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Add FAIRK2 time reasoning

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Tian Cheng (Riccardo) Xia
2023-12-03 13:57:44 +01:00
parent ec3d1752a8
commit 2bd1d90bc8
4 changed files with 219 additions and 4 deletions
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8
src/fundamentals-of-ai-and-kr/module2/sections/_ontologies.tex
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@ -58,11 +58,11 @@
\item[Necessity] \marginnote{Necessity}
Members of a category enjoy some properties
(e.g. $(\text{x} \in \texttt{Car}) \rightarrow \texttt{hasWheels(x)}$).
(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. $\texttt{hasPlate(x)} \land \texttt{hasWheels(x)} \rightarrow \texttt{x} \in \texttt{Car}$).
(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\\
@ -70,7 +70,7 @@
\item[Disjointness] \marginnote{Disjointness}
Given a set of categories $S$, the categories in $S$ are disjoint iff they all have different objects:
\[ \texttt{disjoint($S$)} \iff (\forall c_1, c_2 \in S, c_1 \neq c_2 \rightarrow c_1 \cap c_2 = \emptyset) \]
\[ \texttt{disjoint($S$)} \iff (\forall c_1, c_2 \in S, c_1 \neq c_2 \Rightarrow c_1 \cap c_2 = \emptyset) \]
\item[Exhaustive decomposition] \marginnote{Exhaustive decomposition}
Given a category $c$ and a set of categories $S$, $S$ is an exhaustive decomposition of $c$ iff
@ -92,7 +92,7 @@ Objects (meronyms) are part of a whole (holonym).
Properties:
\begin{descriptionlist}
\item[Transitivity] $\texttt{partOf(x, y)} \land \texttt{partOf(y, z)} \rightarrow \texttt{partOf(x, z)}$
\item[Transitivity] $\texttt{partOf(x, y)} \land \texttt{partOf(y, z)} \Rightarrow \texttt{partOf(x, z)}$
\item[Reflexivity] $\texttt{partOf(x, x)}$
\end{descriptionlist}