Interpretation

logic

Definition

Interpretation

An interpretation $I$ is a function $I$:

$$I:X\to \{\text{true},\text{false}\}$$

$I(\cdot )$ is defined inductively using atoms:

• $\varphi =\neg {\varphi }_1$ :

\quad I(\phi) = \text{true} \iff I(\phi_{1}) = \text{false}

- $\phi = \phi_{1} \land \phi_{2}$:

I(\phi) = \text{true} \iff I(\phi_{1}) = I(\phi_{2}) = \text{true}

- $\phi = \phi_{1} \lor \phi_{2}$:

I(\phi) = \text{true} \iff I(\phi_{1}) = \text{true} \lor I(\phi_{2}) = \text{true}