What is $\beta(p_i)$ where $p_i$ is a propositional variable?

Question

Let $\beta \in \mathscr{A}$ and let $P$ be a an infinite set of propositional variables.

Is $\beta(p_i)$, for $p_i \in P$ just the value of $p_i$ under the truth assignment $\beta$?

Sorry if this seems like an obvious question, I just came across this notation in a homework assignment and I've never seen it before, so I don't want to make the wrong assumption.

Thanks for your help.

Answer 1

A truth assignment, or valuation is a function that maps atoms, i.e. propositionals variables to truth values :

$\beta : \text P \to \{ \text T, \text F \}$,

where $\text P = \{ p_0, p_1, p_2, \ldots \}$.

Thus $\beta(p_i)$ is either $\text T$ or $\text F$.