Logical frameworks with a logic programing interpretation such as hereditary Harrop formulae (HHF) do not allow to express directly negative information, in order to preserve goal-oriented proof search. Since negation-as-failure does not fit well in a logical framework especially one endowed with hypothetical and parametric judgments, we adapt the idea of elimination of negation in Horn logic to a fragment of higher-order HHF. This entails finding a middle ground between the Closed World Assumption usually associated with negation and the Open World Assumption typical of logical frameworks; the main technical idea is to isolate a set of programs where static and dynamic clauses do not overlap.

The slides are available here.