From 237d62bda61e206c29f2a7e73a9a81960869bef8 Mon Sep 17 00:00:00 2001
From: Francisco Coelho <fc@uevora.pt>
Date: Wed, 9 Nov 2022 16:49:40 +0000
Subject: [PATCH] Further rewriting of 00_PASP
---
text/00_PASP.aux | 122 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++---------------------------------------------------------------
text/00_PASP.fdb_latexmk | 19 +++++++++----------
text/00_PASP.fls | 4 ----
text/00_PASP.log | 169 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++--------------------------------------------------------------------------------------
text/00_PASP.nav | 73 +++++++++++++++++++++++++++++++++++--------------------------------------
text/00_PASP.out | 13 ++++++-------
text/00_PASP.pdf | Bin 92937 -> 0 bytes
text/00_PASP.snm | 14 +++++++-------
text/00_PASP.synctex.gz | Bin 83177 -> 0 bytes
text/00_PASP.tex | 290 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++-----------------------------------------------------------------------------------------------------------------------------------
text/00_PASP.toc | 11 +++++------
text/00_PASP.xdv | Bin 214680 -> 0 bytes
12 files changed, 363 insertions(+), 352 deletions(-)
diff --git a/text/00_PASP.aux b/text/00_PASP.aux
index ff189b2..9f6f3eb 100644
--- a/text/00_PASP.aux
+++ b/text/00_PASP.aux
@@ -51,119 +51,115 @@
\@writefile{nav}{\headcommand {\slideentry {1}{0}{8}{9/9}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {9}{9}}}
\HyPL@Entry{9<</P(\376\377\0001\0000)>>}
-\@writefile{toc}{\beamer@sectionintoc {2}{Motivation}{10}{0}{2}}
-\@writefile{nav}{\headcommand {\beamer@sectionpages {2}{9}}}
-\@writefile{nav}{\headcommand {\beamer@subsectionpages {2}{9}}}
-\@writefile{nav}{\headcommand {\sectionentry {2}{Motivation}{10}{Motivation}{0}}}
-\@writefile{nav}{\headcommand {\slideentry {2}{0}{1}{10/10}{}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {1}{0}{9}{10/10}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {10}{10}}}
\HyPL@Entry{10<</P(\376\377\0001\0001)>>}
-\@writefile{nav}{\headcommand {\slideentry {2}{0}{2}{11/11}{}{0}}}
+\@writefile{toc}{\beamer@sectionintoc {2}{Extending Probability to Samples}{11}{0}{2}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {2}{10}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {2}{10}}}
+\@writefile{nav}{\headcommand {\sectionentry {2}{Extending Probability to Samples}{11}{Extending Probability to Samples}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{1}{11/11}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {11}{11}}}
\HyPL@Entry{11<</P(\376\377\0001\0002)>>}
-\@writefile{toc}{\beamer@sectionintoc {3}{Resolution}{12}{0}{3}}
-\@writefile{nav}{\headcommand {\beamer@sectionpages {10}{11}}}
-\@writefile{nav}{\headcommand {\beamer@subsectionpages {10}{11}}}
-\@writefile{nav}{\headcommand {\sectionentry {3}{Resolution}{12}{Resolution}{0}}}
-\@writefile{nav}{\headcommand {\slideentry {3}{0}{1}{12/12}{}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{2}{12/12}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {12}{12}}}
\HyPL@Entry{12<</P(\376\377\0001\0003)>>}
-\@writefile{nav}{\headcommand {\slideentry {3}{0}{2}{13/13}{}{0}}}
+\newlabel{prop:lucases}{{13}{13}{Extending Probability to Samples}{Doc-Start}{}}
+\@writefile{snm}{\beamer@slide {prop:lucases}{13}}
+\newlabel{prop:lucases.a}{{1}{13}{Extending Probability to Samples}{Doc-Start}{}}
+\@writefile{snm}{\beamer@slide {prop:lucases.a}{13}}
+\newlabel{prop:lucases.b}{{2}{13}{Extending Probability to Samples}{Doc-Start}{}}
+\@writefile{snm}{\beamer@slide {prop:lucases.b}{13}}
+\newlabel{prop:lucases.c}{{3}{13}{Extending Probability to Samples}{Doc-Start}{}}
+\@writefile{snm}{\beamer@slide {prop:lucases.c}{13}}
+\newlabel{prop:lucases.d}{{4}{13}{Extending Probability to Samples}{Doc-Start}{}}
+\@writefile{snm}{\beamer@slide {prop:lucases.d}{13}}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{3}{13/13}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {13}{13}}}
\HyPL@Entry{13<</P(\376\377\0001\0004)>>}
-\newlabel{prop:lucases}{{14}{14}{Resolution}{Doc-Start}{}}
-\@writefile{snm}{\beamer@slide {prop:lucases}{14}}
-\newlabel{prop:lucases.a}{{1}{14}{Resolution}{Doc-Start}{}}
-\@writefile{snm}{\beamer@slide {prop:lucases.a}{14}}
-\newlabel{prop:lucases.b}{{2}{14}{Resolution}{Doc-Start}{}}
-\@writefile{snm}{\beamer@slide {prop:lucases.b}{14}}
-\newlabel{prop:lucases.c}{{3}{14}{Resolution}{Doc-Start}{}}
-\@writefile{snm}{\beamer@slide {prop:lucases.c}{14}}
-\newlabel{prop:lucases.d}{{4}{14}{Resolution}{Doc-Start}{}}
-\@writefile{snm}{\beamer@slide {prop:lucases.d}{14}}
-\@writefile{nav}{\headcommand {\slideentry {3}{0}{3}{14/14}{}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{4}{14/14}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {14}{14}}}
\HyPL@Entry{14<</P(\376\377\0001\0005)>>}
-\@writefile{nav}{\headcommand {\slideentry {3}{0}{4}{15/15}{}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{5}{15/15}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {15}{15}}}
\HyPL@Entry{15<</P(\376\377\0001\0006)>>}
\@writefile{snm}{\beamer@slide {def:w.inconsistent}{16}}
-\newlabel{def:w.inconsistent}{{2}{16}{Resolution}{Doc-Start}{}}
+\newlabel{def:w.inconsistent}{{2}{16}{Extending Probability to Samples}{Doc-Start}{}}
\@writefile{snm}{\beamer@slide {eq:prob.sm}{16}}
-\newlabel{eq:prob.sm}{{3}{16}{Resolution}{Doc-Start}{}}
+\newlabel{eq:prob.sm}{{3}{16}{Extending Probability to Samples}{Doc-Start}{}}
\@writefile{snm}{\beamer@slide {def:w.disj}{16}}
-\newlabel{def:w.disj}{{4}{16}{Resolution}{Doc-Start}{}}
+\newlabel{def:w.disj}{{4}{16}{Extending Probability to Samples}{Doc-Start}{}}
\@writefile{snm}{\beamer@slide {def:w.conj}{16}}
-\newlabel{def:w.conj}{{5}{16}{Resolution}{Doc-Start}{}}
+\newlabel{def:w.conj}{{5}{16}{Extending Probability to Samples}{Doc-Start}{}}
\@writefile{snm}{\beamer@slide {def:w.empty}{16}}
-\newlabel{def:w.empty}{{6}{16}{Resolution}{Doc-Start}{}}
-\@writefile{snm}{\beamer@slide {eq:def.prob}{16}}
-\newlabel{eq:def.prob}{{7}{16}{Resolution}{Doc-Start}{}}
-\@writefile{snm}{\beamer@slide {eq:def.prob.event}{16}}
-\newlabel{eq:def.prob.event}{{8}{16}{Resolution}{Doc-Start}{}}
-\@writefile{nav}{\headcommand {\slideentry {3}{0}{5}{16/16}{}{0}}}
+\newlabel{def:w.empty}{{6}{16}{Extending Probability to Samples}{Doc-Start}{}}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{6}{16/16}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {16}{16}}}
\HyPL@Entry{16<</P(\376\377\0001\0007)>>}
-\@writefile{toc}{\beamer@sectionintoc {4}{Cases \& Examples}{17}{0}{4}}
-\@writefile{nav}{\headcommand {\beamer@sectionpages {12}{16}}}
-\@writefile{nav}{\headcommand {\beamer@subsectionpages {12}{16}}}
-\@writefile{nav}{\headcommand {\sectionentry {4}{Cases \& Examples}{17}{Cases \& Examples}{0}}}
-\@writefile{nav}{\headcommand {\slideentry {4}{0}{1}{17/17}{}{0}}}
+\@writefile{snm}{\beamer@slide {eq:def.prob}{17}}
+\newlabel{eq:def.prob}{{7}{17}{Extending Probability to Samples}{Doc-Start}{}}
+\@writefile{snm}{\beamer@slide {eq:def.prob.event}{17}}
+\newlabel{eq:def.prob.event}{{8}{17}{Extending Probability to Samples}{Doc-Start}{}}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{7}{17/17}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {17}{17}}}
\HyPL@Entry{17<</P(\376\377\0001\0008)>>}
-\@writefile{toc}{\beamer@subsectionintoc {4}{1}{Programs with disjunctive heads}{18}{0}{4}}
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-\@writefile{nav}{\headcommand {\beamer@subsectionentry {0}{4}{1}{18}{Programs with disjunctive heads}}}
-\@writefile{nav}{\headcommand {\slideentry {4}{1}{1}{18/18}{Programs with disjunctive heads}{0}}}
+\@writefile{toc}{\beamer@sectionintoc {3}{Cases \& Examples}{18}{0}{3}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {11}{17}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {11}{17}}}
+\@writefile{nav}{\headcommand {\sectionentry {3}{Cases \& Examples}{18}{Cases \& Examples}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{0}{1}{18/18}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {18}{18}}}
\HyPL@Entry{18<</P(\376\377\0001\0009)>>}
-\@writefile{nav}{\headcommand {\slideentry {4}{1}{2}{19/19}{Programs with disjunctive heads}{0}}}
+\@writefile{toc}{\beamer@subsectionintoc {3}{1}{Programs with disjunctive heads}{19}{0}{3}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {18}{18}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionentry {0}{3}{1}{19}{Programs with disjunctive heads}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{1}{1}{19/19}{Programs with disjunctive heads}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {19}{19}}}
\HyPL@Entry{19<</P(\376\377\0002\0000)>>}
-\@writefile{nav}{\headcommand {\slideentry {4}{1}{3}{20/20}{Programs with disjunctive heads}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{1}{2}{20/20}{Programs with disjunctive heads}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {20}{20}}}
\HyPL@Entry{20<</P(\376\377\0002\0001)>>}
-\@writefile{nav}{\headcommand {\slideentry {4}{1}{4}{21/21}{Programs with disjunctive heads}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{1}{3}{21/21}{Programs with disjunctive heads}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {21}{21}}}
\HyPL@Entry{21<</P(\376\377\0002\0002)>>}
-\@writefile{nav}{\headcommand {\slideentry {4}{1}{5}{22/22}{Programs with disjunctive heads}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{1}{4}{22/22}{Programs with disjunctive heads}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {22}{22}}}
\HyPL@Entry{22<</P(\376\377\0002\0003)>>}
-\@writefile{toc}{\beamer@subsectionintoc {4}{2}{Non-stratified programs}{23}{0}{4}}
-\@writefile{nav}{\headcommand {\beamer@subsectionpages {18}{22}}}
-\@writefile{nav}{\headcommand {\beamer@subsectionentry {0}{4}{2}{23}{Non-stratified programs}}}
-\@writefile{nav}{\headcommand {\slideentry {4}{2}{1}{23/23}{Non-stratified programs}{0}}}
+\@writefile{toc}{\beamer@subsectionintoc {3}{2}{Non-stratified programs}{23}{0}{3}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {19}{22}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionentry {0}{3}{2}{23}{Non-stratified programs}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{2}{1}{23/23}{Non-stratified programs}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {23}{23}}}
\HyPL@Entry{23<</P(\376\377\0002\0004)>>}
-\@writefile{nav}{\headcommand {\slideentry {4}{2}{2}{24/24}{Non-stratified programs}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{2}{2}{24/24}{Non-stratified programs}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {24}{24}}}
\HyPL@Entry{24<</P(\376\377\0002\0005)>>}
-\@writefile{nav}{\headcommand {\slideentry {4}{2}{3}{25/25}{Non-stratified programs}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{2}{3}{25/25}{Non-stratified programs}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {25}{25}}}
\HyPL@Entry{25<</P(\376\377\0002\0006)>>}
-\@writefile{nav}{\headcommand {\slideentry {4}{2}{4}{26/26}{Non-stratified programs}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{2}{4}{26/26}{Non-stratified programs}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {26}{26}}}
\HyPL@Entry{26<</P(\376\377\0002\0007)>>}
-\@writefile{nav}{\headcommand {\slideentry {4}{2}{5}{27/27}{Non-stratified programs}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{2}{5}{27/27}{Non-stratified programs}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {27}{27}}}
\HyPL@Entry{27<</P(\376\377\0002\0008)>>}
-\@writefile{toc}{\beamer@sectionintoc {5}{Conclusions}{28}{0}{5}}
-\@writefile{nav}{\headcommand {\beamer@sectionpages {17}{27}}}
+\@writefile{toc}{\beamer@sectionintoc {4}{Conclusions}{28}{0}{4}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {18}{27}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {23}{27}}}
-\@writefile{nav}{\headcommand {\sectionentry {5}{Conclusions}{28}{Conclusions}{0}}}
-\@writefile{nav}{\headcommand {\slideentry {5}{0}{1}{28/28}{}{0}}}
+\@writefile{nav}{\headcommand {\sectionentry {4}{Conclusions}{28}{Conclusions}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {4}{0}{1}{28/28}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {28}{28}}}
\HyPL@Entry{28<</P(\376\377\0002\0009)>>}
-\@writefile{nav}{\headcommand {\slideentry {5}{0}{2}{29/29}{}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {4}{0}{2}{29/29}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {29}{29}}}
\HyPL@Entry{29<</P(\376\377\0003\0000)>>}
\@writefile{nav}{\headcommand {\beamer@sectionpages {28}{29}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {28}{29}}}
-\@writefile{nav}{\headcommand {\sectionentry {6}{ASP \& related definitions}{30}{ASP \& related definitions}{0}}}
-\@writefile{nav}{\headcommand {\slideentry {6}{0}{1}{30/30}{}{0}}}
+\@writefile{nav}{\headcommand {\sectionentry {5}{ASP \& related definitions}{30}{ASP \& related definitions}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {5}{0}{1}{30/30}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {30}{30}}}
\HyPL@Entry{30<</P(\376\377\0003\0001)>>}
-\@writefile{nav}{\headcommand {\slideentry {6}{0}{2}{31/31}{}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {5}{0}{2}{31/31}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {31}{31}}}
\@writefile{nav}{\headcommand {\beamer@partpages {1}{31}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {30}{31}}}
diff --git a/text/00_PASP.fdb_latexmk b/text/00_PASP.fdb_latexmk
index 042a539..28e241d 100644
--- a/text/00_PASP.fdb_latexmk
+++ b/text/00_PASP.fdb_latexmk
@@ -1,10 +1,10 @@
# Fdb version 3
-["xdvipdfmx"] 1667935664 "00_PASP.xdv" "00_PASP.pdf" "00_PASP" 1667935664
- "00_PASP.xdv" 1667935663 214680 71a3fe8c0e42560f8631e0d09f4181a7 "xelatex"
+["xdvipdfmx"] 1668012215 "00_PASP.xdv" "00_PASP.pdf" "00_PASP" 1668012216
+ "00_PASP.xdv" 1668012215 203892 0858b8d4b4e7e8aa8085e0bea6b8815a "xelatex"
(generated)
"00_PASP.pdf"
-["xelatex"] 1667935657 "/home/fc/sci/projetos/zugzwang/text/00_PASP.tex" "00_PASP.xdv" "00_PASP" 1667935664
- "/home/fc/sci/projetos/zugzwang/text/00_PASP.tex" 1667935656 32020 e7e67df128d9c518e87afbb7c6491ef3 ""
+["xelatex"] 1668012209 "/home/fc/sci/projetos/zugzwang/text/00_PASP.tex" "00_PASP.xdv" "00_PASP" 1668012216
+ "/home/fc/sci/projetos/zugzwang/text/00_PASP.tex" 1668012208 32880 d2ff92ff8b2ef9e5a1bd016ddcdcb92a ""
"/usr/share/texmf-dist/fonts/map/fontname/texfonts.map" 1650183167 3524 cb3e574dea2d1052e39280babc910dc8 ""
"/usr/share/texmf-dist/fonts/tfm/adobe/zapfding/pzdr.tfm" 1650183167 1528 f853c4d1b4e0550255e02831fdc8496f ""
"/usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1650183167 1004 54797486969f23fa377b128694d548df ""
@@ -32,7 +32,6 @@
"/usr/share/texmf-dist/fonts/tfm/public/lm/ec-lmss10.tfm" 1650183167 11176 53ebf7a171df1f9447b387b178768bb5 ""
"/usr/share/texmf-dist/fonts/tfm/public/lm/ec-lmss12.tfm" 1650183167 11232 955a7245396175d9219648eadc654ac9 ""
"/usr/share/texmf-dist/fonts/tfm/public/lm/ec-lmss8.tfm" 1650183167 11180 705632ac6b4fb69204ad970192cdf4e5 ""
- "/usr/share/texmf-dist/fonts/tfm/public/lm/ec-lmssbo10.tfm" 1650183167 11304 1bf3f99c327bf3c434fc66d6737a89a2 ""
"/usr/share/texmf-dist/fonts/tfm/public/lm/ec-lmssbx10.tfm" 1650183167 11168 06d87f5698fd1b642d96449b7c8d90b0 ""
"/usr/share/texmf-dist/fonts/tfm/public/lm/ec-lmsso10.tfm" 1650183167 11316 701b7748a8cc1abea04b4bcc027674ae ""
"/usr/share/texmf-dist/fonts/tfm/public/lm/ec-lmsso8.tfm" 1650183167 11312 6908420b41cb9ad797e206f7391721ea ""
@@ -226,11 +225,11 @@
"/usr/share/texmf-dist/tex/latex/xcolor/xcolor.sty" 1650183167 56029 3f7889dab51d620aa43177c391b7b190 ""
"/usr/share/texmf-dist/web2c/texmf.cnf" 1650183167 39911 2da6c67557ec033436fe5418a70a8a61 ""
"/var/lib/texmf/web2c/xetex/xelatex.fmt" 1667607223 5825155 acc75abcaf8e6f881414fa8770610f6c ""
- "00_PASP.aux" 1667935663 10150 06d1cb9804fa13f9caa5b87bee738349 "xelatex"
- "00_PASP.nav" 1667935663 4557 bd5b660e37644e87cd38eeeceb472239 "xelatex"
- "00_PASP.out" 1667935663 1097 ff89349dbd8e3874420c8d8c57eb7504 "xelatex"
- "00_PASP.tex" 1667935656 32020 e7e67df128d9c518e87afbb7c6491ef3 ""
- "00_PASP.toc" 1667935663 384 d39373a67753c9668ace5a0f122dc338 "xelatex"
+ "00_PASP.aux" 1668012215 10175 631506c17974104545ec9f7326871ea2 "xelatex"
+ "00_PASP.nav" 1668012215 4415 70ff7441078bcca01fe957123d46aa96 "xelatex"
+ "00_PASP.out" 1668012215 1123 b2bcf7d8938de98bdfd00e76ac45d7c1 "xelatex"
+ "00_PASP.tex" 1668012208 32880 d2ff92ff8b2ef9e5a1bd016ddcdcb92a ""
+ "00_PASP.toc" 1668012215 359 90550d08e709a3bd1267d8fa48d5648b "xelatex"
"Pabc_alpha03.pdf" 1663331875 12659 e50124c327299028f63ecb501d23eb0d ""
(generated)
"00_PASP.aux"
diff --git a/text/00_PASP.fls b/text/00_PASP.fls
index 7592f11..99123d0 100644
--- a/text/00_PASP.fls
+++ b/text/00_PASP.fls
@@ -1471,10 +1471,6 @@ INPUT /usr/share/texmf-dist/fonts/tfm/public/lm/ec-lmss12.tfm
INPUT ./00_PASP.toc
INPUT 00_PASP.toc
INPUT 00_PASP.toc
-INPUT /usr/share/texmf-dist/fonts/tfm/public/lm/ec-lmssbo10.tfm
-INPUT ./00_PASP.toc
-INPUT 00_PASP.toc
-INPUT 00_PASP.toc
INPUT /usr/share/texmf-dist/fonts/tfm/public/lm/ec-lmssbx10.tfm
INPUT ./00_PASP.toc
INPUT 00_PASP.toc
diff --git a/text/00_PASP.log b/text/00_PASP.log
index b928231..6c348f6 100644
--- a/text/00_PASP.log
+++ b/text/00_PASP.log
@@ -1,4 +1,4 @@
-This is XeTeX, Version 3.141592653-2.6-0.999994 (TeX Live 2022/Arch Linux) (preloaded format=xelatex 2022.11.5) 8 NOV 2022 19:27
+This is XeTeX, Version 3.141592653-2.6-0.999994 (TeX Live 2022/Arch Linux) (preloaded format=xelatex 2022.11.5) 9 NOV 2022 16:43
entering extended mode
\write18 enabled.
file:line:error style messages enabled.
@@ -608,7 +608,7 @@ LaTeX Font Info: Trying to load font information for T1+lmss on input line 11
(/usr/share/texmf-dist/tex/latex/lm/t1lmss.fd
File: t1lmss.fd 2015/05/01 v1.6.1 Font defs for Latin Modern
))
-Package hyperref Info: Option `colorlinks' set `true' on input line 34.
+Package hyperref Info: Option `colorlinks' set `true' on input line 46.
(/usr/share/texmf-dist/tex/latex/l3backend/l3backend-xetex.def
File: l3backend-xetex.def 2022-04-14 L3 backend support: XeTeX
\l__color_backend_stack_int=\count343
@@ -621,30 +621,30 @@ File: l3backend-xetex.def 2022-04-14 L3 backend support: XeTeX
) (./00_PASP.aux)
\openout1 = `00_PASP.aux'.
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+LaTeX Font Info: ... okay on input line 77.
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+LaTeX Font Info: ... okay on input line 77.
+LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 77.
+LaTeX Font Info: ... okay on input line 77.
+LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 77.
+LaTeX Font Info: ... okay on input line 77.
+LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 77.
+LaTeX Font Info: Trying to load font information for TS1+cmr on input line 77.
(/usr/share/texmf-dist/tex/latex/base/ts1cmr.fd
File: ts1cmr.fd 2019/12/16 v2.5j Standard LaTeX font definitions
)
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+\beamer@slide {prop:lucases.c}{13}
+\beamer@slide {prop:lucases.d}{13}
\beamer@slide {def:w.inconsistent}{16}
\beamer@slide {eq:prob.sm}{16}
\beamer@slide {def:w.disj}{16}
\beamer@slide {def:w.conj}{16}
\beamer@slide {def:w.empty}{16}
-\beamer@slide {eq:def.prob}{16}
-\beamer@slide {eq:def.prob.event}{16}
+\beamer@slide {eq:def.prob}{17}
+\beamer@slide {eq:def.prob.event}{17}
diff --git a/text/00_PASP.synctex.gz b/text/00_PASP.synctex.gz
index 56d8ecd..4b0a202 100644
Binary files a/text/00_PASP.synctex.gz and b/text/00_PASP.synctex.gz differ
diff --git a/text/00_PASP.tex b/text/00_PASP.tex
index 7f256f5..8852d0e 100644
--- a/text/00_PASP.tex
+++ b/text/00_PASP.tex
@@ -23,6 +23,18 @@
\usepackage[overridenote]{pdfpc}
\usepackage{tikz}
+\tikzset{
+rrect/.style={
+ rectangle,
+ rounded corners,
+ fill=gray!10,
+ % minimum width=1em,
+ % text width=2em,
+ % draw=blue!75,
+ % very thick,
+ align=center,
+ }
+}
\usepackage{commath}
\usepackage{amssymb}
@@ -96,10 +108,10 @@
\item \textbf{Atoms} $\fml{A}$,
$\overline{\fml{A}} = \cset{\neg a}{a \in \fml{A}}$,
% --------------------------------
- \item \textbf{Inputs} $\fml{Z}$:
+ \item \textbf{Samples} $\fml{Z}$:
$$\fml{Z} = \cset{z = \alpha \cup \beta }{ \alpha \subseteq \fml{A} \land \beta \subseteq \overline{\fml{A}} }$$
% --------------------------------
- \item \textbf{Interpretations} or \textit{consistent inputs} $\fml{I}$ :
+ \item \textbf{Interpretations} or \textit{consistent samples} $\fml{I}$ :
$$\fml{I} = \cset{z \in \fml{Z} }{ \forall a \in \fml{A}~\envert{\set{a,\neg a} \cap z} \leq 1}.$$
% --------------------------------
\item \textit{PASP Problem} or \textbf{Specification:} $P = C \land F \land R$ where
@@ -112,7 +124,7 @@
% --------------------------------
\item $R = R_P$ \textit{rules}.
% --------------------------------
- \item $\fml{A}_P, \fml{Z}_P$ and $\fml{I}_P$: \textit{atoms}, \textit{inputs} and \textit{interpretations} of $P$.
+ \item $\fml{A}_P, \fml{Z}_P$ and $\fml{I}_P$: \textit{atoms}, \textit{samples} and \textit{interpretations} of $P$.
\end{itemize}
% --------------------------------
\item \textbf{Stable Models} of $P$, $\fml{S} = \fml{S}_P$, are the stable models of $\delta P = \delta C + F + R$.
@@ -142,9 +154,11 @@
This is the \emph{distribution semantic} as set by Sato.
\end{frame}
% ================================================================
-\begin{frame}{Problem Statement}
- % --------------------------------
- How to \textit{extend} probability from total choices to stable models, interpretations and inputs?
+\begin{frame}
+ % --------------------------------
+ \begin{block}{Problem Statement}
+ How to \textit{extend} probability from total choices to stable models, interpretations and samples?
+ \end{block}
% --------------------------------
\begin{quotation}
There's a problem right at extending to stable models.
@@ -179,7 +193,7 @@
% --------------------------------
\item $\pr{\set{\neg a}} = 0.7$ is straightforward.
% --------------------------------
- \item But, no \textit{unbiased} choice for $\alpha\in\intcc{0,1}$ in
+ \item But, no \textit{informed} choice for $\alpha\in\intcc{0,1}$ in
$$
\begin{aligned}
\pr{\set{a, b}} &= 0.3 \alpha, \cr
@@ -202,17 +216,17 @@
\pr{\set{a, c}} &= 0.3 \co{\alpha}.
\end{aligned}
$$
- \item A \textit{random variable} captures this:
+ \item A \textit{random variable} captures this uncertainty:
$$
\begin{aligned}
- \pr{\set{\neg a} \given\ A = \alpha } &= 0.7, \cr
- \pr{\set{a, b} \given\ A = \alpha } &= 0.3 \alpha, \cr
- \pr{\set{a, c} \given\ A = \alpha } &= 0.3 \co{\alpha}.
+ \pr{\set{\neg a} \given A = \alpha } &= 0.7, \cr
+ \pr{\set{a, b} \given A = \alpha } &= 0.3 \alpha, \cr
+ \pr{\set{a, c} \given A = \alpha } &= 0.3 \co{\alpha}.
\end{aligned}
$$
\item Other uncertainties lead to further parameters:
$$
- \pr{s \given\ A_1 = \alpha_1, \ldots, A_n = \alpha_n }.
+ \pr{s \given A_1 = \alpha_1, \ldots, A_n = \alpha_n }.
$$
% --------------------------------
\end{itemize}
@@ -220,14 +234,14 @@
% --------------------------------
\end{frame}
% ================================================================
-\begin{frame}{Main Research Question}
+\begin{frame}%{Main Research Question}
% --------------------------------
- A \textit{random variable} captures this:
+ A \textit{random variable} captures this uncertainty:
$$
\begin{aligned}
- \pr{\set{\neg a} \given\ A = \alpha } &= 0.7, \cr
- \pr{\set{a, b} \given\ A = \alpha } &= 0.3 \alpha, \cr
- \pr{\set{a, c} \given\ A = \alpha } &= 0.3 \co{\alpha}.
+ \pr{\set{\neg a} \given A = \alpha } &= 0.7, \cr
+ \pr{\set{a, b} \given A = \alpha } &= 0.3 \alpha, \cr
+ \pr{\set{a, c} \given A = \alpha } &= 0.3 \co{\alpha}.
\end{aligned}
$$
% --------------------------------
@@ -237,49 +251,51 @@
% --------------------------------
\begin{itemize}
% --------------------------------
- \item Follow ASP syntax; for each case, consider the possible uncertainty scenarios.
+ \item Follow ASP syntax; for each case, what are the uncertainty scenarios?
+ % --------------------------------
+ \item The disjunction example illustrates one such scenario.
% --------------------------------
- \item The disjunction example illustrates one such step.
+ \item \textit{Neat} means a function $d: \fml{S} \to \intcc{0, 1}$ such that
+ $$
+ \sum_{s\in\fml{S}_\theta} d\at{s} = 1
+ $$
+ for each $\theta \in \Theta$.
% --------------------------------
\end{itemize}
% --------------------------------
\end{frame}
% ================================================================
-\section{Motivation}
-% ================================================================
-\begin{frame}{Specification, Data \& Evaluation}
+\begin{frame}%{Specification, Data \& Evaluation}
% --------------------------------
- Given some procedure to extend probabilities to stable models, interpretations and inputs, and given:
+ Given a method that produces a distribution of samples, $p$, from a specification, $P$ and:
% --------------------------------
\begin{itemize}
% --------------------------------
- \item $P$, a specification.
- % --------------------------------
- \item $p$, the distribution of inputs from above.
- % --------------------------------
- \item $Z$, a dataset of inputs.
+ \item $Z$, a dataset of samples.
% --------------------------------
\item $e$, the respective empirical distribution.
% --------------------------------
\item $D$, some probability divergence, \textit{e.g.} Kullback-Leibler.
% --------------------------------
\end{itemize}
- % --------------------------------
- \begin{quotation}
- For a dataset $Z$, $D\at{P} = D\at{e, p}$ is a \textbf{performance} measure of $P$ and can be used, \textit{e.g.} as fitness, by algorithms searching for \textbf{optimal specifications of a dataset}.
- \end{quotation}
+ % --------------------------------
+ \begin{block}{Motivation}
+ Then $D\at{P} = D\at{e, p}$ is a \textbf{performance} measure of $P$ and can be used, \textit{e.g.} as fitness, by algorithms searching for \textbf{optimal specifications of a dataset}.
+ \end{block}
% --------------------------------
\end{frame}
% ================================================================
-\section{Resolution}
+\section{Extending Probability to Samples}
% ================================================================
\begin{frame}{Resolution Path}
+ Prior to \textit{conciliation} with data:
\begin{enumerate}
- \item \textit{Parametrize} lack of knowledge \emph{e.g.} $\alpha$ in the disjunction example.
- \item This extends probability from total choices to \textit{standard models}.
- \item Extend probability from standard models to \textit{interpretations}. \textbf{How?} Later.
- \item Set $\pr{z} = 0$ for $z \in \fml{Z} \setminus \fml{I}$.
+ \item Use \textit{conditional parameters} to represent lack of knowledge \emph{e.g.} $\alpha$ in the disjunction example.
+ \item This extends probability from total choices to \textit{standard models} --- \alert{hopefully}.
+ \item Assume probability set on standard models; Extend it to \textit{interpretations}. \textbf{How?} Later.
+ \item Set $\pr{z} = 0$ for $z \in \fml{Z} \setminus \fml{I}$ (inconsistent samples).
\end{enumerate}
+ Assuming a conditional probability set on stable models, \textit{How to extend it to interpretations?}
\end{frame}
\begin{frame}{Bounds of Interpretations}
% --------------------------------
@@ -295,7 +311,7 @@
% --------------------------------
\end{itemize}
% --------------------------------
- \item\label{prop:lucases} \textbf{Proposition.} Stable models are \textit{minimal} so \textit{one} of the following cases takes place:
+ \item\label{prop:lucases} \textbf{Proposition.} Exactly \textit{one} of the following cases takes place:
% --------------------------------
\begin{enumerate}
% --------------------------------
@@ -308,50 +324,125 @@
\item\label{prop:lucases.d} $\lset{x} = \emptyset = \uset{x}$.
% --------------------------------
\end{enumerate}
+ because stable models are \textit{minimal}.
% --------------------------------
\end{itemize}
% --------------------------------
\end{frame}
% ================================================================
+\begin{frame}{Disjunction Example | The Interpretation's Lattice}
+ \begin{center}
+ \begin{tikzpicture}
+ %
+ \draw [help lines, color=gray!20] grid (11,7);
+ %
+ \node [fill=gray!50] (sm) at (1, 7) {sm};
+ \node [draw,rrect] (sub) at (2, 7) {sub};
+ \node [draw, fill=gray!10] (sup) at (3, 7) {sup};
+ \node (ind) at (4, 7) {ind};
+ %
+ \node [draw, rrect] (E) at (5.5,0) {$\emptyset$};
+ %
+ \node [draw, rrect] (a) at (1.5,1.5) {$a$};
+ \node [draw, rrect] (b) at (0,1.5) {$b$};
+ \node [draw, rrect] (c) at (4.5,1.5) {$c$};
+ \node [fill=gray!50] (A) at (8.5,1.5) {$\co{a}$};
+ \node (B) at (9.5,1.5) {$\co{b}$};
+ \node (C) at (10.5,1.5) {$\co{c}$};
+ %
+ \node [fill=gray!50] (ab) at (0,4) {$ab$};
+ \node [fill=gray!50] (ac) at (3,4) {$ac$};
+ \node (aB) at (1,4) {$a\co{b}$};
+ \node (aC) at (2,4) {$a\co{c}$};
+ \node [draw, fill=gray!10] (Ab) at (4,4) {$\co{a}b$};
+ \node [draw, fill=gray!10] (Ac) at (5,4) {$\co{a}c$};
+ \node [draw, fill=gray!10] (AB) at (6,4) {$\co{a}\co{b}$};
+ \node [draw, fill=gray!10] (AC) at (7,4) {$\co{a}\co{c}$};
+ \node [fill=white] (bc) at (10,4) {$bc$};
+ \node [fill=white] (bC) at (11,4) {$b\co{c}$};
+ \node [fill=white] (Bc) at (12,4) {$\co{b}c$};
+ \node [fill=white] (BC) at (13,4) {$\co{b}\co{c}$};
+ %
+ \node [draw, fill=gray!10] (abc) at (1.5,6) {$abc$};
+ \node (abC) at (3,6) {$ab\co{c}$};
+ \node (aBc) at (4,6) {$a\co{b}c$};
+ \node (aBC) at (5,6) {$a\co{b}\co{c}$};
+ \node [draw, fill=gray!10] (Abc) at (7,6) {$\co{a}bc$};
+ \node [draw, fill=gray!10] (AbC) at (8,6) {$\co{a}b\co{c}$};
+ \node [draw, fill=gray!10] (ABc) at (9,6) {$\co{a}\co{b}c$};
+ \node [draw, fill=gray!10] (ABC) at (10,6) {$\co{a}\co{b}\co{c}$};
+ %
+ \draw [->] (ab) to [out=270,in=180] (E);
+ \draw [->] (ab) to [out=270,in=90] (a);
+ \draw [->] (ab) to [out=270,in=90] (b);
+ \draw [->] (ab) to [out=90,in=270] (abc);
+ %
+ \draw [->] (ac) to [out=270,in=180] (E);
+ \draw [->] (ac) to [out=270,in=90] (a);
+ \draw [->] (ac) to [out=270,in=90] (c);
+ \draw [->] (ac) to [out=90,in=270] (abc);
+ %
+ \draw [->] (A) to [out=270,in=0] (E);
+ %
+ \draw [->] (A) to [out=90,in=270] (Abc);
+ \draw [->] (A) to [out=90,in=270] (AbC);
+ \draw [->] (A) to [out=90,in=270] (ABc);
+ \draw [->] (A) to [out=90,in=270] (ABC);
+ %
+ \draw [->] (A) to [out=90,in=270] (Ab);
+ \draw [->] (A) to [out=90,in=270] (Ac);
+ \draw [->] (A) to [out=90,in=270] (AB);
+ \draw [->] (A) to [out=90,in=270] (AC);
+ \end{tikzpicture}
+ \end{center}
+\end{frame}
+% ================================================================
\begin{frame}
- Next we try to formalize the possible configurations of this scenario. Consider the ASP program $P = C \land F \land R$ with total choices $\Theta $ and stable models $\fml{S}$. Let $d :: \fml{S} \to \intcc{0,1}$ such that $\sum_{s\in\fml{S}_\theta} d\at{s} = 1$.
+
+ \begin{itemize}
+ \item Consider the ASP program $P = C \land F \land R$ with total choices $\Theta $ and stable models $\fml{S}$.
+
+ \item Let $d : \fml{S} \to \intcc{0,1}$ such that $\sum_{s\in\fml{S}_\theta} d\at{s} = 1$ for each $\theta \in \Theta$.
+ \end{itemize}
\end{frame}
% ================================================================
\begin{frame}
-
+ For each $z\in\fml{Z}$ only one of the following cases takes place
\begin{enumerate}
- \item For each $z\in\fml{Z}$ only one of the following cases takes place
+ \item $z$ is inconsistent. Then \textbf{define}
+ \begin{equation}
+ w_d\at{x} = 0.\label{def:w.inconsistent}
+ \end{equation}
+ %
+ \item $z$ is an interpretation and $\lset{z} = \set{z} = \uset{z}$. Then $z$ is a stable model and \textbf{define}
+ \begin{equation}
+ w_d\at{z} = w\at{z} = d\at{z} \pr{\theta_z}.\label{eq:prob.sm}
+ \end{equation}
+ %
+ \item $z$ is an interpretation and $\lset{z} \neq \emptyset \land \uset{x} = \emptyset$. Then \textbf{define}
+ \begin{equation}
+ w_d\at{z} = \sum_{s \in \lset{z}} w_d\at{s}.\label{def:w.disj}
+ \end{equation}
+ %
+ \item $z$ is an interpretation and $\lset{z} = \emptyset \land \uset{z} \neq \emptyset$. Then \textbf{define}
+ \begin{equation}
+ w_d\at{z} = \prod_{s \in \uset{z}} w_d\at{s}.\label{def:w.conj}
+ \end{equation}
+ %
+ \item $z$ is an interpretation and $\lset{z} = \emptyset \land \uset{z} = \emptyset$. Then \textbf{define}
+ \begin{equation}
+ w_d\at{z} = 0.\label{def:w.empty}
+ \end{equation}
+ \end{enumerate}
+ \end{frame}
+ % ================================================================
+ \begin{frame}
\begin{enumerate}
- \item $z$ is inconsistent. Then \textbf{define}
- \begin{equation}
- w_d\at{x} = 0.\label{def:w.inconsistent}
- \end{equation}
- %
- \item $z$ is an interpretation and $\lset{z} = \set{z} = \uset{x}$. Then $z = s$ is a stable model and \textbf{define}
- \begin{equation}
- w_d\at{z} = w\at{s} = d\at{s} \pr{\theta_s}.\label{eq:prob.sm}
- \end{equation}
- %
- \item $z$ is an interpretation and $\lset{z} \neq \emptyset \land \uset{x} = \emptyset$. Then \textbf{define}
- \begin{equation}
- w_d\at{z} = \sum_{s \in \lset{z}} w_d\at{s}.\label{def:w.disj}
- \end{equation}
- %
- \item $z$ is an interpretation and $\lset{z} = \emptyset \land \uset{z} \neq \emptyset$. Then \textbf{define}
- \begin{equation}
- w_d\at{z} = \prod_{s \in \uset{z}} w_d\at{s}.\label{def:w.conj}
- \end{equation}
- %
- \item $z$ is an interpretation and $\lset{z} = \emptyset \land \uset{z} = \emptyset$. Then \textbf{define}
- \begin{equation}
- w_d\at{z} = 0.\label{def:w.empty}
- \end{equation}
- \end{enumerate}
%
- \item The last point defines a ``weight'' function on the inputs that depends not only on the total choices and stable models of a PASP but also on a certain function $d$ that must respect some conditions. To simplify the notation we use the subscript in $w_d$ only when necessary.
+ \item The last point defines a ``weight'' function on the samples that depends not only on the total choices and stable models of a PASP but also on a certain function $d$ that must respect some conditions. To simplify the notation we use the subscript in $w_d$ only when necessary.
%
- \item At first, it may seem counter-intuitive that $w\at{\emptyset} = \sum_{s\in\fml{S}} w\at{s}$ is the largest ``weight'' in the lattice. But $\emptyset$, as an interpretation, sets zero restrictions on the ``compatible'' stable models. The ``complement'' of $\bot = \emptyset$ is the \emph{maximal inconsistent} input $\top = \fml{A} \cup \cset{\neg a }{ a \in \fml{A}}$.
+ \item At first, it may seem counter-intuitive that $w\at{\emptyset} = \sum_{s\in\fml{S}} w\at{s}$ is the largest ``weight'' in the lattice. But $\emptyset$, as an interpretation, sets zero restrictions on the ``compatible'' stable models. The ``complement'' of $\bot = \emptyset$ is the \emph{maximal inconsistent} sample $\top = \fml{A} \cup \cset{\neg a }{ a \in \fml{A}}$.
%
\item \textbf{We haven't yet defined a probability measure.} To do so we must define a set of samples $\Omega$, a set of events $F\subseteq \pset{\Omega}$ and a function $P:F\to\intcc{0,1}$ such that:
\begin{enumerate}
@@ -432,69 +523,6 @@
% ================================================================
\begin{frame}
- Now consider all the interpretations for this program:
- \begin{center}
- \begin{tikzpicture}
- %\draw [help lines] grid (11,3);
- %
- \node [draw, circle] (E) at (5.5,0) {$\emptyset$};
- %
- \node [draw, circle] (a) at (3,2) {$a$};
- \node [draw, circle] (b) at (2,2) {$b$};
- \node [draw, circle] (c) at (4,2) {$c$};
- \node [fill=gray!50] (A) at (8,2) {$\co{a}$};
- \node (B) at (9,2) {$\co{b}$};
- \node (C) at (7,2) {$\co{c}$};
- %
- \node [fill=gray!50] (ab) at (0,4) {$ab$};
- \node [fill=gray!50] (ac) at (1,4) {$ac$};
- \node (aB) at (2,4) {$a\co{b}$};
- \node (aC) at (3,4) {$a\co{c}$};
- \node [draw] (Ab) at (4,4) {$\co{a}b$};
- \node [draw] (Ac) at (5,4) {$\co{a}c$};
- \node [draw] (AB) at (6,4) {$\co{a}\co{b}$};
- \node [draw] (AC) at (7,4) {$\co{a}\co{c}$};
- \node [fill=white] (bc) at (10,4) {$bc$};
- \node [fill=white] (bC) at (11,4) {$b\co{c}$};
- \node [fill=white] (Bc) at (12,4) {$\co{b}c$};
- \node [fill=white] (BC) at (13,4) {$\co{b}\co{c}$};
- %
- \node [draw] (abc) at (0.5,6) {$abc$};
- \node (abC) at (3,6) {$ab\co{c}$};
- \node (aBc) at (4,6) {$a\co{b}c$};
- \node (aBC) at (5,6) {$a\co{b}\co{c}$};
- \node [draw] (Abc) at (7,6) {$\co{a}bc$};
- \node [draw] (AbC) at (8,6) {$\co{a}b\co{c}$};
- \node [draw] (ABc) at (9,6) {$\co{a}\co{b}c$};
- \node [draw] (ABC) at (10,6) {$\co{a}\co{b}\co{c}$};
- %
- \draw [->] (ab) to [out=270,in=180] (E);
- \draw [->] (ab) to [out=270,in=90] (a);
- \draw [->] (ab) to [out=270,in=90] (b);
- \draw [->] (ab) to [out=90,in=270] (abc);
- %
- \draw [->] (ac) to [out=270,in=180] (E);
- \draw [->] (ac) to [out=270,in=90] (a);
- \draw [->] (ac) to [out=270,in=90] (c);
- \draw [->] (ac) to [out=90,in=270] (abc);
- %
- \draw [->] (A) to [out=270,in=0] (E);
- %
- \draw [->] (A) to [out=90,in=270] (Abc);
- \draw [->] (A) to [out=90,in=270] (AbC);
- \draw [->] (A) to [out=90,in=270] (ABc);
- \draw [->] (A) to [out=90,in=270] (ABC);
- %
- \draw [->] (A) to [out=90,in=270] (Ab);
- \draw [->] (A) to [out=90,in=270] (Ac);
- \draw [->] (A) to [out=90,in=270] (AB);
- \draw [->] (A) to [out=90,in=270] (AC);
- \end{tikzpicture}
- \end{center}
-\end{frame}
-% ================================================================
-\begin{frame}
-
In this diagram:
\begin{itemize}
\item Negations are represented as \emph{e.g.} $\co{a}$ instead of $\neg a$; Stable models are denoted by shaded nodes as \tikz{\node[fill=gray!50] {$ab$}}.
diff --git a/text/00_PASP.toc b/text/00_PASP.toc
index 4f507b5..3d8ca93 100644
--- a/text/00_PASP.toc
+++ b/text/00_PASP.toc
@@ -1,7 +1,6 @@
\beamer@sectionintoc {1}{Introduction}{2}{0}{1}
-\beamer@sectionintoc {2}{Motivation}{10}{0}{2}
-\beamer@sectionintoc {3}{Resolution}{12}{0}{3}
-\beamer@sectionintoc {4}{Cases \& Examples}{17}{0}{4}
-\beamer@subsectionintoc {4}{1}{Programs with disjunctive heads}{18}{0}{4}
-\beamer@subsectionintoc {4}{2}{Non-stratified programs}{23}{0}{4}
-\beamer@sectionintoc {5}{Conclusions}{28}{0}{5}
+\beamer@sectionintoc {2}{Extending Probability to Samples}{11}{0}{2}
+\beamer@sectionintoc {3}{Cases \& Examples}{18}{0}{3}
+\beamer@subsectionintoc {3}{1}{Programs with disjunctive heads}{19}{0}{3}
+\beamer@subsectionintoc {3}{2}{Non-stratified programs}{23}{0}{3}
+\beamer@sectionintoc {4}{Conclusions}{28}{0}{4}
diff --git a/text/00_PASP.xdv b/text/00_PASP.xdv
index f0966dd..8249b8a 100644
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