From 62caefa927e3067596c550585d90b700c66c0d85 Mon Sep 17 00:00:00 2001 From: NotXia <35894453+NotXia@users.noreply.github.com> Date: Wed, 22 Nov 2023 22:02:47 +0100 Subject: [PATCH] Add FAIKR2 ontologies --- .../module2/main.tex | 1 + .../module2/sections/_ontoligies.tex | 163 ++++++++++++++++++ 2 files changed, 164 insertions(+) create mode 100644 src/fundamentals-of-ai-and-kr/module2/sections/_ontoligies.tex diff --git a/src/fundamentals-of-ai-and-kr/module2/main.tex b/src/fundamentals-of-ai-and-kr/module2/main.tex index 793d031..2007969 100644 --- a/src/fundamentals-of-ai-and-kr/module2/main.tex +++ b/src/fundamentals-of-ai-and-kr/module2/main.tex @@ -7,5 +7,6 @@ \makenotesfront \input{sections/_logic.tex} + \input{sections/_ontoligies.tex} \end{document} \ No newline at end of file diff --git a/src/fundamentals-of-ai-and-kr/module2/sections/_ontoligies.tex b/src/fundamentals-of-ai-and-kr/module2/sections/_ontoligies.tex new file mode 100644 index 0000000..1f14640 --- /dev/null +++ b/src/fundamentals-of-ai-and-kr/module2/sections/_ontoligies.tex @@ -0,0 +1,163 @@ +\chapter{Ontologies} + +\begin{description} + \item[Ontology] \marginnote{Ontology} + Formal (non-ambiguous) and explicit (obtainable through a finite sound procedure) + description of a domain. + + \item[Category] \marginnote{Category} + Can be organized hierarchically on different levels of generality. + + \item[Object] \marginnote{Object} + Belongs to one or more categories. + + \item[Upper/general ontology] \marginnote{Upper/general ontology} + Ontology focused on the most general domain. + + Properties: + \begin{itemize} + \item Should be applicable to almost any special domain. + \item Combining general concepts should not incur in inconsistences. + \end{itemize} + + Approaches to create ontologies: + \begin{itemize} + \item Created by philosophers/logicians/researchers. + \item Automatic knowledge extraction from well-structured databases. + \item Created from text documents (e.g. web). + \item Crowd-sharing information. + \end{itemize} +\end{description} + + +\section{Categories} +\begin{description} + \item[Category] \marginnote{Category} + Used in human reasoning when the goal is category-driven (in contrast to specific-instance-driven). + + In first order logic, categories can be represented through: + \begin{descriptionlist} + \item[Predicate] \marginnote{Predicate categories} + A predicate to tell if an object belongs to a category + (e.g. \texttt{Car(c1)} indicates that \texttt{c1} is a car). + + \item[Reification] \marginnote{Reification} + Represent categories as objects as well (e.g. $\texttt{c1} \in \texttt{Car}$). + \end{descriptionlist} +\end{description} + +\subsection{Reification properties and operations} +\begin{description} + \item[Membership] \marginnote{Membership} + Indicates if an object belongs to a category. + (e.g. $\texttt{c1} \in \texttt{Car}$). + + \item[Subclass] \marginnote{Subclass} + Indicates if a category is a subcategory of another one. + (e.g. $\texttt{Car} \subset \texttt{Vehicle}$). + + \item[Necessity] \marginnote{Necessity} + Members of a category enjoy some properties + (e.g. $(\text{x} \in \texttt{Car}) \rightarrow \texttt{hasWheels(x)}$). + + \item[Sufficiency] \marginnote{Sufficiency} + Sufficient conditions to be part of a category\\ + (e.g. $\texttt{hasPlate(x)} \land \texttt{hasWheels(x)} \rightarrow \texttt{x} \in \texttt{Car}$). + + \item[Category-level properties] \marginnote{Category-level properties} + Category themselves can enjoy properties\\ + (e.g. $\texttt{Car} \in \texttt{VehicleType}$) + + \item[Disjointness] \marginnote{Disjointness} + Given a set of categories $S$, the categories in $S$ are disjoint iff they all have different objects: + \[ \texttt{disjoint($S$)} \iff (\forall c_1, c_2 \in S, c_1 \neq c_2 \rightarrow c_1 \cap c_2 = \emptyset) \] + + \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 $S$: + \[ \texttt{exhaustiveDecomposition($S$, $c$)} \iff (\forall o \in c \iff \exists c_2 \in S: o \in c_2) \] + + \item[Partition] \marginnote{Partition} + Given a category $c$ and a set of categories $S$, $S$ is a partition of $c$ when: + \[ \texttt{partition($S$, $c$)} \iff \texttt{disjoint($S$)} \land \texttt{exhaustiveDecomposition($S$, $c$)} \] +\end{description} + + +\subsection{Physical composition} +Objects (meronyms) are part of a whole (holonym). + +\begin{description} + \item[Part-of] \marginnote{Part-of} + If the objects have a structural relation (e.g. $\texttt{partOf(cylinder1, engine1)}$). + + Properties: + \begin{descriptionlist} + \item[Transitivity] $\texttt{partOf(x, y)} \land \texttt{partOf(y, z)} \rightarrow \texttt{partOf(x, z)}$ + \item[Reflexivity] $\texttt{partOf(x, x)}$ + \end{descriptionlist} + + \item[Bunch-of] \marginnote{Bunch-of} + If the objects do not have a structural relation. + Useful to define a composition of countable objects + (e.g. $\texttt{bunchOf({nail1, nail3, nail4})}$). +\end{description} + + +\subsection{Measures} + +A property of objects. + +\begin{description} + \item[Quantitative measure] \marginnote{Quantitative measure} + Something that can be measured using some unit\\ + (e.g. $\texttt{length(table1)} = \texttt{cm(80)}$). + + Qualitative measures propagate when using \texttt{partOf} or \texttt{bunchOf} + (e.g. the weight of a car is the sum of its parts). + + \item[Qualitative measure] \marginnote{Qualitative measure} + Something that can be measured using terms with a partial or total order relation + (e.g. $\{ \texttt{good}, \texttt{neutral}, \texttt{bad} \}$). + + Qualitative measures do not propagate when using \texttt{partOf} or \texttt{bunchOf}. + + \item[Fuzzy logic] \marginnote{Fuzzy logic} + Provides a semantics to qualitative measures (i.e. convert qualitative to quantitative). +\end{description} + + +\subsection{Things vs stuff} + +\begin{description} + \item[Intrinsic property] \marginnote{Intrinsic property} + Related to the substance of the object. It is retained when the object is divided + (e.g. water boils at 100°C). + + \item[Extrinsic property] \marginnote{Extrinsic property} + Related to the structure of the object. It is not retained when the object is divided + (e.g. the weight of an object changes when split). + + \item[Substance] \marginnote{Substance} + Category of objects with only intrinsic properties. + + \begin{description} + \item[Stuff] \marginnote{Stuff} + The most general substance category. + \end{description} + + \item[Count noun] \marginnote{Count noun} + Category of objects with only extrinsic properties. + + \begin{description} + \item[Things] \marginnote{Things} + The most general object category. + \end{description} +\end{description} + + + +\section{Semantic networks} + + + +\section{Frames} \ No newline at end of file