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Commit 6ad9c886 authored by Michael Kohlhase's avatar Michael Kohlhase
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adding textbook example and then xscaling tikz figures

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adoptions/paper-blx.bib
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@Comment{$ biblatex control file $}
@Comment{$ biblatex version 2.4 $}
@Comment{$ biblatex version 2.3 $}
Do not modify this file!
This is an auxiliary file used by the 'biblatex' package.
......@@ -7,5 +7,5 @@ This file may safely be deleted. It will be recreated as
required.
@Control{biblatex-control,
options = {2.4:0:0:1:0:0:1:1:0:1:0:0:12:1:3:1:79:+},
options = {2.3:0:0:1:0:0:1:1:0:1:0:0:12:1:3:1:79:+},
}
adoptions/paper.pdf
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adoptions/paper.tex
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......@@ -98,4 +98,5 @@
%%% End:
% LocalWords: maketitle semi-selfcontained emph prel pheno conc printbibliography
% LocalWords: setcounter tocdepth tableofcontents newpage oldparts
% LocalWords: setcounter tocdepth tableofcontents newpage oldparts flexiformal
% LocalWords: formalized
adoptions/patterns.tex
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......@@ -43,8 +43,8 @@ theorems and derived symbols (i.e. adds no axioms or primitive symbols). An esse
of $S$ then there is view $v$ between $T$ and $S$ iff there is a view between $T$ and $S'$ in the same direction. In fact, we will often talk about views \emph{modulo conservativity}
below.
\begin{wrapfigure}r{6.3cm}\vspace*{-2em}
\begin{tikzpicture}[xscale=.7]
\begin{wrapfigure}r{5.3cm}\vspace*{-2em}
\begin{tikzpicture}[xscale=.6]
%realm
\draw[realm] (-1,-1.8) rectangle (8,2.8) {};
%p1
......@@ -54,10 +54,10 @@ below.
%pn
\draw[draw=blue!40, fill=gray!10,rectangle, rounded corners, inner sep=10pt, inner ysep=20pt] (5.5,-1.5) rectangle (7.5,1.8) {};
\node (r-name) at (7.3,2.6) {$\mathit{Realm}$};
\node (p1-name) at (0.2,1.6) {$\mathit{Pillar_1}$};
\node (r-name) at (7.1,2.6) {$\mathit{Realm}$};
\node (p1-name) at (0.4,1.6) {$\mathit{Pillar_1}$};
% \node (p2-name) at (3,1.6) {$\mathit{Pillar_{\ldots}}$};
\node (p3-name) at (6.8,1.6) {$\mathit{Pillar_n}$};
\node (p3-name) at (6.6,1.6) {$\mathit{Pillar_n}$};
\node[thy] (top1) at (0.5,1) {$\top_1$};
......@@ -123,7 +123,7 @@ on others from the same realm for results, context, and support.
%I.e. every statement in the paper holds for the original definition too, but not necessarily the converse.
\begin{figure}[ht]\centering
\begin{tikzpicture}
\begin{tikzpicture}[xscale=.7]
%realm
\draw[realm] (-1,-1.7) rectangle (5,2.8) {};
%p-paper
......@@ -140,10 +140,10 @@ on others from the same realm for results, context, and support.
\node[thy] (recap) at (-3,0) {Recap};
\node[thy] (pcont) at (-3,2) {Contribution};
\node[thy] (pcont) at (-3,2) {Contrib.};
\node[thy] (top1) at (0.5,1) {$\top$};
\node[thy] (citp) at (0.5,0) {Cited Paper};
\node[thy] (citp) at (0.5,0) {CPaper};
\node[thy] (bot1) at (0.5,-1) {$\bot$};
......@@ -184,15 +184,16 @@ sub-cases depending on the relation between the recap and cited theory: \emph{eq
One situation is that of plain recaps where the relation $r$ is an inclusion into the
recap from the cited paper. Typically the include $r$ is a conservative extension of the
cited paper. For instance the ``\textsf{covers of the multiplicative group}'' from
Example \ref{ex:covers} directly uses the concept from the cited paper, but gives a
concise verbalization of its definition. This allows it to make use of the
Example \ref{ex:covers} directly uses the concept from the cited paper (\textsf{CPaper}),
but gives a concise verbalization of its definition. This allows it to make use of the
results in two other papers higher up in the pillar of the cited paper. The situation is
shown in Figure \ref{fig:rec-covers}. Note that, if $r$ is conservative, then we have a
\textbf{pillar extension} for the realm which justifies the new paper becoming part of the
realm's literature (see Figure \ref{fig:agg-covers}). It also makes $v$ exist as induced by $v_1$ modulo conservativity.
realm's literature (see Figure \ref{fig:agg-covers}). It also makes $v$ exist as induced
by $v_1$ modulo conservativity.
\begin{figure}[ht]\centering
\begin{tikzpicture}
\begin{tikzpicture}[xscale=.7]
%realm
\draw[realm] (-1,-1.7) rectangle (5,2.8) {};
%p-paper
......@@ -212,7 +213,7 @@ realm's literature (see Figure \ref{fig:agg-covers}). It also makes $v$ exist as
\node[thy] (pcont) at (-3,2) {\cn{MToCACF}};
\node[thy] (top1) at (0.5,1) {$\top$};
\node[thy] (citp) at (0.5,0) {Cited Paper};
\node[thy] (citp) at (0.5,0) {CPaper};
\node[thy] (bot1) at (0.5,-1) {$\bot$};
\node[thy] (top2) at (3.5,1) {$\top$};
......@@ -240,7 +241,7 @@ realm's literature (see Figure \ref{fig:agg-covers}). It also makes $v$ exist as
\begin{figure}[ht]\centering
\begin{tikzpicture}
\begin{tikzpicture}[xscale=.7]
%realm
\draw[realm] (-3,-3.7) rectangle (5,2.8) {};
%p1
......@@ -258,7 +259,7 @@ realm's literature (see Figure \ref{fig:agg-covers}). It also makes $v$ exist as
\node[thy] (top1) at (-0.5,1) {$\top$};
\node[thy] (tcdots1) at (0.5,-0.5) {$\cdots$};
\node[thy] (citp) at (-0.5,-2) {Cited Paper};
\node[thy] (citp) at (-0.5,-2) {CPaper};
\node[thy] (bot1) at (-0.5,-3) {$\bot$};
\node[thy] (top2) at (3.5,1) {$\top$};
......@@ -303,7 +304,7 @@ sample papers we studied.
% Moreover, examples \ref{ex:quant} and \ref{ex:calculi} also fit in this category.
\begin{figure}[ht]\centering
\begin{tikzpicture}
\begin{tikzpicture}[xscale=.7]
%realm
\draw[realm] (-1,-1.7) rectangle (5,2.8) {};
%p-paper
......@@ -323,7 +324,7 @@ sample papers we studied.
\node[thy] (pcont) at (-3,2) {\cn{ICMnets}};
\node[thy] (top1) at (0.5,1) {$\top$};
\node[thy] (citp) at (0.5,0) {Cited Paper};
\node[thy] (citp) at (0.5,0) {CPaper};
\node[thy] (bot1) at (0.5,-1) {$\bot$};
\node[thy] (top2) at (3.5,1) {$\top$};
......@@ -363,7 +364,7 @@ equivalence is ensured by $v_{from}$ and $v_{to}$ as we take into account conser
to reduce them to the $\bot$ theory.
\begin{figure}[ht]\centering
\begin{tikzpicture}
\begin{tikzpicture}[xscale=.7]
%realm
\draw[realm] (-4,-1.7) rectangle (5,2.8) {};
%p0
......@@ -382,7 +383,7 @@ to reduce them to the $\bot$ theory.
\node[thy] (pcont) at (-2.5,1) {\cn{ICMnets}};
\node[thy] (top1) at (0.5,1) {$\top$};
\node[thy] (citp) at (0.5,0) {Cited Paper};
\node[thy] (citp) at (0.5,0) {CPaper};
\node[thy] (bot1) at (0.5,-1) {$\bot$};
......@@ -435,7 +436,7 @@ for simplicity -- the aggregation is similar as for equivalence recaps, except w
realm.
\begin{figure}[ht]\centering
\begin{tikzpicture}
\begin{tikzpicture}[xscale=.7]
%realm
\draw[realm] (-1,-1.7) rectangle (5,2.8) {};
%p-paper
......@@ -510,7 +511,7 @@ implying that the semantics of the two symbols is compatible with that given in
literature (which we represent as a realm).
\begin{figure}[ht]\centering
\begin{tikzpicture}
\begin{tikzpicture}[xscale=.7]
%realm
\draw[realm] (-1,-1.7) rectangle (5,2.8) {};
%p-paper
......
adoptions/phenomena.tex
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......@@ -63,7 +63,7 @@ dissemination\footnote{\ref{md:metadata}. for referencing, \ref{md:abstract}. f
latter is mainly driven by the common ground (point \ref{md:cg}. above), which we will
analyze in more detail next.
\subsection{Common Ground/Recapitulation in Mathematical Preprints}\label{sec:cg-preprints}
\subsection{Common Ground/Recapitulation in Mathematical Research}\label{sec:cg-preprints}
To get an overview over recaps in the literature, we randomly selected 15 papers from the
new submissions to \url{http://arxiv.org/archive/math} and analyzed their structure. All
......@@ -177,13 +177,45 @@ which allows arbitrary time structures.
% \ednote{MK@MK: more, e.g. about the distinction of notations and
% differing concepts.}
\begin{newpart}{MK: re-read}
\subsection{Common Ground and Recaps in Mathematical Textbooks}
The situation in mathematical textbooks is similar in structure to that in research papers
--perhaps more pronounced. Consider the following passage from Rudin's classical
introductory textbook to Functional Analysis~\cite[p. 6f]{Rudin:fa73}.
\begin{labeledquote}\sf
\textbf{1.5 Topological spaces} A \emph{topological space} is a set $S$ in which a
collection $\tau$ of subsets (called \emph{open sets}) has been specified, with the
following properties: $S$ is open, $\emptyset$ is open, [\ldots] Such a collection is
called a \emph{topology} on $S$. [\ldots]
\end{labeledquote}
and later -- vector spaces have been recapped earlier in section 1.4:
\begin{labeledquote}\sf
\textbf{1.6 Topological vector spaces} Suppose $\tau$ is a topology on a vector space $X$
such that
\begin{compactenum}[(a)]
\item \emph{every point of $X$ is a closed set, and}
\item \emph{the vector space operations are continuous with respect to $\tau$}
\end{compactenum}
Under these conditions, $\tau$ is said to be a \emph{vector topology} on $X$, and $X$ is a
\emph{topological vector space}.
\end{labeledquote}
Note that Rudin does not directly cite the literature in these quotes, but in the preface
he mentions the vast literature on function analysis and in Appendix B he cites the
original literature for each chapter. The situation in textbooks is also different from
research articles in that textbooks -- like survey articles, and by their very nature --
do not add new knowledge or new results, but aggregate and organize the already published
ones, possibly reformulating them for a more uniform exposition. But still, one can
distinguish
\end{newpart}
\subsection{Secondary Literature: Education/Survey}
A similar effect can be observed with educational materials or survey articles, whose
concern is not to make an original contribution to the knowledge commons, but to prepare a
document that helps an individual or group study or better understand a body of already
established knowledge. Consider for instance, slides and background materials (lecture
notes, books, encyclopedias), where the slides often have telegraphic versions of the real
notes, books, encyclopaedias), where the slides often have telegraphic versions of the real
statements, which verbalize more rigorous definition.
This is illustrated in Example \ref{ex:course} which is inspired from the notes of a first
......@@ -248,4 +280,7 @@ $n$ is a natural number.
% LocalWords: relwork concl atm covers-orig labeledquote emph arr arr arr arr arr cdot
% LocalWords: exp textsf cong mnets mnets-orig multinets Ceva mathit multinet ednote th
% LocalWords: CalStai natm09 textsuperscript langle rangle subseteq mathbb infty textsc
% LocalWords: self-containedness textsc geq topalg ldots RicKor fgs13
% LocalWords: self-containedness textsc geq topalg ldots RicKor fgs13 summarizes Rudin
% LocalWords: analyze analyzed generalization generalizations generalizing Rudin's
% LocalWords: flexiformalized verbalization verbalizations emptyset extensionality
% LocalWords: emphasize organized Mizar
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