A1Q3 solution question

[Roman]

Before doing induction, we define valuation s by p^s = [S(p)]^t for all
prop. variables where S is the substitution into p.

I don't understand what this means exactly, can someone clarify? It
makes sense when we replace p with a non-atomic formula A, then I see it
as the substitution and the formula A having the same values under
valuation t/s (ie. A^s = [S(A)]^t = 1 => both valid).

Thanks...

[Curtis Bright]

Post by Roman
Before doing induction, we define valuation s by p^s = [S(p)]^t for all
prop. variables where S is the substitution into p.
I don't understand what this means exactly, can someone clarify?

To define a valuation, you need to specify what its output value is for
every propositional variable. In this case, valuation s is being
defined so that on input p its output is [S(p)]^t where 'p' represents
an arbitrary propositional variable.

Curtis