{0}{$\bot$}
\escmathcom{\porder}{0}{$\leq$}
\escmathcom{\sorder}{1}{$\sqsubset_{\mathcal{#1}}$}
%\escmathcom{\specord}{0}{$\sqsubset_{\mbox{\tiny $\Opens$}}$}
%\escmathcom{\specord}{0}{$\prec_{\mbox{\tiny $\Opens$}}$}
\escmathcom{\specord}{0}{$\prec$}
\escmathcom{\rspecord}{0}{$\prec_{\mbox{\tiny $\Regions$}}$}
\escmathcom{\finer}{0}{$\ll$}
\escmathcom{\smeet}{0}{$ \ \sqcap \ $}
\escmathcom{\sjoin}{0}{$ \ \sqcup \ $}
\escmathcom{\meet}{0}{$\sqcap$}
\escmathcom{\join}{0}{$\sqcup$}
\escmathcom{\ameet}{0}{$\bigwedge$}
\escmathcom{\ajoin}{0}{$\bigvee$}
\escmathcom{\bigjoin}{0}{$\bigvee$}
\escmathcom{\diimp}{0}{$\Leftrightarrow$}
\escmathcom{\upclosedA}{1}{$\{ \wt{#1} \upharpoonright \}$}
\escmathcom{\upclosed}{1}{$\{ \wt{#1} \uparrow \}$}
\escmathcom{\pointset}{1}{$ \wt{#1} \uparrow_{\mbox{\tiny $\Regions$}}$}
% Logical symbols
\escmathcom{\niimp}{0}{$\nRightarrow$}
\escmathcom{\nto}{0}{$\nrightarrow$}
\escmathcom{\bnot}{0}{$\neg$}
\escmathcom{\divc}{0}{$\Vert$}
\escmathcom{\diva}{0}{$\Vert$}
% Spatial IPL2 (heyt13)
\escmathcom{\retre}{0}{$\mathsf{res}$}
\escmathcom{\exte}{0}{$\mathsf{ext}$}
\escmathcom{\inst}{0}{$\mathsf{inst}$}
\escmathcom{\recoOne}{0}{$\mathsf{rec1}$}
\escmathcom{\recoTwo}{0}{$\mathsf{rec2}$}
\escmathcom{\wff}{0}{$\mathsf{wff}$}
\escmathcom{\terM}{0}{$\mathsf{term}$}
\escmathcom{\iovl}{0}{$\mathsf{overlap}_{i}$}
\escmathcom{\overlapping}{0}{$\mathsf{overlap}$}
\escmathcom{\ovl}{0}{$\mathsf{overlap}$}
%\escmathcom{\tp}{0}{$\mathsf{tp}$}
\escmathcom{\src}{0}{$\mathsf{ic}_{s}$}
\escmathcom{\wrc}{0}{$\mathsf{ic}_{w}$}
\escmathcom{\sdc}{0}{$\mathsf{ap}_{s}$}
\escmathcom{\wdc}{0}{$\mathsf{ap}_{w}$}
\escmathcom{\isrc}{0}{$\mathsf{ic}_{i}$}
\escmathcom{\tp}{0}{$\mathsf{tp}$}
\escmathcom{\stp}{0}{$\mathsf{tp}_{s}$}
\escmathcom{\istp}{0}{$\mathsf{tp}_{i}$}
\escmathcom{\Regular}{0}{$\mathsf{regl}$}
%\escmathcom{\spc}{0}{$\mathsf{spc}$}
%\escmathcom{\Tspc}{0}{$\mathsf{SPC}$}
\escmathcom{\Models}{0}{$\mathsf{\Vdash}$}
\escmathcom{\screen}{0}{$\mathsf{screen}$}
\escmathcom{\Alpha}{0}{$\Lambda$}
\escmathcom{\cell}{0}{$\mathsf{cell}$}
\escmathcom{\disjoint}{0}{$\mathsf{disjoint}$}
\escmathcom{\rprime}{0}{$\mathsf{prime}$}
\escmathcom{\atom}{0}{$\mathsf{atmcell}$}
\escmathcom{\Ascreen}{0}{$\mathsf{atoms}$}
\escmathcom{\Aatom}{0}{$\mathsf{atom}$}
\escmathcom{\twocover}{0}{$\mathsf{2cover}$}
\escmathcom{\primecomp}{0}{$\mathsf{pcomp}$}
\escmathcom{\concomp}{0}{$\mathsf{ccomp}$}
\escmathcom{\tessel}{0}{$\mathsf{tll}$}
\escmathcom{\diip}{0}{$\mathsf{diip}$}
\escmathcom{\doip}{0}{$\mathsf{doip}$}
\escmathcom{\diic}{0}{$\mathsf{diic}$}
\escmathcom{\doic}{0}{$\mathsf{doic}$}
\escmathcom{\spc}{0}{$\mathsf{con}_{s}$}
\escmathcom{\Tspc}{0}{$\mathsf{SC}$}
%\escmathcom{\mcon}{0}{$\mathsf{c}$}
\escmathcom{\connec}{0}{$\mathsf{con}$}
\escmathcom{\dc}{0}{$\mathsf{ap}$}
\escmathcom{\ntp}{0}{$\mathsf{ntp}$}
\escmathcom{\wtp}{0}{$\mathsf{tp}_{w}$}
\escmathcom{\wntp}{0}{$\mathsf{ntp}_{w}$}
\escmathcom{\ers}{0}{$\mathsf{ers}$}
\escmathcom{\rc}{0}{$\mathsf{ic}$}
\escmathcom{\cim}{0}{$\mathsf{cell\_of\_mesh}$}
%\escmathcom{\split}{0}{$\mathsf{nspl}$}
%\escmathcom{\Tsplit}{0}{$\mathsf{NSPL}$}
\escmathcom{\rcon}{0}{$\mathsf{con}$}
\escmathcom{\nsplit}{0}{$\mathsf{ndiv}$}
\escmathcom{\srcon}{0}{$\mathsf{con}_{s}$}
\escmathcom{\snsplit}{0}{$\mathsf{ndiv}_{s}$}
\escmathcom{\split}{0}{$\mathsf{ndiv}$}
\escmathcom{\regular}{0}{$\mathsf{regl}$}
%\escmathcom{\Ttriv}{0}{$\mathsf{triv}$}
\escmathcom{\triv}{0}{$\mathsf{degnr}$}
%\escmathcom{\Tnemp}{0}{$\mathsf{ne}$}
\escmathcom{\nempty}{0}{$\mathsf{nempt}$}
\escmathcom{\nesc}{0}{$\mathsf{nesc}$}
%\escmathcom{\pos}{0}{$\mathsf{pos}$}
\escmathcom{\pos}{0}{$\mathsf{nempt}$}
\escmathcom{\unispace}{0}{$\mathsf{unisp}$}
\escmathcom{\comp}{0}{$\circ$}
\escmathcom{\isgran}{0}{$\mathsf{is\_gran}$}
\escmathcom{\gran}{0}{$\mathsf{gran}$}
\escmathcom{\hasgran}{0}{$\mathsf{has\_gran}$}
\escmathcom{\maxgran}{0}{$\mathsf{maxgran}$}
\escmathcom{\yolk}{0}{$\mathsf{yolk}$}
\escmathcom{\Tsplit}{0}{$\mathsf{NS}$}
\escmathcom{\Trc}{0}{$\mathsf{RC}$}
\escmathcom{\Ters}{0}{$\mathsf{ERS}$}
\escmathcom{\Tntp}{0}{$\mathsf{NTP}$}
\escmathcom{\Tdc}{0}{$\mathsf{DC}$}
\escmathcom{\Tpos}{0}{$\mathsf{EXT}$}
%\escmathcom{\white}{0}{$\mathsf{white}$}
\escmathcom{\digcom}{0}{$\mathsf{dcomp}$}
\escmathcom{\digsup}{0}{$\mathsf{dsup}$}
\escmathcom{\inreg}{0}{$\mathsf{dint}$}
\escmathcom{\outreg}{0}{$\mathsf{dout}$}
\escmathcom{\digrep}{0}{$\mathsf{drep}$}
\escmathcom{\cpd}{0}{$\mathsf{cpd}$}
\escmathcom{\connectedA}{0}{$\mathsf{scon}$}
\escmathcom{\connectedB}{0}{$\mathsf{sc}$}
\escmathcom{\connectedC}{0}{$\mathsf{rsc}$}
\escmathcom{\rbo}{0}{$\mathsf{rbo}$}
\escmathcom{\rcccon}{0}{$\mathsf{RC}$}
\escmathcom{\rccover}{0}{$\mathsf{OL}$}
\escmathcom{\rccdisc}{0}{$\mathsf{DC}$}
\escmathcom{\rccdisj}{0}{$\mathsf{DJ}$}
\escmathcom{\srcccon}{0}{$\mathsf{RCsc}$}
\escmathcom{\srccover}{0}{$\mathsf{OLsc}$}
\escmathcom{\rccconN}{0}{$\mathsf{RCn}$}
\escmathcom{\rccoverN}{0}{$\mathsf{OLn}$}
% Spatial IPL2 (ARW2001)
\escmathcom{\Disj}{0}{$\mathsf{DJ}$}
\escmathcom{\Hpart}{0}{$\mathsf{p}$}
\escmathcom{\Hdc}{0}{$\mathsf{wdc}$}
\escmathcom{\Hdj}{0}{$\mathsf{dj}$}
\escmathcom{\Hcon}{0}{$\mathsf{spc}$}
\escmathcom{\Hsc}{0}{$\mathsf{spc}$}
\escmathcom{\Hwc}{0}{$\mathsf{wc}$}
\escmathcom{\Hdisc}{0}{$\mathsf{dsc}$}
\escmathcom{\Hol}{0}{$\mathsf{cov}$}
\escmathcom{\Hrc}{0}{$\mathsf{fmc}$}
%\escmathcom{\nemp}{0}{$\mathsf{cpos}$}
\escmathcom{\nemp}{0}{$\mathsf{nempty}$}
\escmathcom{\Wpart}{0}{$\mathsf{Part}$}
\escmathcom{\Wdc}{0}{$\mathsf{wDC}$}
\escmathcom{\Wdj}{0}{$\mathsf{DJ}$}
\escmathcom{\Wcon}{0}{$\mathsf{Con}$}
\escmathcom{\Wsc}{0}{$\mathsf{Con}$}
\escmathcom{\Wol}{0}{$\mathsf{OV}$}
\escmathcom{\Wrc}{0}{$\mathsf{fmC}$}
\escmathcom{\Wne}{0}{$\mathsf{NE}$}
%\escmathcom{\conn}{0}{$\odot$}
\escmathcom{\conn}{0}{$\Hcon$}
%\escmathcom{\nemp}{0}{$\triangledown$}
%\escmathcom{\nempt}{0}{$\triangledown$}
% Spatial intuitive relations (ARW2001 slides, fig.)
\escmathcom{\HHpart}{0}{$\mathsf{part\_of}$}
\escmathcom{\HHdc}{0}{$\mathsf{r\_discon}$}
\escmathcom{\HHdj}{0}{$\mathsf{disj}$}
\escmathcom{\HHcon}{0}{$\mathsf{s\_con}$}
\escmathcom{\HHdisc}{0}{$\mathsf{s\_discon}$}
\escmathcom{\HHol}{0}{$\mathsf{overlap}$}
\escmathcom{\HHrc}{0}{$\mathsf{r\_con}$}
\escmathcom{\HHreg}{0}{$\mathsf{regular}$}
\escmathcom{\HHint}{0}{$\mathsf{Int}$}
\escmathcom{\HHclos}{0}{$\mathsf{Clos}$}
\escmathcom{\horse}{0}{$\to$}
% Topology
\escmathcom{\Regions}{0}{$\mcal{R}$}
\escmathcom{\Region}{0}{$\mcal{R}$}
\escmathcom{\ran}{0}{$\mcal{R}$}
\escmathcom{\Opens}{0}{$\mcal{O}$}
\escmathcom{\Closeds}{0}{$\mcal{C}$}
\escmathcom{\Inter}{0}{$\mathsf{i}$}
\escmathcom{\Closure}{0}{$\mathsf{c}$}
\escmathcom{\Int}{1}{$\mathsf{i}(#1)$}
\escmathcom{\Clos}{1}{$\mathsf{c}(#1)$}
\escmathcom{\Boun}{1}{$\mathsf{b}(#1)$}
%\escmathcom{\Reg}{1}{$\mathsf{r}(#1)$}
\escmathcom{\Reg}{0}{$\mathsf{R}$}
\escmathcom{\Heyt}{1}{$\mathsf{h}(#1)$}
\escmathcom{\SComp}{1}{$\ov{#1}$}
\escmathcom{\setimp}{0}{$\iimp$}
\escmathcom{\hcomp}{0}{$\backsim$}
%\escmathcom{\atom}{0}{$\mathsf{atom}$}
\escmathcom{\region}{0}{$\mathsf{region}$}
\escmathcom{\Base}{1}{$\phi (\wt{#1})$}
\escmathcom{\zInt}{0}{$\mathsf{I}$}
\escmathcom{\zClos}{0}{$\mathsf{C}$}
\escmathcom{\zBoun}{0}{$\mathsf{Bd}$}
\escmathcom{\zRegl}{0}{$\approx$}
\escmathcom{\Rr}{0}{$\approx$}
\escmathcom{\zHco}{0}{$\ineg$}
\escmathcom{\zBco}{0}{$\neg$}
\escmathcom{\emp}{0}{$\varnothing$}
\escmathcom{\sseq}{0}{$ \ \subseteq \ $}
\escmathcom{\nsseq}{0}{$ \ \nsubseteq \ $}
\escmathcom{\qsseq}{0}{$ \ \sqsubseteq \ $}
\escmathcom{\nqsseq}{0}{$ \ \not\sqsubseteq \ $}
\escmathcom{\qsset}{0}{$ \ \sqsubset \ $}
\escmathcom{\sqsseq}{0}{$\sqsubseteq$}
\escmathcom{\nqseq}{0}{$\nsqsubseteq$}
\escmathcom{\nsqsseq}{0}{$\not\sqsubseteq$}
% Names of Logical Systems
\escmathcom{\Itwo}{0}{$\mathit{I2}$}
\escmathcom{\Ctwo}{0}{$\mathit{C2}$}
\escmathcom{\Dtwo}{0}{$\mathit{D2}$}
\escmathcom{\Ctwor}{0}{$\mathit{C2}_{r}$}
\escmathcom{\Dtwor}{0}{$\mathit{D2}_{r}$}
\escmathcom{\Ctwoc}{0}{$\mathit{C2}_{c}$}
\escmathcom{\Dtwoc}{0}{$\mathit{D2}_{c}$}
\escmathcom{\Htwo}{0}{$\mathit{I2}$}
\escmathcom{\Htwoi}{0}{$\mathit{I2}_{m}$}
\escmathcom{\Htwor}{0}{$\mathit{I2}_{r}$}
\escmathcom{\Htwoc}{0}{$\mathit{I2}_{c}$}
%\escmathcom{\twoC}{0}{$\mathit{2C}$}
%\escmathcom{\twoD}{0}{$\mathit{2D}$}
\escmathcom{\NCtwo}{0}{$\mathit{NC2}$}
\escmathcom{\NDtwo}{0}{$\mathit{ND2}$}
\escmathcom{\VCtwo}{0}{$\mathit{VC2}$}
\escmathcom{\VDtwo}{0}{$\mathit{VD2}$}
\escmathcom{\Sfour}{0}{$\mathit{S4}$}
\escmathcom{\Sfive}{0}{$\mathit{S5}$}
\escmathcom{\IP}{0}{\emph{H}}
%\escmathcom{\Sfour}{0}{\emph{S4}}
%\escmathcom{\Sfive}{0}{\emph{S5}}
\escmathcom{\Sfourfive}{0}{\emph{S4-S5}}
\escmathcom{\IPtwo}{0}{\emph{H2}}
\escmathcom{\IPD}{0}{\emph{D2}}
%\escmathcom{\IPD}{0}{\emph{2tA}}
\escmathcom{\NIPD}{0}{\emph{ND2}}
\escmathcom{\VIPD}{0}{\emph{VD2}}
%\escmathcom{\NIPD}{0}{\emph{N2tA}}
%\escmathcom{\VIPD}{0}{\emph{V2tA}}
\escmathcom{\SIPD}{0}{$\Sigma$\emph{H2D}}
\escmathcom{\CP}{0}{\emph{C}}
\escmathcom{\CPP}{0}{\emph{2C}}
\escmathcom{\IPT}{0}{\emph{IPT}}
\escmathcom{\IPC}{0}{\emph{IPC}}
\escmathcom{\IPQ}{0}{\emph{IPC}}
\escmathcom{\IPL}{0}{\emph{IPL}}
\escmathcom{\IPLtwo}{0}{\emph{IP2}}
\escmathcom{\IPLK}{0}{$\mathit{IP2N}$}
\escmathcom{\IPCcd}{0}{$\mathit{IPC}_{D}$}
\escmathcom{\IPCk}{0}{$\mathit{IPC}_{K}$}
\escmathcom{\IPCcdk}{0}{$\mathit{IPC}_{DK}$}
\escmathcom{\RCC}{0}{\emph{RCC}}
\escmathcom{\RCCe}{0}{\emph{RCC8}}
\escmathcom{\RCCint}{0}{$\mcal{I}_{8}$}
\escmathcom{\CPC}{0}{\emph{CPC}}
\escmathcom{\CPL}{0}{\emph{CPL}}
\escmathcom{\LLAMA}{0}{\emph{LLAMA}}
% Sets of Expressions
\escmathcom{\TERM}{0}{$\mbox{\emph{Term}}$}
\escmathcom{\SUBST}{0}{$\mbox{\emph{Subst}}$}
\escmathcom{\PROP}{0}{$\mbox{\emph{Prop}}$}
\escmathcom{\WFF}{0}{$\mbox{\emph{Wff}}$}
\escmathcom{\OPER}{0}{$\mbox{\emph{Oper}}$}
\escmathcom{\ATOM}{0}{$\mbox{\emph{PropAtom}}$}
\escmathcom{\VAR}{0}{$\mbox{\emph{Var}}$}
\escmathcom{\CONS}{0}{$\mbox{\emph{Cons}}$}
\escmathcom{\CONST}{0}{$\mbox{\emph{Const}}$}
\escmathcom{\EVAL}{0}{$\mbox{\emph{EvalExp}}$}
\escmathcom{\FUN}{0}{$\mbox{\emph{Fun}}$}
\escmathcom{\PRED}{0}{$\mbox{\emph{Pred}}$}
\escmathcom{\ATOMwff}{0}{$\mbox{\emph{AtomWff}}$}
% Semantical Symbolism
\escmathcom{\vtopol}{0}{$\Vdash$}
\escmathcom{\zInter}{0}{$\rho$}
\escmathcom{\zIVal}{2}{$\Vert #1 \Vert_{#2}$}
\escmathcom{\zVal}{1}{$\Vert #1 \Vert$}
\escmathcom{\kVal}{1}{$\lceil #1 \rceil$}
\escmathcom{\Root}{0}{$\textbf{0}$}
\escmathcom{\bool}{0}{$\mbox{\emph{Bool}}$}
\escmathcom{\Domain}{1}{$\mathcal{#1}$}
\escmathcom{\KDomain}{2}{\tindset{#2}{#1}}
\escmathcom{\FDomain}{2}{\tindset{#2}{#1}}
\escmathcom{\Th}{0}{$\Delta$}
\escmathcom{\tModel}{0}{$\vDash \ $}
\escmathcom{\ntModel}{0}{$\nvDash \ $}
\escmathcom{\tpModel}{0}{$\vDash_{+} \ $}
\escmathcom{\MODEL}{1}{$\vDash_{#1}$}
\escmathcom{\REAL}{0}{$\rho$}
\escmathcom{\VAL}{0}{$\mbox{\emph{VAL}}$}
\escmathcom{\VALR}{0}{${\mbox{\emph{VAL}}}_{\rho}$}
\escmathcom{\intt}{1}{$\Vert #1 \Vert$}
\escmathcom{\ASG}{0}{$\mbox{\emph{Assg}}$}
\escmathcom{\KASG}{1}{${\emph{Assg}}_{#1}$}
\escmathcom{\ASSG}{0}{$\sigma$}
\escmathcom{\eqASSG}{1}{$\sigma' =_{#1} \sigma$}
\escmathcom{\tVAL}{0}{$\mbox{\emph{Val}}$}
\escmathcom{\tVALR}{0}{${\mbox{\emph{Val}}}_{\rho}$}
\escmathcom{\tVALRT}{0}{${\mbox{\emph{ValSet}}}_{\rho}$}
%\escmathcom{\kVAL}{1}{$\mbox{\emph{Val}}^{#1}$}
\escmathcom{\kVALR}{0}{${\mbox{\emph{Val}}}_{\rho}$}
\escmathcom{\kkVALR}{1}{${\mbox{\emph{Val}}}_{\rho}^{#1}$}
\escmathcom{\INTa}{2}{$\vert #1 \vert_{#2}$}
\escmathcom{\INTt}{3}{$\Vert #2 \Vert_{#3}^{#1}$}
\escmathcom{\INTk}{3}{$\lceil #2 \rceil_{#3}^{#1}$}
\escmathcom{\TSETR}{2}{$\Vert #1 \Vert_{#2}$}
\escmathcom{\KSETR}{2}{$\lceil #1 \rceil_{#2}$}
% Other symbols
\escmathcom{\And}{0}{\textnormal{and}}
\escmathcom{\Or}{0}{\textnormal{or}}
\escmathcom{\If}{0}{\textnormal{if}}
\escmathcom{\Then}{0}{\textnormal{then}}
\escmathcom{\EX}{0}{\textnormal{exists}}
\escmathcom{\FOR}{0}{\textnormal{for all}}
% END NEW MACROS
\def\h{\hbox}
\newcommand{\mathcom}[3]{ \newcommand{#1}[#2]{\mbox{$#3$}}}
\newcommand{\remathcom}[3]{ \renewcommand{#1}[#2]{\mbox{$#3$}}}
\newcommand{\mdef}[2]{ \newcommand{#1}{\mbox{$#2$}} }
\mathcom{\y}{0}{\ \vdash\ } % yeilds
\mathcom{\ys}{0}{\vdash_{\cal S}} % yeilds sub S
\mathcom{\yt}{0}{\vdash_{\theta}} % yeilds sub theta
\mathcom{\absurd}{0}{\mathbf{f}} % absurdity
\mathcom{\imp}{0}{\ \rightarrow\ } % implication arrow
\mathcom{\con}{0}{\ \wedge\ } % conjunction
\mathcom{\dis}{0}{\ \vee\ } % disjunction
\mathcom{\n}{0}{\neg} % negation
\mathcom{\dimp}{0}{\ \leftrightarrow\ } % mat equiv
\mathcom{\corresponds}{0}{\ \Lleftarrow\! \! \Rrightarrow\ }
%%\mathcom{\th}{0}{\theta} % theta
\mathcom{\A}{0}{\forall} % universal quantifier
\mathcom{\E}{0}{\exists} % existential quant
\mathcom{\Dec}{1}{{\cal D}(#1)} % D(#1)
\mathcom{\elt}{0}{\in}
\mathcom{\tuple}{1}{\langle #1 \rangle}
% \mathcom{\equivdef}{0}{\equiv_{\mbox{\em \tiny def}}}
% \mathcom{\eqdef}{0}{=_{\mbox{\em \tiny def}}}
\def\equivdef{\mathrel{\ \equiv_{\mbox{\em \tiny
def}}\ }}
\def\eqdef{\mathrel{\ =_{\mbox{\em \tiny def}}\ }}
\newtheorem{Rule}{Rule}
\newtheorem{Lemma}{Lemma}
\newtheorem{Theorem}{Theorem}
% Redeclaration of symbols for intuitionistic logic
% see Diller p.126
\def\ineg{\mathop\sim}
\def\iimp{\mathbin\Rightarrow}
\def\iiff{\mathbin\Leftrightarrow}
% new symbols from amssymb
%\def\iimp{\mathbin\rightarrowtail}
%\def\iiff{\mathbin\leftrightsquigarrow}
\def\icon{\mathbin\curlywedge}
\def\idis{\mathbin\curlyvee}
%Definitions for RCC inserts
\newcommand{\notch}{\Longrightarrow\kern-16pt{/}\ \ \ }
\newcommand{\ch}{\Longrightarrow}
\newcommand{\pr}[1]{\mbox{\sf #1}}
\newcommand{\ov}[1]{\overline{#1}}
\newcommand{\void}[0]{\emptyset}
% RCC relations
\mathcom{\C}{0}{\pr{C}}
\remathcom{\P}{0}{\pr{P}}
\remathcom{\O}{0}{\pr{O}}
\mathcom{\PO}{0}{\pr{PO}}
\mathcom{\PP}{0}{\pr{PP}}
\mathcom{\NTPP}{0}{\pr{NTPP}}
\mathcom{\NTPPI}{0}{\pr{NTPP}^{-1}}
\mathcom{\TPP}{0}{\pr{TPP}}
\mathcom{\TPPI}{0}{\pr{TPP}^{-1}}
\mathcom{\TP}{0}{\pr{TP}}
\mathcom{\NTP}{0}{\pr{NTP}}
\mathcom{\NTPi}{0}{\pr{NTPi}}
\mathcom{\EC}{0}{\pr{EC}}
\mathcom{\DC}{0}{\pr{DC}}
\mathcom{\DR}{0}{\pr{DR}}
\mathcom{\EQ}{0}{\pr{EQ}}
\mathcom{\CG}{0}{\pr{CG}}
\mathcom{\TC}{0}{\pr{TC}}
\mathcom{\NTC}{0}{\pr{NTC}}
\mathcom{\Pin}{0}{\pr{Pi}} % \Pi is Greek letter
\mathcom{\PPi}{0}{\pr{PPi}}
\mathcom{\NTPPi}{0}{\pr{NTPPi}}
\mathcom{\OP}{0}{\pr{OP}}
\mathcom{\conv}{0}{\pr{conv}}
\mathcom{\rsum}{0}{\pr{sum}}
\mathcom{\rdiff}{0}{\pr{diff}}
\mathcom{\rcompl}{0}{\pr{compl}}
\mathcom{\rprod}{0}{\pr{prod}}
\mathcom{\cp}{0}{\pr{cp}}
\mathcom{\Us}{0}{\pr{Us}}
\mathcom{\us}{0}{\pr{u}}
\mathcom{\NULL}{0}{\pr{NULL}}
\mathcom{\rnull}{0}{\emptyset}
\mathcom{\CONV}{0}{\pr{CONV}}
\mathcom{\CON}{0}{\pr{CON}}
% Adaptations for new latex compatibility
\renewcommand{\Box}{\square}
\def\cal{\mathcal}
% meta language in definitions etc
\mathcom{\ml}{1}{\;\;\;\; \mbox{#1} \;\;\;\;}
%-- TOPLOG SYMBOLS
\mathcom{\Co}{0}{{\cal C}_{0} \ }
\mathcom{\CoX}{0}{{\cal C}_{0}}
\mathcom{\Cop}{0}{{\cal C}_{0}^+ \ }
\mathcom{\CopX}{0}{{\cal C}_{0}^+}
\mathcom{\mcop}{0}{\models_{C_o^+}}
\mathcom{\Lop}{0}{{\cal L}_{0}^+ \ }
\mathcom{\LopX}{0}{{\cal L}_{0}^+}
\def\mlo{\models_{{\mathcal L}_0}}
\def\mlop{\models_{{\mathcal L}_0^+}}
\mathcom{\Ci}{0}{{\cal C}_{1} \ }
\mathcom{\CiX}{0}{{\cal C}_{1}}
\mathcom{\Io}{0}{{\cal I}_{0} \ }
\mathcom{\IoX}{0}{{\cal I}_{0}}
\mathcom{\Iop}{0}{{\cal I}_{0}^+ \ }
\mathcom{\IopX}{0}{{\cal I}_{0}^+}
%%\mathcom{\inter}{1}{\langle #1 \rangle}
\mathcom{\inter}{1}{i( #1 )}
\newfont{\myssfont}{cmss12}
\mathcom{\Maps}{2}{\, _{#1}\!\!\!\rightleftharpoons^{#2} \ }
\mathcom{\CotoST}{0}{\Maps{C_0}{ST}}
\mathcom{\CtoST}{0}{\Maps{C\,}{ST}}
\mathcom{\IotoST}{0}{\Maps{I_0}{ST}}
\mathcom{\uni}{0}{\cal U \, }
\mathcom{\uniX}{0}{\cal U}
\mathcom{\U}{0}{\cal U}
\mathcom{\eu}{0}{\,=\,\uni}
\mathcom{\ol}{1}{\overline{#1}}
\mathcom{\Lsse}{0}{{\cal L}_{sse}}
\mathcom{\Lssei}{0}{{\cal L}_{ssei}}
\mathcom{\Luse}{0}{{\cal L}_{use}}
\mathcom{\Lusei}{0}{{\cal L}_{usei}}
\mathcom{\disdots}{0}{\dis\!\!\!\ldots\!\!\dis}
\mathcom{\condots}{0}{\con\ldots\con}
%% Miscelleneous
% Enclose arguments in square double brackets to
% refer to semantic value of an expression
\def\semvalue#1{[\![#1]\!]}
\def\forces{\mathop{\setbox0=\hbox{$\vdash$}\ \rule{0.04em}{1\ht0}\mkern1.5mu\box0}}
\mathcom{\hence}{0}{\Longrightarrow \hspace{2em}}
\def\sliderule{\centerline{\rule{4in}{1mm}}}
\def\Cbox{\mathop{\square\mkern-10mu
\mbox{\raise0.45ex\hbox{\tiny\sf C}}
\mkern2mu
}
}
\def\letterbox#1{\mathop{\square\mkern-10mu
\mbox{\raise0.2ex\hbox{\small\sf #1}}
\mkern2mu
}
}
%\def\tBox{\letterbox{\lower0.4ex\hbox{t}}}
\def\sBox{\letterbox{s}}
\def\tBox{\letterbox{t}}
\def\overstrike#1#2{\mathop{%
\setbox1=\hbox{$#1$}%
\setbox2=\hbox{$#2$}%
\ifdim 1\wd1<1\wd2 %
{ \rlap{\mbox{\kern0.5\wd2\kern-0.5\wd1 \box1}} \box2 }
\else { \rlap{\mbox{$#1$}}
\rlap{\mbox{\kern0.5\wd1\kern-0.5\wd2 \box2}}
\phantom{#1} }
\fi }}
\def\rbox{\boxminus}
\def\rdia{\overstrike{\Diamond}{-}}
\def\cdia{\overstrike{\Diamond}{\rule{0.04em}{1.5ex}}}
\def\cbox{\inbox{\rule{0.04em}{1.6ex}}}
\def\cbox{\mathop{\setbox0=\hbox{$\square$}
\overstrike{\square}{\hbox{\rule{0.04em}{1\ht0}}}
}}
\def\diaplus{\overstrike{\Diamond}{+}}
%% Make a modal box with a symbol centred inside
\def\inbox#1{\mathop{\setbox0=\hbox{$\square$}%
\setbox1=\hbox{#1}%
\rlap{\hbox{$\square$}}
\rlap{\mbox{\kern0.5\wd0\kern-0.5\wd1%
\box1}}%
\phantom{\square}}}
\def\ibox{\mathop{\square\mkern-10mu
\mbox{\raise0.45ex\hbox{\tiny\em i}}
\mkern7mu
}
}
\def\cdiamond{\mathop{\Diamond\mkern-12.7mu
\mbox{\raise0.4ex\hbox{\tiny\em c}}
\mkern7mu
}
}
\def\s5box{\mathop{\square\mkern-10mu
\mbox{\raise0.45ex\hbox{\tiny 5}}
\mkern7mu
}
}
\def\Fbox{\mathop{\square\mkern-11mu
\mbox{\raise0.45ex\hbox{\tiny \bf F}}
\mkern2mu
}
}
\def\Box{\mathop\square}
\def\Diamond{\mathop\lozenge}
\def\bigI{\mathop{%
\hbox{%
%%
\def\thickness{1pt}%
\def\width{6pt}%
\def\height{0.6em}%
\def\gap{0.15em}%
%%
\dimen0=\thickness%
\divide\dimen0 by 2%
\dimen1=\width%
\divide\dimen1 by 2%
%%
\kern\gap%
\rlap{\vrule width\width height\thickness depth0pt}%
\rlap{\kern\dimen1 \kern-\dimen0%
\vrule width\thickness height\height depth0pt}%
\raise\height\hbox{\vrule width\width height\thickness depth0pt}%
\kern\gap}}}
\def\mconv{\mathop{%
\mbox{\raise0.35ex\hbox{$\scriptstyle\bigcirc$}}
}
}
\def\mpconv{\circleddash}
\def\ri{\mathclose{\raise1ex\hbox{$\smile$}}}
\def\eqtag#1{\eqno ({\bf #1})}
\def\mc:#1{\hbox{${\mathcal{#1}}$}}
\def\mb#1{{\mathbf{#1}}}
\def\ifff{\qquad \hbox{if and only if} \qquad}
\def\d{\delta}
\def\QED{$\blacksquare$}
\def\epsrcgrant{GR/K65041}
\def\VUGgrant{GR/M56807}
\def\Boxx{\boxtimes}
%% Force a math symbol to go into scriptsize
\def\mscriptsize#1{\hbox{\scriptsize $#1$}}
\def\mlarge#1{\hbox{\large $#1$}}
\def\boxtheorem#1#2{~\\
\centerline{\fbox{
\parbox{5in}{
\centerline{\bf #1}
#2
}}}
\vspace{1ex}}
\def\proof#1#2{
\begin{quotation}
\noindent {\bf Proof of #1:}
#2
\QED
\end{quotation}
}
\def\proofpar{\\ \hspace*{1.5em}}
%%%% ENVIRONMENTS
%% specify my list parameters
%% These can be overridden by declarations within
%% a document.
\def\mytopsep{1ex}
\def\mypartopsep{0ex}
\def\myitemsep{0.3ex}
\def\myparsep{0ex}
\def\mylistparindent{2em}
\def\myleftmargin{4.5em}
\def\mylabelwidth{4.5em}
\def\mylabelsep{1em}
\def\myitemindent{0em}
\def\setmylistparams{%
\setlength{\topsep}{\mytopsep}
\setlength{\partopsep}{\mypartopsep}
\setlength{\itemsep}{\myitemsep}
\setlength{\parsep}{\myparsep}
\setlength{\listparindent}{\mylistparindent}
\setlength{\leftmargin}{\myleftmargin}
\setlength{\labelwidth}{\mylabelwidth}
\setlength{\labelsep}{\mylabelsep}
\setlength{\itemindent}{\myitemindent}
}
\newcounter{tempvalue}
% A compact list making environment
\newenvironment{clist}
{ %\vspace{1ex}
\begin{list}
{$\bullet$}
\setmylistparams
}
{ \end{list}\addvspace{1ex}
}
% A compact list making environment
% with -- as the default item tag
\newenvironment{cdashlist}
{ %\vspace{1ex}
\begin{list}
{--}
{\setlength{\topsep}{0.2ex}
\setlength{\partopsep}{0ex}
\setlength{\itemsep}{0.3ex}
\setlength{\parsep}{0ex}
\setlength{\listparindent}{2em}
}
}
{ \end{list}\addvspace{1ex}
}
% compact list with wide labels for item tags
\newenvironment{taglist}[1]
{ %\vspace{1ex}
\begin{list}
{$\bullet$}
{\setlength{\topsep}{0.2ex}
\setlength{\partopsep}{0ex}
\setlength{\itemsep}{0.3ex}
\setlength{\parsep}{0ex}
\setlength{\listparindent}{2em}
\setlength{\leftmargin}{#1}
\setlength{\labelwidth}{#1}
%\addtolength{\labelwidth}{-1em}
\setlength{\labelsep}{0em}
}
}
{ \end{list}\addvspace{1ex}
}
\newcounter{cenumcount}
\newenvironment{cenum}
{ %\vspace{1ex}
\begin{list}
{\arabic{cenumcount}.}
{\usecounter{cenumcount}
\setlength{\topsep}{0.2ex}
\setlength{\partopsep}{0ex}
\setlength{\itemsep}{0.3ex}
\setlength{\parsep}{0ex}
\setlength{\listparindent}{2em}
}
}
{ \end{list}\addvspace{1ex}
}
%% Labelled list environment
\newenvironment{llist}[1]{%
\newcounter{#1}
\begin{list}{{\bf #1\arabic{#1}})\hspace{1em}}{\usecounter{#1}}
}
{\end{list}}
%% Labelled list continued
%% (assumes counter already exists)
\newenvironment{llistcont}[1]{%
\setcounter{tempvalue}{\value{#1}}
\begin{list}{{\bf #1\arabic{#1}})\hspace{1em}}{%
\usecounter{#1}
\setcounter{#1}{\value{tempvalue}}
}
}
{\end{list}}
%%% compact versions of llist and llistcont
\newenvironment{cllist}[1]{%
\newcounter{#1}
\begin{list}{{\bf #1\arabic{#1}})}
{ \usecounter{#1}
\setmylistparams
}
}
{\end{list}}
%% Labelled list continued
%% (assumes counter already exists)
\newenvironment{cllistcont}[1]{%
\setcounter{tempvalue}{\value{#1}}
\begin{list}{{\bf #1\arabic{#1}})}{%
\usecounter{#1}
\setcounter{#1}{\value{tempvalue}}
\setmylistparams
}
}
{\end{list}}
%% Define a labelled list type
%% #1 name of control sequence for the list type
%% #2 prefix for numbering
\def\llisttype#1#2{%
\newcounter{#2}
\expandafter\def\csname #1list\endcsname##1{%
\begin{cllistcont}{#2}
##1
\end{cllistcont}}
\expandafter\def\csname #1\endcsname##1{%
\begin{cllistcont}{#2}
\item
##1
\end{cllistcont}}
}
\def\litem#1#2{%
\begin{clist}
\item[{\bf #1})]
#2
\end{clist}}
\newenvironment{chapabst}%
{\begin{quotation}\small\noindent }{\end{quotation}}
% Split line displayed formulae
% (not actually an environment)
\newcommand{\splitdismath}[4]{%
{\setlength{\arraycolsep}{0em}
\begin{eqnarray}
& #1 & #2 \nonumber \\
& & #3
\label{#4}
\end{eqnarray}
}
}
% Displayed equation with tabbing
\newcommand{\tabmathn}[2]
{ \begin{equation}
\vbox{
\vspace{-2ex}
\begin{tabbing}
#1
\end{tabbing}
\vspace{-3.5ex}
}
\label{#2}
\end{equation}
}
\newcommand{\displaytab}[1]
{ \begin{displaymath}
\vbox{
\vspace{-2ex}
\begin{tabbing}
#1
\end{tabbing}
\vspace{-3.5ex}
}
\end{displaymath}
}
\def\myeq#1{$$\eqalign{#1}$$}
%%% Reinstate \eqalign macros removed by Lamport
\catcode`\@=11
\def\eqalign#1{\null \,\vcenter {\openup \jot \m@th
\ialign {\strut \hfil $\displaystyle{##}$&$\displaystyle {{}##}$\hfil
\crcr #1\crcr }}\,}
\def\eqalignno#1{\displ@y \tabskip \centering
\halign to\displaywidth {\hfil $\@lign \displaystyle{##}$\tabskip \z@skip
&$\@lign \displaystyle {{}##}$\hfil \tabskip \centering
&\llap {$\@lign ##$}\tabskip \z@skip \crcr
#1\crcr }}
\def\leqalignno#1{\displ@y \tabskip \centering
\halign to\displaywidth {\hfil $\@lign \displaystyle {##}$\tabskip \z@skip
&$\@lign \displaystyle {{}##}$\hfil \tabskip \centering
&\kern -\displaywidth \rlap {$\@lign ##$}\tabskip \displaywidth \crcr
#1\crcr}}
%%% Define something like \bibliography but only records the
%%% bibfiles (does not input the bbl file)
\def\bibliographyfiles#1{%
\if@filesw
\immediate\write\@auxout{\string\bibdata{#1}}%
\fi}
%%% Define a separate command to input the bbl file.
\def\bibliographytext{%
\@input@{\jobname.bbl}}
%% Change indent space allocated by \thebibliography
%% use before \bibliography or \bibliographytext
\def\setbibindent#1{%
\let\oldthebibliography\thebibliography
\def\thebibliography##1{\oldthebibliography{#1}}
}
\catcode`\@=12
\long\def\skipover#1{}
\long\def\correction#1{\footnote{TO CORRECT: #1}}
\def\nocorrections{\long\def\correction##1{}}
\def\question#1{{\bf Question:} {\em #1} }
\long\def\todo#1{{\bf To Do:} {\em #1} }
\def\twiddle{$\sim$}
%% Macro for URLs
%% puts them in tt format and breaks line after dot if needed.
\def\urlspace{-0.5em}
\def\url#1{{\tt \urlsub#1\end}}
%\def\urldot{. \hspace{-1em}\urlsub}
\def\urldot{. \linebreak[1]\hspace\urlspace\urlsub}
\def\urlcolon{: \linebreak[1]\hspace\urlspace\hspace\urlspace\urlsub}
\def\urlslash{/ \linebreak[1]\hspace\urlspace\urlsub}
\def\urltilde{\twiddle\urlsub}
\def\urlsub#1{\ifx#1\end \let\next=\relax
\else \ifx#1.\let\next=\urldot
\else \ifx#1:\let\next=\urlcolon
\else \ifx#1/\let\next=\urlslash
\else \ifx#1~\let\next=\urltilde
\else#1\let\next=\urlsub\fi\fi\fi\fi\fi\next}
% Input a file in verbatim mode (eg a program file)
\def\verbinput#1{\expandafter\begin{verbatim}\input#1}
%NB: usage: \verbinput{filename}\end{verbatim}
\def\mb#1{{\mathbf{#1}}}
%%% MACROS for SLIDES
\def\headd#1{%
\centerline{
\begin{tabular}{|c|} \hline #1 \\ \hline \end{tabular}
}
\vspace{1ex minus 1ex}
}
\def\head1#1{%
\centerline{
\large \begin{tabular}{c} #1 \end{tabular}
}
\vspace{1ex minus 1ex}
}
\def\heading#1{%
\centerline{\shadowbox{
\large \begin{tabular}{c} #1 \end{tabular}
} }
\vspace{1ex minus 1ex}
}
\def\bheading#1{%
\centerline{\shadowbox{
\large\bf \begin{tabular}{c} #1 \end{tabular}
} }
\vspace{1ex minus 1ex}
}
\def\printlandscape{\special{landscape}} % Works with dvips.
\def\printportrait{\special{portrait}}
\def\leedslogo#1{\centerline{
\psfig{file=uol.eps,width=#1} %% May look wrong in xdvi
}}
\def\titleslide#1#2{
\begin{slide*}
~
\vfill
\heading{#1}
\vfill
\begin{center}
{\large\bf Brandon Bennett}
\vspace{3ex}
Division of AI \\
School of Computer Studies \\
University of Leeds\\
Leeds LS2 9JT, England \\
{\tt brandon@scs.leeds.ac.uk} \\
\end{center}
\vfill
\centerline{
\psfig{file=uol.eps,width=0.7in} %% May look wrong in xdvi
}
\vfill
\centerline{#2}
\vfill
\end{slide*}
}
\def\nlf{\\ \mbox{} \hfill}
%%\def\fixhyphens{\usepackage[english]{babel}}
%% FIX HYPHENATION
\lefthyphenmin=2
\righthyphenmin=3
%% special commands for spell checker
\def\sic#1{#1}
\def\sico!#1!{#1}
\def\sicname#1{#1}
\def\accept#1{}
\def\acceptname#1{}
%\newenvironment{nospell}{}{}
\def\spelloff{}
\def\spellon{}
\def\ifundefined#1{\expandafter\ifx\csname#1\endcsname\relax}
\ifundefined{pdfoutput}
\def\graftype{eps}
\else
\def\graftype{png}
\fi
\def\graphic[#1]#2{\includegraphics[#1]{#2.\graftype}}
\def\dayth{\number\day\ifcase\day \or
st\or nd\or rd\or th\or th\or th\or th\or th\or th\or th\or
th\or th\or th\or th\or th\or th\or th\or th\or th\or th\or
st\or nd\or rd\or th\or th\or th\or th\or th\or th\or th\or
st\fi}
\def\monthname{\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}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End: