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Fix typos <noupdate>

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Tian Cheng (Riccardo) Xia
2023-12-10 17:01:15 +01:00
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4
src/fundamentals-of-ai-and-kr/module1/sections/_games.tex
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@ -18,7 +18,7 @@ the opponent as the entity that (optimally) minimizes (\textsc{Min}) the utility
\caption{Example of game tree with propagated scores}
\end{figure}
In a game tree, each level represents the actions a that single player can do.
In a game tree, each level represents the actions that a single player can do.
In minimax, the levels where the player plays are the \textsc{Max} levels,
while the levels of the opponent are the \textsc{Min} levels.
@ -70,7 +70,7 @@ an iteration of the minimax algorithm can be described as follows:
\end{center}
\begin{algorithm}
\caption{Minimax algorithm}
\caption{Minimax}
\begin{lstlisting}[mathescape=true]
def minimax(node, max_depth, who_is_next):
if node.isLeaf() or max_depth == 0:

77
src/fundamentals-of-ai-and-kr/module1/sections/_planning.tex
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@ -27,13 +27,13 @@
\item[Planner] \marginnote{Planner}
Process to decide the actions that solve a planning problem.
In this phase, actions are considered:
\begin{description}
\begin{descriptionlist}
\item[Non decomposable]
An action is atomic (it starts and finishes).
Actions interact with each other by reaching sub-goals.
\item[Reversible]
Choices are backtrackable.
\end{description}
\end{descriptionlist}
A planner can have the following properties:
\begin{descriptionlist}
@ -99,7 +99,7 @@ The direction of the search can be:
\]
\begin{example}[Moving blocks]
Given the action \texttt{unstack(X, Y)} with:
Given the action \texttt{UNSTACK(X, Y)} with:
\[
\begin{split}
\texttt{d\_list} &= \{ \texttt{handempty}, \texttt{on(X, Y)}, \texttt{clear(X)} \} \\
@ -109,10 +109,10 @@ The direction of the search can be:
We have that:
\[
\begin{split}
\texttt{regr[holding(b), unstack(b, Y)]} &= \texttt{true} \\
\texttt{regr[handempty, unstack(X, Y)]} &= \texttt{false} \\
\texttt{regr[ontable(c), unstack(X, Y)]} &= \texttt{ontable(c)} \\
\texttt{regr[clear(c), unstack(X, Y)]} &= \begin{cases}
\texttt{regr[holding(b), UNSTACK(b, Y)]} &= \texttt{true} \\
\texttt{regr[handempty, UNSTACK(X, Y)]} &= \texttt{false} \\
\texttt{regr[ontable(c), UNSTACK(X, Y)]} &= \texttt{ontable(c)} \\
\texttt{regr[clear(c), UNSTACK(X, Y)]} &= \begin{cases}
\texttt{true} & \text{if \texttt{Y}=\texttt{c}} \\
\texttt{clear(c)} & \text{otherwise}
\end{cases}
@ -149,15 +149,15 @@ The main concepts are:
\[ \texttt{pre-conditions} \rightarrow \texttt{post-conditions} \]
Applying the equivalence $A \rightarrow B \equiv \lnot A \vee B$, actions can be described by means of disjunctions.
\begin{example}[Moving blocks]
The action \texttt{stack(X, Y)} has pre-conditions \texttt{holding(X)} and \texttt{clear(Y)}, and
The action \texttt{STACK(X, Y)} has pre-conditions \texttt{holding(X)} and \texttt{clear(Y)}, and
post-conditions \texttt{on(X, Y)}, \texttt{clear(X)} and \texttt{handfree}.
Its representation in Green's formulation is:
\[
\begin{split}
\texttt{holding(X, S)} \land \texttt{clear(Y, S)} &\rightarrow \\
&\texttt{on(X, Y, do(stack(X, Y), s))} \land \\
&\texttt{clear(X, do(stack(X, Y), s))} \land \\
&\texttt{handfree(do(stack(X, Y), s))} \\
&\texttt{on(X, Y, do(STACK(X, Y), s))} \land \\
&\texttt{clear(X, do(STACK(X, Y), s))} \land \\
&\texttt{handfree(do(STACK(X, Y), s))} \\
\end{split}
\]
\end{example}
@ -166,7 +166,7 @@ The main concepts are:
Besides the effects of actions, each state also have to define for all non-changing fluents their frame axioms.
If the problem is complex, the number of frame axioms becomes unreasonable.
\begin{example}[Moving blocks]
\[ \texttt{on(U, V, S)}, \texttt{diff(U, X)} \rightarrow \texttt{on(U, V, do(move(X, Y, Z), S))} \]
\[ \texttt{on(U, V, S)} \land \texttt{diff(U, X)} \rightarrow \texttt{on(U, V, do(MOVE(X, Y, Z), S))} \]
\end{example}
\end{descriptionlist}
@ -194,33 +194,35 @@ The main concepts are:
\includegraphics[width=\linewidth]{img/_moving_block_example_green.pdf}
\end{minipage}\\[0.5em]
For simplicity, we only consider the action \texttt{move(X, Y, Z)} that moves \texttt{X} from \texttt{Y} to \texttt{Z}.
For simplicity, we only consider the action \texttt{MOVE(X, Y, Z)} that moves \texttt{X} from \texttt{Y} to \texttt{Z}.
It is defined as:
\[
\begin{split}
\texttt{clear(X, S)}&, \texttt{clear(Z, S)}, \texttt{on(X, Y, S)}, \texttt{diff(X, Z)} \rightarrow \\
&\texttt{clear(Y, do(move(X, Y, Z), S))}, \texttt{on(X, Z, do(move(X, Y, Z), S))}
&\texttt{clear(Y, do(MOVE(X, Y, Z), S))}, \texttt{on(X, Z, do(MOVE(X, Y, Z), S))}
\end{split}
\]
This action can be translated into the following effect axioms:
\[
\begin{split}
\lnot\texttt{clear(X, S)} &\vee \lnot\texttt{clear(Z, S)} \vee \lnot\texttt{on(X, Y, S)} \vee \lnot\texttt{diff(X, Z)} \vee \\
&\texttt{clear(Y, do(move(X, Y, Z), S))}
&\texttt{clear(Y, do(MOVE(X, Y, Z), S))}
\end{split}
\]
\[
\begin{split}
\lnot\texttt{clear(X, S)} &\vee \lnot\texttt{clear(Z, S)} \vee \lnot\texttt{on(X, Y, S)} \vee \lnot\texttt{diff(X, Z)} \vee \\
&\texttt{on(X, Z, do(move(X, Y, Z), S))}
&\texttt{on(X, Z, do(MOVE(X, Y, Z), S))}
\end{split}
\]
\end{example}
Given the goal \texttt{on(a, b, s1)}, we prove that $\lnot\texttt{on(a, b, s1)}$ leads to an inconsistency.
We decide to make the following substitutions:
\[ \{ \texttt{X}/\texttt{a}, \texttt{Z}/\texttt{b}, \texttt{s1}/\texttt{do(move(a, Y, b), S)} \} \]
The premise of \texttt{move} leads to an inconsistency (when applying \texttt{move} its premise is false):
Given the goal \texttt{on(a, b, s1)}, we look for an action whose effects together with $\lnot\texttt{on(a, b, s1)}$ lead to an inconsistency.
We decide to achieve this by using the action \texttt{MOVE(a, Y, b)},
therefore making the following substitutions:
\[ \{ \texttt{X}/\texttt{a}, \texttt{Z}/\texttt{b}, \texttt{s1}/\texttt{do(MOVE(a, Y, b), S)} \} \]
Using the disjunctive formulation (effect axioms), we need to show that the negated preconditions are false
(therefore, making the action applicable):
\begin{center}
\begin{tabular}{c|c|c|c}
$\lnot\texttt{clear(a, S)}$ & $\lnot\texttt{clear(b, S)}$ & $\lnot\texttt{on(a, Y, S)}$ & $\lnot\texttt{diff(a, b)}$ \\
@ -228,7 +230,7 @@ The premise of \texttt{move} leads to an inconsistency (when applying \texttt{mo
& False with $\{ \texttt{S}/\texttt{s0}, \texttt{Y}/\texttt{d} \}$ & False
\end{tabular}
\end{center}
Therefore, the substitution $\{ \texttt{s1}/\texttt{do(move(a, Y, b), S)} \}$ defines the plan to reach the goal \texttt{on(a, b, s1)}.
Therefore, the action \texttt{do(MOVE(a, d, b), s0)} defines the plan to reach the goal \texttt{on(a, b, s1)}.
\subsubsection{Kowalsky's formulation}
@ -269,7 +271,7 @@ In the Kowalsky's formulation, each action requires a frame assertion (in Green'
\end{example}
\begin{example}[Moving blocks]
The action \texttt{unstack(X, Y)} has:
The action \texttt{UNSTACK(X, Y)} has:
\begin{descriptionlist}
\item[Pre-conditions] \texttt{on(X, Y)}, \texttt{clear(X)} and \texttt{handempty}
\item[Effects] \phantom{}
@ -285,20 +287,20 @@ In the Kowalsky's formulation, each action requires a frame assertion (in Green'
\[
\begin{split}
\texttt{holds(on(X, Y), S)}&, \texttt{holds(clear(X), S)}, \texttt{holds(handempty, S)} \rightarrow \\
&\texttt{pact(unstack(X, Y), S)}
&\texttt{pact(UNSTACK(X, Y), S)}
\end{split}
\]
\item[Effects] (use add-list)
\[ \texttt{holds(holding(X), do(unstack(X, Y), S))} \]
\[ \texttt{holds(clear(Y), do(unstack(X, Y), S))} \]
\[ \texttt{holds(holding(X), do(UNSTACK(X, Y), S))} \]
\[ \texttt{holds(clear(Y), do(UNSTACK(X, Y), S))} \]
\item[Frame condition] (uses delete-list)
\[
\begin{split}
\texttt{holds(V, S)}&, \texttt{V} \neq \texttt{on(X, Y)}, \texttt{V} \neq \texttt{clear(X)}, \texttt{V} \neq \texttt{handempty}
\rightarrow \\
& \texttt{holds(V, do(unstack(X, Y), S))}
& \texttt{holds(V, do(UNSTACK(X, Y), S))}
\end{split}
\]
\end{descriptionlist}
@ -332,7 +334,7 @@ STRIPS uses two data structures:
\item[Current state] Represents the forward application of the actions found using the goal stack.
\end{descriptionlist}
\begin{algorithm}
\begin{algorithm}[H]
\caption{STRIPS}
\begin{lstlisting}[mathescape=true]
def strips(problem):
@ -365,17 +367,17 @@ def strips(problem):
\begin{example}[Moving blocks]
\begin{center}
\includegraphics[trim={0 16cm 0 0}, clip, width=0.85\textwidth]{img/_strips_example.pdf}
\includegraphics[trim={0 32.2cm 0 0}, clip, width=0.85\textwidth]{img/_strips_example.pdf}
\end{center}
\begin{center}
\includegraphics[trim={0 0 0 33.8cm}, clip, width=0.85\textwidth]{img/_strips_example.pdf}
\includegraphics[trim={0 0 0 17.5cm}, clip, width=0.85\textwidth]{img/_strips_example.pdf}
\end{center}
\end{example}
Since there are non-deterministic choices, the search space may become very large.
Heuristics may be used to avoid this.
Since there are non-deterministic choices, the search space might become very large.
Heuristics can be used to avoid this.
Conjunction of goals are solved separately, but this could lead to the \marginnote{Sussman anomaly} \textbf{Sussman anomaly}
Conjunction of goals are solved separately, but this can lead to the \marginnote{Sussman anomaly} \textbf{Sussman anomaly}
where a sub-goal destroys what another sub-goal has done.
For this reason, when a conjunction is encountered, it is not immediately popped from the goal stack
and is left as a final check.
@ -398,7 +400,7 @@ A non-linear plan is represented by:
between actions.
\item[Causal links] \marginnote{Causal links}
triplet $\langle S_i, S_j, c \rangle$ where $S_i$ and $S_j$ are actions and $c$ is a sub-goal.
$c$ should be the effect of $S_i$ and precondition of $S_j$.
$c$ should be the effects of $S_i$ and preconditions of $S_j$.
Causal links represent causal relations between actions (i.e. interaction between sub-goals):
to execute $S_j$, the effect $c$ of $S_i$ is required first.
@ -635,7 +637,7 @@ MTC refinement methods are:
\begin{enumerate}
\item Insert a new action in the plan.
\item Add an ordering constraint.
\item Do a variable assignement.
\item Do a variable assignment.
\end{enumerate}
\item[Promotion] \marginnote{Promotion}
@ -664,7 +666,8 @@ Different meta-level searches are executed to generate meta-level plans that are
\marginnote{ABSTRIPS}
In ABSTRIPS, a criticality value is assigned to each precondition based on the complexity of its achievement.
At each level, a plan is found assuming that the preconditions corresponding to lower levels of criticality are true.
At each level, a plan is found assuming that the preconditions corresponding to lower levels of criticality are true
(i.e. solve harder goals first).
At the next level, the previously found plan and its preconditions are used as starting point in the goal stack.
\begin{algorithm}
@ -755,7 +758,7 @@ It generates a different plan for each source of uncertainty and therefore has e
\includegraphics[width=0.65\textwidth]{img/_conditional_planning.pdf}
\end{center}
When executing a sensing action, a copy of the goal is generated for each possible scenario.
When executing a sensing action (\texttt{CHECK(tire1)}), a copy of the goal is generated for each possible scenario.
\end{example}
@ -968,7 +971,7 @@ def extractSolution(graph, goal):
\item \texttt{a} and \texttt{b} are objects.
\item \texttt{l} and \texttt{p} are locations.
\end{itemize}
and the initial state is:
and the initial state:
\begin{center}
\texttt{at(a, l)} $\cdot$ \texttt{at(b, l)} $\cdot$ \texttt{at(r, l)} $\cdot$ \texttt{hasFuel(r)}
\end{center}

15
src/fundamentals-of-ai-and-kr/module1/sections/_swarm_intelligence.tex
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@ -148,7 +148,7 @@ The algorithm has the following phases:
\end{descriptionlist}
\begin{algorithm}
\caption{ABC algorithm}
\caption{ABC}
\begin{lstlisting}[mathescape=true]
def abcAlgorithm(problem):
initPhase()
@ -206,27 +206,26 @@ Each particle is described by:
\end{itemize}
\begin{algorithm}
\caption{PSO algorithm}
\caption{PSO}
\begin{lstlisting}[mathescape=true]
def pco(f, n_particles, $\vec{l}$, $\vec{u}$, $\omega$, $\varphi_p$, $\varphi_g$):
def pso(f, n_particles, $\vec{l}$, $\vec{u}$, $\omega$, $\varphi_p$, $\varphi_g$):
particles = [Particle()] * n_particles
global_best = None
gb = None # Global best
for particle in particles:
particle.value = randomUniform($\vec{l}$, $\vec{u}$) # Search space bounds
particle.vel = randomUniform($-\vert \vec{u}-\vec{l} \vert$, $\vert \vec{u}-\vec{l} \vert$)
particle.best = particle.value
if f(particles.best) < f(g): g = particles.best
if f(particles.best) < f(gb): gb = particles.best
while not terminationConditions():
for particle in particles:
$r_p$, $r_g$ = randomUniform(0, 1), randomUniform(0, 1)
$\vec{x}_i$, $\vec{p}_i$, $\vec{v}_i$ = particle.value, particle.best, particle.vel
$\vec{g}$ = global_best
particle.vel = $\omega$*$\vec{v}_i$ + $\varphi_p$*$r_p$*($\vec{p}_i$-$\vec{x}_i$) + $\varphi_g$*$r_g$*($\vec{g}$-$\vec{x}_i$)
particle.vel = $\omega$*$\vec{v}_i$ + $\varphi_p$*$r_p$*($\vec{p}_i$-$\vec{x}_i$) + $\varphi_g$*$r_g$*(gb-$\vec{x}_i$)
particle.value = particle.value + particle.vel
if f(particle.value) < f(particle.best):
particle.best = particle.value
if f(particle.best) < f(g): g = particle.best
if f(particle.best) < f(gb): gb = particle.best
\end{lstlisting}
\end{algorithm}