  In the modal mu-calculus, a formula is well-formed if each recursive variable
occurs underneath an even number of negations. By means of De Morgan's laws, it
is easy to transform any well-formed formula into an equivalent formula without
negations -- its negation normal form. Moreover, if the formula is of size n,
its negation normal form of is of the same size O(n). The full modal
mu-calculus and the negation normal form fragment are thus equally expressive
and concise.
  In this paper we extend this result to the higher-order modal fixed point
logic (HFL), an extension of the modal mu-calculus with higher-order recursive
predicate transformers. We present a procedure that converts a formula into an
equivalent formula without negations of quadratic size in the worst case and of
linear size when the number of variables of the formula is fixed.
