Questionnaire-2024/predicate_logic/0015_sol.tex

\textbf{Definition - Model in Predicate Logic.} \textit{A model $\mathcal{M}$ consists of the following set of data:}
\begin{itemize}
    \item \textit{A non-empty set $\mathcal{A}$, the universe/domain of concrete values;}
    \item \textit{for each nullary function symbol $f \in \mathcal{F}$, a concrete element $f^\mathcal{M} \in \mathcal{A}$;}
    \item \textit{for each nullary predicate symbol $P \in \mathcal{P}$, a truth value;}
    \item \textit{for each function symbol $f \in \mathcal{F}$ with arity $n > 0$ a concrete function $f^\mathcal{M}: \mathcal{A}^n \imp \mathcal{A}$;}
    \item \textit{for each predicate smybol $P \in \mathcal{P}$ with arity $n > 0$: subset $P^\mathcal{M} \subseteq	\mathcal{A}^n$;}
    \item \textit{for any free variable} var: \textit{a lookup-table $t:$} var \textit{$\imp \mathcal{A}$.}
\end{itemize}