The ontological analysis of parts and wholes gathers recently increasing interest, and develops into a specific research area called mereology. So far, most research has focused on directions motivated by engineering examples and by linguistic analysis. In contrast to these, the related archeological problem is characterized by missing pieces and information, which cannot easily be recovered, and by reasoning and experimentation with multiple hypotheses. This aspect of mereology has not yet been formally analyzed. In this paper, we continue previous work by addressing the formalization of some of the reasoning needed to identify other parts of the same whole through knowledge about some parts, or to narrow down the category of wholes a part may have belonged to. We define a hierarchical and an associative part-of relation with conservative assumptions about dependency and sharing, and proceed to develop a metamodel and a novel reasoning methodology from factual to categorical knowledge. The ontological commitment and utility of this theory is discussed on the base of practical examples. This work is intended as a first step towards a more comprehensive theory covering the problem of reasoning about partially lost items.