## Truth evaluation in FOL


## Technical application

A limited though useful device for depicting truth-evaluative relations between interpretation and truth-functional semantics in FOL is what is called a **model**.


A model is comprised of:

- a **domain of discourse** $\mathbb{D}$, or set of all objects occuring in the domain;
- extensions of $n$-tuples of objects in the domain for all $n$-ary predicates; and
- referents (objects in the domain) for all constants.

### Example

The following model satisfies the set of sentences:

$$ \{\forall x (Px \to Qx), \exists x (Px \wedge Qx), (Qa \wedge \neg Pa)\}$$

$$
\begin{align}
\mathbb{D} &= \{\text{El, Al}\}\\
P & =\{\text{El}\}\\
Q & =\{\text{El, Al}\}\\
a & = \text{Al}
\end{align}
$$
