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))

Chris Fox, September 1995