If F, G are PropFormulas, then so are
,
,
and
.
Nothing else is a PropFormula.
We can assign to every formula a mathematical meaning as a pure proposition.
Given a formula F, let
be the propositional variables
occurring in it (say ordered from left to right); let
be the vector
of them. Define a map from n variable propositional formulas,
PropFormulasn, into
inductively by
For each variable Pi, corresponds to the projection function
.
Say that F is validvalid iff
is a valid pure proposition.