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.
1	1	person(joey).
	2	+
2	3	married(X); -married(X) :- person(X).
	4	+
3	5	male(X); female(X) :- person(X).
4		-bachelor(X) :- male(X), not married(X).
5	6	\ No newline at end of file
	7	+
	8	+bachelor(X) :- male(X), not married(X).
	9	+
	10	+#show bachelor/1.
6	11	\ No newline at end of file
...	...
1	1	% prob(a) = 0.3
2	2	a ; -a.
3		-b ; c :- a.
4		-
5		-d ; -d.
6		-b :- c, d.
7	3	\ No newline at end of file
	4	+b ; c :- a.
8	5	\ No newline at end of file
...	...
...	...	@@ -8,6 +8,7 @@ blocked(werder, brandenburg).
8	8	route(X, Y) :- road(X, Y), not blocked(X, Y).
9	9	route(X, Y) :- route(X, Z), route(Z, Y).
10	10
	11	+% prob: 0.5
11	12	drive(X) :- route(berlin, X).
12	13
13	14	#show drive/1.
14	15	\ No newline at end of file
...	...
...	...	@@ -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	84	\ No newline at end of file
...	...
...	...	@@ -3,7 +3,16 @@
3	3	\usepackage[x11colors]{xcolor}
4	4	%
5	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	17	\usepackage{hyperref}
9	18	\hypersetup{
...	...	@@ -93,6 +102,44 @@ Currently, we are on the step two above: Extending a probability function (with
93	102
94	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	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	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.
...	...