Coping with the White Knight in Planning

Recent Tweak-based planners replace the White Knight technique of a modal truth criterion by a simple heuristic for choosing the estab-lisher of a term in situation, empirically trading between the rigorous precision of a criterion and the computational complexity. In this paper , I argue that this WK technique does not rely on the opposition between mathematical rigour and eeciency of an implementation, but on the choice of the formal logic a planner implicitly uses. I show that the WK can be eeciently traded for a maximality condition in propo-sitional logic. On the other hand, planners without functional terms are demonstrated not to evolve in a rst order logic; in an intermediate 0 + order logic, the notion of justiication subsumes usual establishers or WKs one, and allows the deenition of the degree of a modal truth criterion. Correction of a plan is preserved when the strength of such a criterion is increased.