Metalogic-- EASY definition question, but crucial!

[nonvestigial]

In the metatheory of Sentential Logic, what is the difference between saying

P is T on \alpha

vs.

\alpha(P)=T

and is it related to the diff between a truth-function and a truth-value assignment?

This is NOT homework or for a grade btw, although it is baffling me as I take a metalogic course, and I would like to know ASAP as we have an exam coming up.

S

[honestrosewater]

I am more used to saying that a formula is true (or whatever) under a given valuation, but I suppose P is T on α makes enough sense. Your two expressions both express the same relationship to me: the value assigned by a function to an input. If you are asking about a definition, though, then the definer (your book or instructor, I imagine) is the only one that can give you a definitive answer.

What is the difference (to you) between a truth-function and a truth-value assignment? The truth-function is from truth-values to truth-values and based on an assignment (which is from (atomic) formulas to truth-values)?