% == 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: 
