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{{{#!latex2
\noindent A {\bf model} for a set $X$ of formulas is an interpretation $M$ for $X$ such that every formula of $X$ is true in $M$.\bigskip		 A '''model''' for a set $$X$$ of formulas is an interpretation $$M$$ for $$X$$ such that every formula of $$X$$ is true in $$M$$.
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\noindent 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}
}}}		 A ''domain'' $$D$$ is any nonempty set. An ''interpretation'' for a set of formulas $$X$$, is a domain $$D$$ together with a rule that

 * assigns to each $$n$$-place predicate symbol (that occurs in a formula) of $$X$$ an $$n$$-place predicate in $$D$$;
 * assigns to each $$n$$-place operation symbol of $$X$$ an $$n$$-place operation in $$D$$;
 * assigns to each constant symbol of $$X$$ an element of $$D$$; and
 * assigns to $$=$$ the identity predicate $$=$$ in $$D$$, defined by: $$a=b$$ iff $$a$$ and $$b$$ are the same.

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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 model for a set $$X$$ of formulas is an interpretation $$M$$ for $$X$$ such that every formula of $$X$$ is true in $$M$$.

A domain $$D$$ is any nonempty set. An interpretation for a set of formulas $$X$$, is a domain $$D$$ together with a rule that

  • assigns to each $$n$$-place predicate symbol (that occurs in a formula) of $$X$$ an $$n$$-place predicate in $$D$$;
  • assigns to each $$n$$-place operation symbol of $$X$$ an $$n$$-place operation in $$D$$;
  • assigns to each constant symbol of $$X$$ an element of $$D$$; and
  • assigns to $$=$$ the identity predicate $$=$$ in $$D$$, defined by: $$a=b$$ iff $$a$$ and $$b$$ are the same.

See: First Order Mathematical Logic by Angelo Margaris p 145

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Model (last edited 2020-01-26 23:01:28 by scot)