model-checking

A formula has a valuation. Valuation means it may have value true or false. This is also called as interpretation of the formula.

If the interpretation results in true value, then we can say that the interpretation is the model of the formula (Not sure about this statement. Some resources say this and some tell some other).

For example, let’s take this formula and try to find its model.

$$\neg (A\to B)$$

We have to find valuation that results in true value for the formula.

$(A\to B)$ has to be false which means, $A$ has to be $true$ and $B$ has to be $false$. So, the whole formula turns into $false$. Refer the truth table for implies.

$\neg (A\to B)$ will becomes $true$. We found the model for this formula.

If $\neg (A\to B)$ has no model, then we can say that $(A\to B)$ is tautology.

References

1. Propositional logic review