Tautology by default?

"A propositional formula is a tautology if it is true under every valuation of its predicate symbols."

How do you call a formula that is always true, but due to valuation restrictions?

To illustrate, consider first the Liar Paradox
S1: This statement (S1) is false.
This is clearly an inconsistent statement: if it’s True then it’s False and vice versa.

Now consider the following
S2: If this statement (S2) is false, then it is logically inconsistent
Denote P = "This statement is false", and Q = "This statement is logically inconsistent".
Suppose S2 is False, then (P,Q) = (T,F) which means it is False by its own admission yet it is Not paradoxical, in contradiction to S1.
Suppose S2 is True; if (P,Q) = (T,T) then it is both True (because the way the statement is constructed), False (because P is evaluated T) and paradoxical (because Q is evaluated T), so clearly (P,Q) cannot be evaluated (T,T). If (P,Q) = (F,T) then again, it is both True (because it is Not False) and paradoxical.
So we have no choice but to assume that both P and Q are False and S2 is True by default.
(Obviously, this question could have been formulated to adress the analogous case of contradiction by default.)