The converse is, however, not true: not every formula in the epsilon calculus is the image of an ordinary quantified formula under this embedding.
In this way, when we check to see whether a sequence satisfies the existentially quantified formula ("interpreting the quantifier"), this determines which sequences we look at in determining whether they satisfy the formula the quantifier fronts (thus "affecting its interpretation").
That is, in accordance with McMichael's recursive definition of truth, (11) unpacks the quantified formula '∃xCxy' in terms of the [child of] relation that is expressed by the embedded atomic formula 'Cxy'.
A prototypical example of a problem in \ \textbf{PSPACE}\) can be formulated using the notion of a quantified boolean formula [QBF] – i.e. a statement of the form \(Q_1 x_i \ldots Q_n x_n\psi\) where \(Q_i = \exists\) or \(\forall\) and \ \psi\) is a formula of propositional logic containing the propositional variables \(x_1,\ldots,x_n\) which are treated as bound by these quantifiers.
We may now define the problem \(\sc{TQBF}\ \) Given a quantified boolean formula \ \phi\), is \ \phi\) true?
Both of these can be quantified and included in a quantified model of emotions.
It follows by the definition of truth at a world for quantified formulas that, for some individual a in the domain of I, φ is trueI,f[x,a] at w1 and, hence, by the definition of truth at a world for modal formulas again, that ◇φ is trueI,f[x,a] at w0.
The name "Jack the Ripper" gets reduced to a description embedded in a quantified statement.
A study of fragments in a quantified manner could provide an answer to these kinds of questions.
