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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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'''Propositional Logic:'''
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+'''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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