$$%% examples
\newcommand{\exGraph}{\graph_{\mathrm{ex}}}
\newcommand{\exOnto}{\onto_{\mathrm{ex}}}
\newcommand{\exMappings}{\mappings_{\mathrm{ex}}}
\newcommand{\exExtensions}{\extensions_{\mathrm{ex}}}
\newcommand{\exRule}{r_{\mathrm{ex}}}
\newcommand{\RDFSrules}{\rules_{\mathrm{RDFS}}}
%% RDF
\newcommand{\triple}[3]{(#1, #2, #3)}
\newcommand{\tuple}[1]{\langle #1 \rangle}
\newcommand{\subject}{\mathtt{s}}
\newcommand{\prop}{\mathtt{p}}
\newcommand{\object}{\mathtt{o}}
\newcommand{\blank}{\_{:}b}
\newcommand{\blankn}[1]{\_{:}#1}
\newcommand{\irin}[1]{{:}\mathrm{#1}}
\newcommand{\class}{\mathtt{c}}
\newcommand{\nsrdf}{\mathrm{rdf{:}}}
\newcommand{\nsrdfs}{\mathrm{rdfs{:}}}
\newcommand{\rdftype}{\mathrm{rdf{:}type}}
\newcommand{\rdfLiteral}{\mathrm{rdf{:}Literal}}
\newcommand{\rdfssubClassOf}{\mathrm{rdfs{:}subClassOf}}
\newcommand{\rdfssubPropertyOf}{\mathrm{rdfs{:}subPropertyOf}}
\newcommand{\rdfsdomain}{\mathrm{rdfs{:}domain}}
\newcommand{\rdfsrange}{\mathrm{rdfs{:}range}}
\newcommand{\rdfsClass}{\mathrm{rdfs{:}Class}}
\newcommand{\rdfProperty}{\mathrm{rdf{:}Property}}
\newcommand{\xsdint}{\mathrm{xsd{:}int}}
%%
\newcommand{\type}{\tau}
\newcommand{\subclass}{\prec_{sc}}
\newcommand{\subproperty}{\prec_{sp}}
\newcommand{\domain}{\hookleftarrow_{d}}
\newcommand{\range}{\hookrightarrow_{r}}
\newcommand{\rdfentailment}{\vdash_{^\mathrm{RDF}}}
\newcommand{\RDFS}[1]{\mathrm{RDFS}(#1)}
\newcommand{\aka}{a.k.a.~}
\newcommand{\etc}{etc}
\newcommand{\wrt}{w.r.t.~}
\newcommand{\st}{s.t.~}
\newcommand{\ie}{i.e.,~}
\newcommand{\eg}{e.g.,~}
\newcommand{\graph}{G}
\newcommand{\rules}{\mathcal{R}}
\newcommand{\sources}{\mathcal{S}}
\newcommand{\views}{\mathcal{V}}
\newcommand{\extensions}{\mathcal{E}}
\newcommand{\onto}{\mathcal{O}}
\newcommand{\mappings}{\mathcal{M}}
\newcommand{\modelsrdf}{\models_\rules}
\newcommand{\bgp}{P}
\newcommand{\Bl}[1]{\mathrm{Bl}(#1)}
\newcommand{\Val}[1]{\mathrm{Val}(#1)}
\newcommand{\Var}[1]{\mathrm{Var(#1)}}
\newcommand{\ext}[1]{\mathrm{ext}(#1)}
\newcommand{\cert}{\mathrm{cert}}
\newcommand{\ans}{\mathrm{ans}}
\newcommand{\query}{\leftarrow}
\newcommand{\body}[1]{\textrm{body}(#1)}
\newcommand{\head}[1]{\textrm{head}(#1)}
\newcommand{\cs}{\mathrm{cs}}
\newcommand{\lcs}{\mathrm{lcs}}
\newcommand{\cl}{\mathrm{cl}}
\newcommand{\lua}{\mathrm{lua}}
\newcommand{\lur}{\mathrm{lur}}
\newtheorem{lemma}{Lemma}
\newtheorem{definition}{Definition}
\newtheorem{problem}{Problem}
\newtheorem{property}{Property}
\newtheorem{corollary}{Corollary}
\newtheorem{example}{Example}
\newtheorem{theorem}{Theorem}
\newcommand{\URIs}{\mathscr U}
\newcommand{\IRIs}{\mathscr I}
\newcommand{\BNodes}{\mathscr B}
\newcommand{\Literals}{\mathscr L}
\newcommand{\Variables}{\mathscr V}
% DB
\newcommand{\CQ}{\ensuremath{\mathtt{CQ}}\xspace}
\newcommand{\UCQ}{\ensuremath{\mathtt{UCQ}}\xspace}
\newcommand{\SQL}{\ensuremath{\mathtt{SQL}}\xspace}
\newcommand{\rel}[1]{\mathsf{#1}}
% Cost model
\newcommand{\cans}[1]{|#1|_t}
\newcommand{\cref}[1]{|#1|_r}
\newcommand{\db}{\mathtt{db}}
% DL
\newcommand{\cn}{\ensuremath{N_{C}}\xspace}
\newcommand{\rn}{\ensuremath{N_{R}}\xspace}
\newcommand{\inds}{\ensuremath{N_{I}}\xspace}
\newcommand{\ainds}{\ensuremath{\mathrm{Ind}}\xspace}
\newcommand{\funct}{\mathit{funct} \ }
\newcommand{\KB}{\mathcal{K}\xspace}
\newcommand{\dlr}{DL-Lite$_{\mathcal{R}}$\xspace}
% Logics
\newcommand{\FOL}{\ensuremath{\mathtt{FOL}}\xspace}
\newcommand{\datalog}{\ensuremath{\mathtt{Datalog}}\xspace}
\newcommand{\dllite}{DL-Lite\xspace}
\newcommand{\true}{\mathrm{true}}
\newcommand{\false}{\mathrm{false}}
\newcommand{\dis}{\mathtt{dis}}
\newcommand{\vars}[1]{\ensuremath{\mathrm{vars}(#1)}}
%\newcommand{\terms}[1]{\ensuremath{\mathrm{terms}(#1)}}
%math
\renewcommand{\phi}{\varphi}
\newcommand\eqdef{\stackrel{\mathclap{\normalfont\mbox{def}}}{=}}
\newcommand\restr[2]{#1_{|#2}}
\newcommand{\ontoBody}[1]{\mathrm{body}_\onto(#1)}
%proof of the rewriting theorem
\newcommand{\rdfGraph}{\graph^{\mappings}_{\extensions}}
\newcommand\systemGraph{\graph^{\mappings \cup \mappings^{\text{STD}}_\onto}_{\extensions \cup \extensions_\onto}}
\newcommand\viewsGraph{\graph^{\mappings^{\rules,\onto} \cup \mappings^{\text{STD}}_\onto}_{\extensions \cup \extensions_\onto}}
\newcommand{\standMappings}{\mappings^{\text{STD}}_\onto}
\newcommand{\reminder}[1]{[\vadjust{\vbox to0pt{\vss\hbox to0pt{\hss{\Large $\Longrightarrow$}}}}{{\textsf{\small #1}}}]}
%\newcommand{\FG}[1]{\textcolor{blue}{\reminder{FG:~#1}}}
\newcommand{\extVersion}{false}
\newcommand{\printIfExtVersion}[2]
{
\ifthenelse{\equal{\extVersion}{true}}{#1}{}
\ifthenelse{\equal{\extVersion}{false}}{#2}{}
}
\newcommand{\bda}{\true}
\newcommand{\ifBDA}[2]%
{%
\ifthenelse{\equal{\bda}{true}}{#1}{}%
\ifthenelse{\equal{\bda}{false}}{#2}{}%
}
%%% Local Variables:
%%% TeX-master: "paper"
%%% End:
$$