First Order Logic Set Notation for clauses

Question

I found a set of clauses expressed in this way in first order logic :

$\left \{ \left \{ -p,q \right \},\left \{ r \right \} \right \}$

I have never seen this kind of formalism, so i ask your help to understand it.

What i think is that the outer comma represent an AND, while the inner comma represent an OR . Is correct ?

Answer 1

Yes, it is.

See Resolution, as well as : Mordechai Ben-Ari, Mathematical Logic for Computer Science, Springer (3rd ed 2012), page 77.

The set of clauses $\{ \{ \lnot p, q \},\{ r \} \}$ is the clausal form of the CNF formula :

$(\lnot p \lor q) \land r$.