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 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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