Model

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Propositional Logic:

In terms of a logic formula, a ["Model"] is some assignment of variables that causes the formula to be true.

First Order Logic:

A {\bf model} for a set $X$ of formulas is an interpretation $M$ for $X$ such that every formula of $X$ is true in $M$.

A {\em domain} $D$ is any nonempty set. An {\em interpretation} for a set of formulas $X$, is a domain $D$ togther with a rule that 
\begin{enumerate}
\item assigns to each $n$-place predicate symbol (that occurs in a formula) of $X$ an $n$-place predicate in $D$;
\item assigns to each $n$-place operation symbol of $X$ an $n$-place operation in $D$;
\item assigns to each constant symbol of $X$ an element of $D$; and
\item assigns to $=$ the identity predicate $=$ in $D$, defined by: $a=b$ iff $a$ and $b$ are the same.
\end{enumerate}

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