2022-11-29 | Reunião com o Bruno.

Francisco Coelho
1 parent 14eb34f8
Showing 10 changed files with 139 additions and 6 deletions Show diff stats
code/asp/bachelor.lp
code/asp/disj.lp
code/asp/roads.lp
text/00_PASP.pdf
text/00_PASP.synctex.gz
text/00_PASP.xdv
text/drafts.pdf
text/drafts.tex
text/paper_01/pre-paper.pdf
text/paper_01/pre-paper.tex
 person(joey).
+
 married(X); -married(X) :- person(X).
+
 male(X); female(X) :- person(X).
-bachelor(X) :- male(X), not married(X).
 \ No newline at end of file
+
+bachelor(X) :- male(X), not married(X).
+
+#show bachelor/1. 
 \ No newline at end of file
 % prob(a) = 0.3
 a ; -a.
-b ; c :- a.
-
-d ; -d.
-b :- c, d.
 \ No newline at end of file
+b ; c :- a.
 \ No newline at end of file
@@ -8,6 +8,7 @@ blocked(werder, brandenburg).
 route(X, Y) :- road(X, Y), not blocked(X, Y).
 route(X, Y) :- route(X, Z), route(Z, Y).
+% prob: 0.5
 drive(X) :- route(berlin, X).
 #show drive/1.
 \ No newline at end of file
@@ -0,0 +1,83 @@
+\documentclass{standalone}
+
+\usepackage[x11colors]{xcolor}
+%
+\usepackage{tikz}
+\tikzset{
+    event/.style={},
+    smodel/.style={fill=gray!25},
+    tchoice/.style={draw, circle},
+    indep/.style={draw, dashed},
+    proptc/.style = {-latex, dashed},
+    propsm/.style = {-latex, thick},
+    doubt/.style = {gray}
+}
+\usetikzlibrary{calc, positioning}
+%
+\usepackage{hyperref}
+\hypersetup{
+    colorlinks=true,
+    linkcolor=blue,
+}
+
+
+\usepackage{commath}
+
+
+%
+% Local commands
+%
+\newcommand{\note}[1]{\marginpar{\scriptsize #1}}
+\newcommand{\naf}{\ensuremath{\sim\!}}
+\newcommand{\larr}{\ensuremath{\leftarrow}}
+\newcommand{\at}[1]{\ensuremath{\!\del{#1}}}
+\newcommand{\co}[1]{\ensuremath{\overline{#1}}}
+\newcommand{\fml}[1]{\ensuremath{{\cal #1}}}
+\newcommand{\deft}[1]{\textbf{#1}}
+\newcommand{\pset}[1]{\ensuremath{\mathbb{P}\at{#1}}}
+\newcommand{\ent}{\ensuremath{\lhd}}
+\newcommand{\cset}[2]{\ensuremath{\set{#1,~#2}}}
+\newcommand{\langof}[1]{\ensuremath{\fml{L}\at{#1}}}
+\newcommand{\uset}[1]{\ensuremath{\left|{#1}\right>}}
+\newcommand{\lset}[1]{\ensuremath{\left<{#1}\right|}}
+\newcommand{\pr}[1]{\ensuremath{\mathrm{P}\at{#1}}}
+\newcommand{\given}{\ensuremath{~\middle|~}}
+
+\begin{document}
+\begin{tikzpicture}
+    \node[event] (E) {$\bot$};
+    \node[tchoice, above left = of E] (a) {$a$};
+    \node[smodel, above left = of a] (ab) {$ab$};
+    \node[smodel, above right = of a] (ac) {$ac$};
+    \node[event, below = of ab] (b) {$b$};
+    \node[event, below = of ac] (c) {$c$};
+    \node[event, above right = of ab] (abc) {$abc$};
+    \node[indep, right = of ac] (bc) {$bc$};
+    \node[tchoice, smodel, below right = of bc] (A) {$\co{a}$};
+    \node[event, above = of A] (Ac) {$\co{a}c$};
+    \node[event, above right = of Ac] (Abc) {$\co{a}bc$};
+    % ----
+    \draw[proptc] (a) to[bend left] (ab);
+    \draw[proptc] (a) to[bend right] (ac);
+
+    \draw[propsm] (ab) to[bend left] (abc);
+    \draw[propsm] (ac) to[bend right] (abc);
+
+    \draw[propsm] (A) to[bend right] (Ac);
+    \draw[propsm] (A) to[bend right] (Abc);
+
+    \draw[doubt] (ab) to[bend right] (E);
+    \draw[doubt] (ac) to[bend right] (E);
+    \draw[doubt] (A) to[bend left] (E);
+
+    \draw[doubt] (ab) to[bend right] (b);
+    \draw[doubt] (ac) to[bend left] (c);
+    \draw[doubt] (ab) to[bend left] (a);
+    \draw[doubt] (ac) to[bend right] (a);
+    \draw[doubt] (c) to[bend right] (bc);
+    \draw[doubt] (abc) to[bend left] (bc);
+    \draw[doubt] (Abc) to (bc);
+    \draw[doubt] (c) to[bend right] (Ac);
+\end{tikzpicture}
+    
+\end{document}
 \ No newline at end of file
@@ -3,7 +3,16 @@
 \usepackage[x11colors]{xcolor}
 %
 \usepackage{tikz}
-\usetikzlibrary{calc}
+\tikzset{
+    event/.style={},
+    smodel/.style={fill=gray!25},
+    tchoice/.style={draw, circle},
+    indep/.style={draw, dashed},
+    proptc/.style = {-latex, dashed},
+    propsm/.style = {-latex, thick},
+    doubt/.style = {gray}
+}
+\usetikzlibrary{calc, positioning}
 %
 \usepackage{hyperref}
 \hypersetup{
@@ -93,6 +102,44 @@ Currently, we are on the step two above: Extending a probability function (with 
 \section{Extending Probabilities}
+\begin{center}
+    \begin{tikzpicture}
+        \node[event] (E) {$\bot$};
+        \node[tchoice, above left = of E] (a) {$a$};
+        \node[smodel, above left = of a] (ab) {$ab$};
+        \node[smodel, above right = of a] (ac) {$ac$};
+        \node[event, below = of ab] (b) {$b$};
+        \node[event, below = of ac] (c) {$c$};
+        \node[event, above right = of ab] (abc) {$abc$};
+        \node[indep, right = of ac] (bc) {$bc$};
+        \node[tchoice, smodel, below right = of bc] (A) {$\co{a}$};
+        \node[event, above = of A] (Ac) {$\co{a}c$};
+        \node[event, above right = of Ac] (Abc) {$\co{a}bc$};
+        % ----
+        \draw[proptc] (a) to[bend left] (ab);
+        \draw[proptc] (a) to[bend right] (ac);
+
+        \draw[propsm] (ab) to[bend left] (abc);
+        \draw[propsm] (ac) to[bend right] (abc);
+
+        \draw[propsm] (A) to (Ac);
+        \draw[propsm] (A) to (Abc);
+
+        \draw[doubt] (ab) to[bend right] (E);
+        \draw[doubt] (ac) to[bend right] (E);
+        \draw[doubt] (A) to[bend left] (E);
+
+        \draw[doubt] (ab) to[bend right] (b);
+        \draw[doubt] (ac) to[bend left] (c);
+        \draw[doubt] (ab) to[bend left] (a);
+        \draw[doubt] (ac) to[bend right] (a);
+        \draw[doubt] (c) to[bend right] (bc);
+        \draw[doubt] (abc) to[bend left] (bc);
+        \draw[doubt] (Abc) to (bc);
+        \draw[doubt] (c) to[bend right] (Ac);
+    \end{tikzpicture}
+\end{center}
+
 Given an ASP specification, we consider the \textit{atoms} $a \in \fml{A}$ and \textit{literals}, $z \in \fml{L}$, \textit{events} $e \in \fml{E} \iff e \subseteq \fml{L}$ and \textit{worlds} $w \in \fml{W}$ (consistent events), \textit{total choices} $c \in \fml{C} \iff c = a \vee \neg a$ and \textit{stable models} $s \in \fml{S}$.
 % In a statistical setting, the outcomes are the literals $x$, $\neg x$ for each atom $x$, the events express a set of possible outcomes (including $\emptyset$, $\set{a, b}$, $\set{a, \neg a, b}$, \textit{etc.}), and worlds are events with no contradictions.
	@@ -8,6 +8,7 @@ blocked(werder, brandenburg).		@@ -8,6 +8,7 @@ blocked(werder, brandenburg).
8	route(X, Y) :- road(X, Y), not blocked(X, Y).	8	route(X, Y) :- road(X, Y), not blocked(X, Y).
9	route(X, Y) :- route(X, Z), route(Z, Y).	9	route(X, Y) :- route(X, Z), route(Z, Y).
10		10
		11	+% prob: 0.5
11	drive(X) :- route(berlin, X).	12	drive(X) :- route(berlin, X).
12		13
13	#show drive/1.	14	#show drive/1.
14	\ No newline at end of file	15	\ No newline at end of file
	@@ -0,0 +1,83 @@		@@ -0,0 +1,83 @@
		1	+\documentclass{standalone}
		2	+
		3	+\usepackage[x11colors]{xcolor}
		4	+%
		5	+\usepackage{tikz}
		6	+\tikzset{
		7	+ event/.style={},
		8	+ smodel/.style={fill=gray!25},
		9	+ tchoice/.style={draw, circle},
		10	+ indep/.style={draw, dashed},
		11	+ proptc/.style = {-latex, dashed},
		12	+ propsm/.style = {-latex, thick},
		13	+ doubt/.style = {gray}
		14	+}
		15	+\usetikzlibrary{calc, positioning}
		16	+%
		17	+\usepackage{hyperref}
		18	+\hypersetup{
		19	+ colorlinks=true,
		20	+ linkcolor=blue,
		21	+}
		22	+
		23	+
		24	+\usepackage{commath}
		25	+
		26	+
		27	+%
		28	+% Local commands
		29	+%
		30	+\newcommand{\note}[1]{\marginpar{\scriptsize #1}}
		31	+\newcommand{\naf}{\ensuremath{\sim\!}}
		32	+\newcommand{\larr}{\ensuremath{\leftarrow}}
		33	+\newcommand{\at}[1]{\ensuremath{\!\del{#1}}}
		34	+\newcommand{\co}[1]{\ensuremath{\overline{#1}}}
		35	+\newcommand{\fml}[1]{\ensuremath{{\cal #1}}}
		36	+\newcommand{\deft}[1]{\textbf{#1}}
		37	+\newcommand{\pset}[1]{\ensuremath{\mathbb{P}\at{#1}}}
		38	+\newcommand{\ent}{\ensuremath{\lhd}}
		39	+\newcommand{\cset}[2]{\ensuremath{\set{#1,~#2}}}
		40	+\newcommand{\langof}[1]{\ensuremath{\fml{L}\at{#1}}}
		41	+\newcommand{\uset}[1]{\ensuremath{\left\|{#1}\right>}}
		42	+\newcommand{\lset}[1]{\ensuremath{\left<{#1}\right\|}}
		43	+\newcommand{\pr}[1]{\ensuremath{\mathrm{P}\at{#1}}}
		44	+\newcommand{\given}{\ensuremath{~\middle\|~}}
		45	+
		46	+\begin{document}
		47	+\begin{tikzpicture}
		48	+ \node[event] (E) {$\bot$};
		49	+ \node[tchoice, above left = of E] (a) {$a$};
		50	+ \node[smodel, above left = of a] (ab) {$ab$};
		51	+ \node[smodel, above right = of a] (ac) {$ac$};
		52	+ \node[event, below = of ab] (b) {$b$};
		53	+ \node[event, below = of ac] (c) {$c$};
		54	+ \node[event, above right = of ab] (abc) {$abc$};
		55	+ \node[indep, right = of ac] (bc) {$bc$};
		56	+ \node[tchoice, smodel, below right = of bc] (A) {$\co{a}$};
		57	+ \node[event, above = of A] (Ac) {$\co{a}c$};
		58	+ \node[event, above right = of Ac] (Abc) {$\co{a}bc$};
		59	+ % ----
		60	+ \draw[proptc] (a) to[bend left] (ab);
		61	+ \draw[proptc] (a) to[bend right] (ac);
		62	+
		63	+ \draw[propsm] (ab) to[bend left] (abc);
		64	+ \draw[propsm] (ac) to[bend right] (abc);
		65	+
		66	+ \draw[propsm] (A) to[bend right] (Ac);
		67	+ \draw[propsm] (A) to[bend right] (Abc);
		68	+
		69	+ \draw[doubt] (ab) to[bend right] (E);
		70	+ \draw[doubt] (ac) to[bend right] (E);
		71	+ \draw[doubt] (A) to[bend left] (E);
		72	+
		73	+ \draw[doubt] (ab) to[bend right] (b);
		74	+ \draw[doubt] (ac) to[bend left] (c);
		75	+ \draw[doubt] (ab) to[bend left] (a);
		76	+ \draw[doubt] (ac) to[bend right] (a);
		77	+ \draw[doubt] (c) to[bend right] (bc);
		78	+ \draw[doubt] (abc) to[bend left] (bc);
		79	+ \draw[doubt] (Abc) to (bc);
		80	+ \draw[doubt] (c) to[bend right] (Ac);
		81	+\end{tikzpicture}
		82	+
		83	+\end{document}
0	\ No newline at end of file	84	\ No newline at end of file
	@@ -3,7 +3,16 @@		@@ -3,7 +3,16 @@
3	\usepackage[x11colors]{xcolor}	3	\usepackage[x11colors]{xcolor}
4	%	4	%
5	\usepackage{tikz}	5	\usepackage{tikz}
6	-\usetikzlibrary{calc}	6	+\tikzset{
		7	+ event/.style={},
		8	+ smodel/.style={fill=gray!25},
		9	+ tchoice/.style={draw, circle},
		10	+ indep/.style={draw, dashed},
		11	+ proptc/.style = {-latex, dashed},
		12	+ propsm/.style = {-latex, thick},
		13	+ doubt/.style = {gray}
		14	+}
		15	+\usetikzlibrary{calc, positioning}
7	%	16	%
8	\usepackage{hyperref}	17	\usepackage{hyperref}
9	\hypersetup{	18	\hypersetup{
	@@ -93,6 +102,44 @@ Currently, we are on the step two above: Extending a probability function (with		@@ -93,6 +102,44 @@ Currently, we are on the step two above: Extending a probability function (with
93		102
94	\section{Extending Probabilities}	103	\section{Extending Probabilities}
95		104
		105	+\begin{center}
		106	+ \begin{tikzpicture}
		107	+ \node[event] (E) {$\bot$};
		108	+ \node[tchoice, above left = of E] (a) {$a$};
		109	+ \node[smodel, above left = of a] (ab) {$ab$};
		110	+ \node[smodel, above right = of a] (ac) {$ac$};
		111	+ \node[event, below = of ab] (b) {$b$};
		112	+ \node[event, below = of ac] (c) {$c$};
		113	+ \node[event, above right = of ab] (abc) {$abc$};
		114	+ \node[indep, right = of ac] (bc) {$bc$};
		115	+ \node[tchoice, smodel, below right = of bc] (A) {$\co{a}$};
		116	+ \node[event, above = of A] (Ac) {$\co{a}c$};
		117	+ \node[event, above right = of Ac] (Abc) {$\co{a}bc$};
		118	+ % ----
		119	+ \draw[proptc] (a) to[bend left] (ab);
		120	+ \draw[proptc] (a) to[bend right] (ac);
		121	+
		122	+ \draw[propsm] (ab) to[bend left] (abc);
		123	+ \draw[propsm] (ac) to[bend right] (abc);
		124	+
		125	+ \draw[propsm] (A) to (Ac);
		126	+ \draw[propsm] (A) to (Abc);
		127	+
		128	+ \draw[doubt] (ab) to[bend right] (E);
		129	+ \draw[doubt] (ac) to[bend right] (E);
		130	+ \draw[doubt] (A) to[bend left] (E);
		131	+
		132	+ \draw[doubt] (ab) to[bend right] (b);
		133	+ \draw[doubt] (ac) to[bend left] (c);
		134	+ \draw[doubt] (ab) to[bend left] (a);
		135	+ \draw[doubt] (ac) to[bend right] (a);
		136	+ \draw[doubt] (c) to[bend right] (bc);
		137	+ \draw[doubt] (abc) to[bend left] (bc);
		138	+ \draw[doubt] (Abc) to (bc);
		139	+ \draw[doubt] (c) to[bend right] (Ac);
		140	+ \end{tikzpicture}
		141	+\end{center}
		142	+
96	Given an ASP specification, we consider the \textit{atoms} $a \in \fml{A}$ and \textit{literals}, $z \in \fml{L}$, \textit{events} $e \in \fml{E} \iff e \subseteq \fml{L}$ and \textit{worlds} $w \in \fml{W}$ (consistent events), \textit{total choices} $c \in \fml{C} \iff c = a \vee \neg a$ and \textit{stable models} $s \in \fml{S}$.	143	Given an ASP specification, we consider the \textit{atoms} $a \in \fml{A}$ and \textit{literals}, $z \in \fml{L}$, \textit{events} $e \in \fml{E} \iff e \subseteq \fml{L}$ and \textit{worlds} $w \in \fml{W}$ (consistent events), \textit{total choices} $c \in \fml{C} \iff c = a \vee \neg a$ and \textit{stable models} $s \in \fml{S}$.
97		144
98	% In a statistical setting, the outcomes are the literals $x$, $\neg x$ for each atom $x$, the events express a set of possible outcomes (including $\emptyset$, $\set{a, b}$, $\set{a, \neg a, b}$, \textit{etc.}), and worlds are events with no contradictions.	145	% In a statistical setting, the outcomes are the literals $x$, $\neg x$ for each atom $x$, the events express a set of possible outcomes (including $\emptyset$, $\set{a, b}$, $\set{a, \neg a, b}$, \textit{etc.}), and worlds are events with no contradictions.