The expression obtained by the parser is not a logical expression. To use the semantics, we must find its truth conditions. These are expressed in First Order Logic. (This is also called Predicate Logic. In papers on Property Theory, this is sometimes called the language of well formed formulae (wff).)
In theory, to find the truth conditions of the Property-theoretic representations, we must first prove that the representation expresses a legitimate proposition (using axioms of propositionhood) and then obtain the logical expression (by applying axioms of truth).
In the Squirrel grammar as it stands, the representations of all allowed sentences form propositions, so the propositionhood of the representation is not explicilty checked.
As with the Property-theoretic representations in Squirrel, the first order logic expression produced by Squirrel is an approximation of the kind of expressions commonly used. The expression
is usually written something like:exists(a,manager(a)&for(fva1,`work,a))