# Semantic Argument Method

Suppose we want to prove the validity of a propositional logic formula . Several methods to do this exists, one of which is called the semantic argument method.

We start the proof by assuming that a falsifying interpretation exists:

and try to show that this leads to a contradiction by applying semantic definitions of the logical connectives.

Thus, we obtain a set of proof rules:

### Extension to First-order logic

The proof rules above apply in addition to the following proof rules for the quantifiers:

for any in the domain of the interpretation.

for any in the domain of the interpretation.

for a fresh in the domain of the interpretation.

for a fresh in the domain of the interpretation.