From 73fe58ed0b0a77db793ff36acff8a8bcf8ac5f4f Mon Sep 17 00:00:00 2001 From: NotXia <35894453+NotXia@users.noreply.github.com> Date: Sun, 7 Jan 2024 17:26:21 +0100 Subject: [PATCH] Fix typos --- .../module2/sections/_business_process.tex | 2 +- .../module2/sections/_descriptive_logic.tex | 33 ++++++++++--------- .../module2/sections/_forward_reasoning.tex | 2 +- .../module2/sections/_ontologies.tex | 2 +- .../module2/sections/_semantic_web.tex | 4 +-- .../module2/sections/_time_reasoning.tex | 12 +++---- 6 files changed, 28 insertions(+), 27 deletions(-) diff --git a/src/fundamentals-of-ai-and-kr/module2/sections/_business_process.tex b/src/fundamentals-of-ai-and-kr/module2/sections/_business_process.tex index b0428d0..59a6342 100644 --- a/src/fundamentals-of-ai-and-kr/module2/sections/_business_process.tex +++ b/src/fundamentals-of-ai-and-kr/module2/sections/_business_process.tex @@ -212,7 +212,7 @@ The most common combination of approaches are: \begin{description} \item[Token play] - A transition is enabled when all the input places of a transition have a token and all the output places have not. + A transition is enabled when all its input places have a token and all its output places have not. An enabled transition can be fired: tokens are removed from the inputs and moved to the outputs. \end{description} diff --git a/src/fundamentals-of-ai-and-kr/module2/sections/_descriptive_logic.tex b/src/fundamentals-of-ai-and-kr/module2/sections/_descriptive_logic.tex index d54e296..a211c4e 100644 --- a/src/fundamentals-of-ai-and-kr/module2/sections/_descriptive_logic.tex +++ b/src/fundamentals-of-ai-and-kr/module2/sections/_descriptive_logic.tex @@ -54,7 +54,7 @@ \end{description} - \item[Assetion box (A-box)] \marginnote{Assetion box (A-box)} + \item[Assertion box (A-box)] \marginnote{Assertion box (A-box)} List of facts about individuals. \item[Terminological box (T-box)] \marginnote{Terminological box (T-box)} @@ -71,7 +71,7 @@ Let \texttt{r} be a role, \texttt{d} be a concept, \texttt{c} be a constant and The semantics of concept-forming operators are: \begin{descriptionlist} \item[\texttt{[ALL r d]}] - Individuals \texttt{r}-related to the individuals of the category \texttt{d}. + Individuals \texttt{r}-related to only individuals of the category \texttt{d}. \begin{example} \texttt{[ALL :HasChild Male]} individuals that have zero children or only male children. \end{example} @@ -140,13 +140,13 @@ The semantics of sentences are: \[ \mathcal{I}[\texttt{[ALL r d]}] = \{ \texttt{x} \in \mathcal{D} \mid \forall \texttt{y}: - \langle \texttt{x}, \texttt{y} \rangle \in \mathcal{I}[r] \text{ then } \texttt{y} \in \mathcal{I}[d] \} + \langle \texttt{x}, \texttt{y} \rangle \in \mathcal{I}[\texttt{r}] \text{ then } \texttt{y} \in \mathcal{I}[\texttt{d}] \} \] \item[\texttt{[EXISTS $n$ r]}] \[ \mathcal{I}[\texttt{[EXISTS $n$ r]}] = \{ \texttt{x} \in \mathcal{D} \mid \text{ exists at least $n$ distinct } \texttt{y}: - \langle \texttt{x}, \texttt{y} \rangle \in \mathcal{I}[r] \} + \langle \texttt{x}, \texttt{y} \rangle \in \mathcal{I}[\texttt{r}] \} \] \item[\texttt{[FILLS r c]}] \[ @@ -186,23 +186,23 @@ The semantics of sentences are: \subsection{T-box reasoning} Given a knowledge base of a set of sentences $S$, we would like to be able to determine the following: -\begin{description} +\begin{descriptionlist} \item[Satisfiability] \marginnote{Satisfiability} A concept \texttt{d} is satisfiable w.r.t. $S$ if: - \[ \exists \mathfrak{I}, (\mathfrak{I} \models S): \mathfrak{I}[\texttt{d}] \neq \varnothing \] + \[ \exists \mathfrak{I}, (\mathfrak{I} \models S): \mathcal{I}[\texttt{d}] \neq \varnothing \] \item[Subsumption] \marginnote{Subsumption} A concept $\texttt{d}_1$ is subsumed by $\texttt{d}_2$ w.r.t. $S$ if: - \[ \forall \mathfrak{I}, (\mathfrak{I} \models S): \mathfrak{I}[\texttt{d}_1] \subseteq \mathfrak{I}[\texttt{d}_2] \] + \[ \forall \mathfrak{I}, (\mathfrak{I} \models S): \mathcal{I}[\texttt{d}_1] \subseteq \mathcal{I}[\texttt{d}_2] \] \item[Equivalence] \marginnote{Equivalence} A concept $\texttt{d}_1$ is equivalent to $\texttt{d}_2$ w.r.t. $S$ if: - \[ \forall \mathfrak{I}, (\mathfrak{I} \models S): \mathfrak{I}[\texttt{d}_1] = \mathfrak{I}[\texttt{d}_2] \] + \[ \forall \mathfrak{I}, (\mathfrak{I} \models S): \mathcal{I}[\texttt{d}_1] = \mathcal{I}[\texttt{d}_2] \] \item[Disjointness] \marginnote{Disjointness} A concept $\texttt{d}_1$ is disjoint to $\texttt{d}_2$ w.r.t. $S$ if: - \[ \forall \mathfrak{I}, (\mathfrak{I} \models S): \mathfrak{I}[\texttt{d}_1] \neq \mathfrak{I}[\texttt{d}_2] \] -\end{description} + \[ \forall \mathfrak{I}, (\mathfrak{I} \models S): \mathcal{I}[\texttt{d}_1] \neq \mathcal{I}[\texttt{d}_2] \] +\end{descriptionlist} \begin{theorem}[Reduction to subsumption] \marginnote{Reduction to subsumption} @@ -216,13 +216,13 @@ Given a knowledge base of a set of sentences $S$, we would like to be able to de \subsection{A-box reasoning} Given a constant \texttt{c}, a concept \texttt{d} and a set of sentences $S$, we can determine the following: -\begin{description} +\begin{descriptionlist} \item[Satisfiability] \marginnote{Satisfiability} A constant \texttt{c} satisfies the concept \texttt{d} if: \[ S \models (\texttt{c} \rightarrow \texttt{d}) \] Note that it can be reduced to subsumption. -\end{description} +\end{descriptionlist} \subsection{Computing subsumptions} @@ -237,18 +237,19 @@ The following algorithms can be employed: \begin{enumerate} \item Normalize \texttt{d} and \texttt{e} into a conjunctive form: \[ \texttt{d} = \texttt{[AND d$_1$ \dots d$_n$]} \hspace*{1cm} \texttt{e} = \texttt{[AND e$_1$ \dots e$_m$]} \] - \item Check if each part of \texttt{e} is accounted by at least a component of \texttt{d}. + \item Check if each part of \texttt{d} is accounted by at least a component of \texttt{e}. \end{enumerate} \item[Tableaux-based algorithms] \marginnote{Tableaux-based algorithms} Exploit the following theorem: - \[ (KB \models (C \sqsubseteq D)) \iff (KB \cup (x : C \sqcap \lnot D)) \text{ is inconsistent} \] + \[ \big( KB \models (\texttt{d} \sqsubseteq \texttt{e}) \big) \iff + \big( KB \cup (x : \texttt{[AND d $\lnot$e]}) \big) \text{ is inconsistent} \] Note: similar to refutation. \end{descriptionlist} -\subsection{Open world assumption} +\subsection{Open-world assumption} \begin{description} \item[Open-world assumption] \marginnote{Open-world assumption} @@ -256,7 +257,7 @@ The following algorithms can be employed: \end{description} Description logics are based on the open-world assumption. -To reason in open world assumption, all the possible models are split upon encountering unknown facts +To reason in open-world assumption, all the possible models are split upon encountering unknown facts depending on the possible cases (Oedipus example). diff --git a/src/fundamentals-of-ai-and-kr/module2/sections/_forward_reasoning.tex b/src/fundamentals-of-ai-and-kr/module2/sections/_forward_reasoning.tex index 64a649b..9889e76 100644 --- a/src/fundamentals-of-ai-and-kr/module2/sections/_forward_reasoning.tex +++ b/src/fundamentals-of-ai-and-kr/module2/sections/_forward_reasoning.tex @@ -162,7 +162,7 @@ RETE-based rule engine that uses Java. Event detected outside an event processing system (e.g. a sensor). It does not provide any information alone. \item[Complex event] \marginnote{Complex event} - Event generated by an event processing system and provides a higher informative payload. + Event generated by an event processing system and able to provides a higher informative payload. \item[Complex event processing (CEP)] \marginnote{Complex event processing} Paradigm for dealing with a large amount of information. diff --git a/src/fundamentals-of-ai-and-kr/module2/sections/_ontologies.tex b/src/fundamentals-of-ai-and-kr/module2/sections/_ontologies.tex index c3fef63..f909a22 100644 --- a/src/fundamentals-of-ai-and-kr/module2/sections/_ontologies.tex +++ b/src/fundamentals-of-ai-and-kr/module2/sections/_ontologies.tex @@ -75,7 +75,7 @@ \item[Exhaustive decomposition] \marginnote{Exhaustive decomposition} Given a category $c$ and a set of categories $S$, $S$ is an exhaustive decomposition of $c$ iff any element in $c$ belongs to at least a category in $S$: - \[ \texttt{exhaustiveDecomposition($S$, $c$)} \iff (\forall o \in c \iff \exists c_2 \in S: o \in c_2) \] + \[ \texttt{exhaustiveDecomposition($S$, $c$)} \iff \forall o: (o \in c \iff \exists c_2 \in S: o \in c_2) \] \item[Partition] \marginnote{Partition} Given a category $c$ and a set of categories $S$, $S$ is a partition of $c$ when: diff --git a/src/fundamentals-of-ai-and-kr/module2/sections/_semantic_web.tex b/src/fundamentals-of-ai-and-kr/module2/sections/_semantic_web.tex index 0a829a5..800e3a5 100644 --- a/src/fundamentals-of-ai-and-kr/module2/sections/_semantic_web.tex +++ b/src/fundamentals-of-ai-and-kr/module2/sections/_semantic_web.tex @@ -130,7 +130,7 @@ xmlns:contact=http://www.w3.org/2000/10/swap/pim/contact#> \item[Graph embedding] \marginnote{Graph embedding} Project entities and relations into a vectorial space for ML applications. \begin{description} - \item[Entity prediction] Given two entities \texttt{h} and \texttt{t}, determine the relation \texttt{r} between them. - \item[Link prediction] Given an entity \texttt{h} and a relation \texttt{t}, determine an entity \texttt{t} related to \texttt{h}. + \item[Link prediction] Given two entities \texttt{h} and \texttt{t}, determine the relation \texttt{r} between them. + \item[Entity prediction] Given an entity \texttt{h} and a relation \texttt{t}, determine an entity \texttt{t}-related to \texttt{h}. \end{description} \end{description} \ No newline at end of file diff --git a/src/fundamentals-of-ai-and-kr/module2/sections/_time_reasoning.tex b/src/fundamentals-of-ai-and-kr/module2/sections/_time_reasoning.tex index d1db8f7..7d68b44 100644 --- a/src/fundamentals-of-ai-and-kr/module2/sections/_time_reasoning.tex +++ b/src/fundamentals-of-ai-and-kr/module2/sections/_time_reasoning.tex @@ -251,11 +251,11 @@ Logic-based on interacting agents with their own knowledge base. Formally, semantics is defined on a set of primitive propositions $\phi$ using a Kripke structure $M = (S, \pi, K_\texttt{1}, \dots, K_\texttt{n})$ where: \begin{itemize} - \item $S$ is a set of states of the world. + \item $S$ is a set of the states of the world. \item $\pi: \phi \rightarrow 2^S$ specifies in which states each primitive proposition holds. \item $K_\texttt{i} \subseteq S \times S$ is a binary relation where $(s, t) \in K_\texttt{i}$ if an agent \texttt{i} considers the world $t$ possible (accessible) from $s$. - In other words, when the agent is in the world $s$, it considers $t$ to be a possibly valid world. + In other words, when the agent is in the world $s$, it considers $t$ to also be a possibly valid world. Obviously, $(s, s) \in K_\texttt{i}$ for all states. \end{itemize} @@ -272,7 +272,7 @@ Logic-based on interacting agents with their own knowledge base. $\pi(\texttt{heads}) = \{ h_1, h_2 \}$\\ $\pi(\texttt{tails}) = \{ t_1, t_2 \}$ \item - $K_\texttt{a} = \{ (s, s) \mid s \in S \}$ as Alice observes everything in each world and does not have doubts.\\ + $K_\texttt{a} = \{ (s, s) \mid s \in S \}$ as Alice observes everything in each world and does not have uncertainty.\\ $K_\texttt{b} = \{ (s, s) \mid s \in S \} \cup \{ (h_1, t_1), (t_1, h_1) \}$ as Bob is unsure of what happens in the second stage.\\ \end{itemize} \vspace*{-1em} @@ -313,7 +313,7 @@ Logic-based on interacting agents with their own knowledge base. \end{description} \end{description} - Different modal logics can be defined based on the valid axioms. + Different modal logics can be defined based on the validity of these axioms. \end{description} @@ -346,7 +346,7 @@ The accessibility relation maps into the temporal dimension with two possible ev $\varphi$ is always true from now on. \item[Future ($\diamond \varphi$)] \marginnote{Future} - $\varphi$ is true sometimes in the future. + $\varphi$ is sometimes true in the future. It is equivalent to $\lnot\square(\lnot \varphi)$. \item[Until ($\varphi \mathcal{U} \psi$)] \marginnote{Until} @@ -360,7 +360,7 @@ The accessibility relation maps into the temporal dimension with two possible ev \item[Semantics] Given a Kripke structure, $M = (S, \pi, K_\texttt{1}, \dots, K_\texttt{n})$ where states are represented using integers, - the semantic of the operators is the following: + the semantics of the operators is the following: \begin{itemize} \item $(M, i) \models P \iff i \in \pi(P)$. \item $(M, i) \models \bigcirc\varphi \iff (M, i+1) \models \varphi$.