Representation of Fragmentary Multilayered Knowledge

Formalization presupposes ‘precisification’. A formal representation, therefore, cannot account for all relevant aspects of imprecise domain knowledge. In this paper we present a methodology for dealing with this problem. In an imprecise domain, part of the expertise is to know the realm within which knowledge may be faithfully specialized. In a computer reasoning system, such expert knowledge can be reproduced as a metatheory for proposing and reasoning with formal object theories, each representing one particular specialization. Metaknowledge of this kind will however most often also be imprecise and the expertise on how it may be specialized resides then at the metametalevel, etc. We show that logic provability and upward reflection are adequate means for representing such hierarchical domain knowledge and the dependencies in it between adjacent levels.