Hi again

I am still reading the book A Short Introduction to Modal Logic by Mintis, and I am still on the Classical propositional logic.

On p.7 Mintis has defined tautologies and a "refutation procedure" for testing whether a formula, a, is a tautology. You do this by assuming not-a, and test for satisfying assignments. If all branches in tree end up as contradictions, a is a tautology. He calls this procedure P.

So far so good. Now the author wants to give "a description of the procedure P for finding a satisfying assignment by construction of a refutation tree, will be given for a finite set of formulas. Assignments are extended to lists of formulas by putting

v(G)=v(a_1)^...^v(a_n)

for G ≡ a_1,...,a_n. So

v(G)=1 iff v(a_1)=1^...^v(a_n)=1".

I guess the crucial phrase that I don't understand is "assignments are extended to lists of formulas"... If he by G meant any formula, such as (p ^ q) ^ not-r, and by the a_1...a_n's would be the atomic formulas which all will have to be true in order for G to be true, I would understand. Would you say this is what he means or does he mean something in addition to this by saying "extending assignments to lists of formulas", and if so, what?