We analyze the behaviour of declarations of independence between existential
quantifiers in quantifier prefixes of IF sentences; we give a syntactical
criterion for deciding whether a sentence beginning with such prefix exists
such that its truth values may be affected by removal of the declaration of
independence. We extend the result also to equilibrium semantics values for
undetermined IF sentences.
The main theorem allows us to describe the behaviour of various particular
classes of quantifier prefixes, and to prove as a remarkable corollary that all
existential IF sentences are equivalent to first-order sentences.
As a further consequence, we prove that the fragment of IF sentences with
knowledge memory has only first-order expressive power (up to truth
equivalence)
